diff --git a/doc/pub/week41/ipynb/week41.ipynb b/doc/pub/week41/ipynb/week41.ipynb
index 207d358c6..64b58f37a 100644
--- a/doc/pub/week41/ipynb/week41.ipynb
+++ b/doc/pub/week41/ipynb/week41.ipynb
@@ -1191,9 +1191,23 @@
    "id": "366417fd",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "x = Symbol('x')\n",
+      "e = exp(x**2)\n",
+      "x = Symbol('x')\n",
+      "e = 2*x*exp(x**2)\n"
+     ]
+    }
+   ],
    "source": [
     "from __future__ import division\n",
     "from sympy import *\n",
@@ -1552,7 +1566,10 @@
    "id": "d11eb5f8",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -2449,7 +2466,10 @@
    "id": "f6b380d8",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -3816,7 +3836,25 @@
    ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.15"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb b/doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb
deleted file mode 100644
index 4b9b797bc..000000000
--- a/doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb
+++ /dev/null
@@ -1,1329 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-<<<<<<< HEAD
-    "<!-- dom:TITLE: Week 42 Convolutional and Recurrent Neural Networks and Autoencoders -->\n",
-    "# Week 42 Convolutional and Recurrent Neural Networks and Autoencoders\n",
-=======
-    "<!-- dom:TITLE: Week 42 Convolutional (CNN) and Recurrent (RNN) Neural Networks and Autoencoders -->\n",
-    "# Week 42 Convolutional (CNN) and Recurrent (RNN) Neural Networks and Autoencoders\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "<!-- dom:AUTHOR: Morten Hjorth-Jensen at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -->\n",
-    "<!-- Author: -->  \n",
-    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
-    "\n",
-    "Date: **Oct 15, 2020**\n",
-    "\n",
-    "Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Plan for week 42\n",
-    "\n",
-<<<<<<< HEAD
-    "* Thursday: Convolutional Neural Networks and examples\n",
-=======
-    "* Thursday: Convolutional Neural Networks and examples. [Video of Lecture](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober15.mp4?vrtx=view-as-webpage)\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "* Friday: Recurrent Neural Networks and Autoencoders\n",
-    "\n",
-    "Reading suggestions for both days: [Aurelien Geron's chapters 13 and 14](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Textbooks/TensorflowML.pdf). Autoencoders are discussed in chapter 15 of Geron's text.\n",
-    "\n",
-<<<<<<< HEAD
-=======
-    "**Excellent lectures on CNNs and RNNs.**\n",
-    "\n",
-    "* [Video  on Convolutional Neural Networks from MIT](https://www.youtube.com/watch?v=iaSUYvmCekI&ab_channel=AlexanderAmini)\n",
-    "\n",
-    "* [Video  on Recurrent Neural Networks from MIT](https://www.youtube.com/watch?v=SEnXr6v2ifU&ab_channel=AlexanderAmini)\n",
-    "\n",
-    "\n",
-    "\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Convolutional Neural Networks (recognizing images)\n",
-    "\n",
-    "\n",
-    "Convolutional neural networks (CNNs) were developed during the last\n",
-    "decade of the previous century, with a focus on character recognition\n",
-    "tasks. Nowadays, CNNs are a central element in the spectacular success\n",
-    "of deep learning methods. The success in for example image\n",
-    "classifications have made them a central tool for most machine\n",
-    "learning practitioners.\n",
-    "\n",
-    "CNNs are very similar to ordinary Neural Networks.\n",
-    "They are made up of neurons that have learnable weights and\n",
-    "biases. Each neuron receives some inputs, performs a dot product and\n",
-    "optionally follows it with a non-linearity. The whole network still\n",
-    "expresses a single differentiable score function: from the raw image\n",
-    "pixels on one end to class scores at the other. And they still have a\n",
-    "loss function (for example Softmax) on the last (fully-connected) layer\n",
-    "and all the tips/tricks we developed for learning regular Neural\n",
-    "Networks still apply (back propagation, gradient descent etc etc).\n",
-    "\n",
-    "What is the difference? **CNN architectures make the explicit assumption that\n",
-    "the inputs are images, which allows us to encode certain properties\n",
-    "into the architecture. These then make the forward function more\n",
-    "efficient to implement and vastly reduce the amount of parameters in\n",
-    "the network.**\n",
-    "\n",
-    "Here we provide only a superficial overview, for the more interested, we recommend highly the course\n",
-    "[IN5400 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html)\n",
-    "and the slides of [CS231](http://cs231n.github.io/convolutional-networks/).\n",
-    "\n",
-    "Another good read is the article here <https://arxiv.org/pdf/1603.07285.pdf>. \n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Neural Networks vs CNNs\n",
-    "\n",
-    "Neural networks are defined as **affine transformations**, that is \n",
-    "a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an\n",
-    "output (to which a bias vector is usually added before passing the result\n",
-    "through a nonlinear activation function). This is applicable to any type of input, be it an\n",
-    "image, a sound clip or an unordered collection of features: whatever their\n",
-    "dimensionality, their representation can always be flattened into a vector\n",
-    "before the transformation.\n",
-    "\n",
-    "\n",
-    "## Why CNNS for images, sound files, medical images from CT scans etc?\n",
-    "\n",
-    "However, when we consider images, sound clips and many other similar kinds of data, these data  have an intrinsic\n",
-    "structure. More formally, they share these important properties:\n",
-    "* They are stored as multi-dimensional arrays (think of the pixels of a figure) .\n",
-    "\n",
-    "* They feature one or more axes for which ordering matters (e.g., width and height axes for an image, time axis for a sound clip).\n",
-    "\n",
-    "* One axis, called the channel axis, is used to access different views of the data (e.g., the red, green and blue channels of a color image, or the left and right channels of a stereo audio track).\n",
-    "\n",
-    "These properties are not exploited when an affine transformation is applied; in\n",
-    "fact, all the axes are treated in the same way and the topological information\n",
-    "is not taken into account. Still, taking advantage of the implicit structure of\n",
-    "the data may prove very handy in solving some tasks, like computer vision and\n",
-    "speech recognition, and in these cases it would be best to preserve it. This is\n",
-    "where discrete convolutions come into play.\n",
-    "\n",
-    "A discrete convolution is a linear transformation that preserves this notion of\n",
-    "ordering. It is sparse (only a few input units contribute to a given output\n",
-    "unit) and reuses parameters (the same weights are applied to multiple locations\n",
-    "in the input).\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Regular NNs don’t scale well to full images\n",
-    "\n",
-    "As an example, consider\n",
-    "an image of size $32\\times 32\\times 3$ (32 wide, 32 high, 3 color channels), so a\n",
-    "single fully-connected neuron in a first hidden layer of a regular\n",
-    "Neural Network would have $32\\times 32\\times 3 = 3072$ weights. This amount still\n",
-    "seems manageable, but clearly this fully-connected structure does not\n",
-    "scale to larger images. For example, an image of more respectable\n",
-    "size, say $200\\times 200\\times 3$, would lead to neurons that have \n",
-    "$200\\times 200\\times 3 = 120,000$ weights. \n",
-    "\n",
-    "We could have\n",
-    "several such neurons, and the parameters would add up quickly! Clearly,\n",
-    "this full connectivity is wasteful and the huge number of parameters\n",
-    "would quickly lead to possible overfitting.\n",
-    "\n",
-    "<!-- dom:FIGURE: [figslides/nn.jpeg, width=500 frac=0.6]  A regular 3-layer Neural Network. -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<p>A regular 3-layer Neural Network.</p>\n",
-    "<img src=\"figslides/nn.jpeg\" width=500>\n",
-    "\n",
-    "<!-- end figure -->\n",
-    "\n",
-    "\n",
-    "## 3D volumes of neurons\n",
-    "\n",
-    "Convolutional Neural Networks take advantage of the fact that the\n",
-    "input consists of images and they constrain the architecture in a more\n",
-    "sensible way. \n",
-    "\n",
-    "In particular, unlike a regular Neural Network, the\n",
-    "layers of a CNN have neurons arranged in 3 dimensions: width,\n",
-    "height, depth. (Note that the word depth here refers to the third\n",
-    "dimension of an activation volume, not to the depth of a full Neural\n",
-    "Network, which can refer to the total number of layers in a network.)\n",
-    "\n",
-    "To understand it better, the above example of an image \n",
-    "with an input volume of\n",
-    "activations has dimensions $32\\times 32\\times 3$ (width, height,\n",
-    "depth respectively). \n",
-    "\n",
-    "The neurons in a layer will\n",
-    "only be connected to a small region of the layer before it, instead of\n",
-    "all of the neurons in a fully-connected manner. Moreover, the final\n",
-    "output layer could  for this specific image have dimensions $1\\times 1 \\times 10$, \n",
-    "because by the\n",
-    "end of the CNN architecture we will reduce the full image into a\n",
-    "single vector of class scores, arranged along the depth\n",
-    "dimension. \n",
-    "\n",
-    "<!-- dom:FIGURE: [figslides/cnn.jpeg, width=500 frac=0.6]  A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels). -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<p>A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).</p>\n",
-    "<img src=\"figslides/cnn.jpeg\" width=500>\n",
-    "\n",
-    "<!-- end figure -->\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "<!-- !split  -->\n",
-    "## Layers used to build CNNs\n",
-    "\n",
-    "\n",
-    "A simple CNN is a sequence of layers, and every layer of a CNN\n",
-    "transforms one volume of activations to another through a\n",
-    "differentiable function. We use three main types of layers to build\n",
-    "CNN architectures: Convolutional Layer, Pooling Layer, and\n",
-    "Fully-Connected Layer (exactly as seen in regular Neural Networks). We\n",
-    "will stack these layers to form a full CNN architecture.\n",
-    "\n",
-    "A simple CNN for image classification could have the architecture:\n",
-    "\n",
-    "* **INPUT** ($32\\times 32 \\times 3$) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.\n",
-    "\n",
-    "* **CONV** (convolutional )layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as $[32\\times 32\\times 12]$ if we decided to use 12 filters.\n",
-    "\n",
-    "* **RELU** layer will apply an elementwise activation function, such as the $max(0,x)$ thresholding at zero. This leaves the size of the volume unchanged ($[32\\times 32\\times 12]$).\n",
-    "\n",
-    "* **POOL** (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as $[16\\times 16\\times 12]$.\n",
-    "\n",
-    "* **FC** (i.e. fully-connected) layer will compute the class scores, resulting in volume of size $[1\\times 1\\times 10]$, where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.\n",
-    "\n",
-    "## Transforming images\n",
-    "\n",
-    "CNNs transform the original image layer by layer from the original\n",
-    "pixel values to the final class scores. \n",
-    "\n",
-    "Observe that some layers contain\n",
-    "parameters and other don’t. In particular, the CNN layers perform\n",
-    "transformations that are a function of not only the activations in the\n",
-    "input volume, but also of the parameters (the weights and biases of\n",
-    "the neurons). On the other hand, the RELU/POOL layers will implement a\n",
-    "fixed function. The parameters in the CONV/FC layers will be trained\n",
-    "with gradient descent so that the class scores that the CNN computes\n",
-    "are consistent with the labels in the training set for each image.\n",
-    "\n",
-    "\n",
-    "## CNNs in brief\n",
-    "\n",
-    "In summary:\n",
-    "\n",
-    "* A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)\n",
-    "\n",
-    "* There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)\n",
-    "\n",
-    "* Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function\n",
-    "\n",
-    "* Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)\n",
-    "\n",
-    "* Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)\n",
-    "\n",
-    "For more material on convolutional networks, we strongly recommend\n",
-    "the course\n",
-    "[IN5400 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html)\n",
-    "and the slides of [CS231](http://cs231n.github.io/convolutional-networks/) which is taught at Stanford University (consistently ranked as one of the top computer science programs in the world). [Michael Nielsen's book is a must read, in particular chapter 6 which deals with CNNs](http://neuralnetworksanddeeplearning.com/chap6.html).\n",
-    "\n",
-    "\n",
-    "\n",
-    "## CNNs in more detail, building convolutional neural networks in Tensorflow and Keras\n",
-    "\n",
-    "\n",
-    "As discussed above, CNNs are neural networks built from the assumption that the inputs\n",
-    "to the network are 2D images. This is important because the number of features or pixels in images\n",
-    "grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.  \n",
-    "\n",
-    "As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks\n",
-    "are the **convolutional** and **pooling** layers stacked in pairs between the input and the hidden layer.\n",
-    "In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D\n",
-    "matrices, typically 1 for each color dimension (Red, Green, Blue). \n",
-    "\n",
-    "\n",
-    "## Setting it up\n",
-    "\n",
-    "It means that to represent the entire\n",
-    "dataset of images, we require a 4D matrix or **tensor**. This tensor has the dimensions:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "(n_{inputs},\\, n_{pixels, width},\\, n_{pixels, height},\\, depth) .\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The MNIST dataset again\n",
-    "\n",
-    "The MNIST dataset consists of grayscale images with a pixel size of\n",
-    "$28\\times 28$, meaning we require $28 \\times 28 = 724$ weights to each\n",
-    "neuron in the first hidden layer.\n",
-    "\n",
-    "If we were to analyze images of size $128\\times 128$ we would require\n",
-    "$128 \\times 128 = 16384$ weights to each neuron. Even worse if we were\n",
-    "dealing with color images, as most images are, we have an image matrix\n",
-    "of size $128\\times 128$ for each color dimension (Red, Green, Blue),\n",
-    "meaning 3 times the number of weights $= 49152$ are required for every\n",
-    "single neuron in the first hidden layer.\n",
-    "\n",
-    "\n",
-    "## Strong correlations\n",
-    "\n",
-    "Images typically have strong local correlations, meaning that a small\n",
-    "part of the image varies little from its neighboring regions. If for\n",
-    "example we have an image of a blue car, we can roughly assume that a\n",
-    "small blue part of the image is surrounded by other blue regions.\n",
-    "\n",
-    "Therefore, instead of connecting every single pixel to a neuron in the\n",
-    "first hidden layer, as we have previously done with deep neural\n",
-    "networks, we can instead connect each neuron to a small part of the\n",
-    "image (in all 3 RGB depth dimensions).  The size of each small area is\n",
-    "fixed, and known as a [receptive](https://en.wikipedia.org/wiki/Receptive_field).\n",
-    "\n",
-    "\n",
-    "<!-- !split  -->\n",
-    "## Layers of a CNN\n",
-    "The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.  \n",
-    "The input image is typically a square matrix of depth 3. \n",
-    "\n",
-    "A **convolution** is performed on the image which outputs\n",
-    "a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as **filters**.\n",
-    "\n",
-    "\n",
-    "Each filter slides along the input image, taking the dot product\n",
-    "between each small part of the image and the filter, in all depth\n",
-    "dimensions. This is then passed through a non-linear function,\n",
-    "typically the **Rectified Linear (ReLu)** function, which serves as the\n",
-    "activation of the neurons in the first convolutional layer. This is\n",
-    "further passed through a **pooling layer**, which reduces the size of the\n",
-    "convolutional layer, e.g. by taking the maximum or average across some\n",
-    "small regions, and this serves as input to the next convolutional\n",
-    "layer.\n",
-    "\n",
-    "\n",
-    "## Systematic reduction\n",
-    "\n",
-    "By systematically reducing the size of the input volume, through\n",
-    "convolution and pooling, the network should create representations of\n",
-    "small parts of the input, and then from them assemble representations\n",
-    "of larger areas.  The final pooling layer is flattened to serve as\n",
-    "input to a hidden layer, such that each neuron in the final pooling\n",
-    "layer is connected to every single neuron in the hidden layer. This\n",
-    "then serves as input to the output layer, e.g. a softmax output for\n",
-    "classification.\n",
-    "\n",
-    "\n",
-    "## Prerequisites: Collect and pre-process data"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-<<<<<<< HEAD
-   "outputs": [],
-=======
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "inputs = (n_inputs, pixel_width, pixel_height, depth) = (1797, 8, 8, 1)\n",
-      "labels = (n_inputs) = (1797,)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": "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\n",
-      "text/plain": [
-       "<Figure size 864x864 with 5 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "%matplotlib inline\n",
-    "\n",
-    "# import necessary packages\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "from sklearn import datasets\n",
-    "\n",
-    "\n",
-    "# ensure the same random numbers appear every time\n",
-    "np.random.seed(0)\n",
-    "\n",
-    "# display images in notebook\n",
-    "%matplotlib inline\n",
-    "plt.rcParams['figure.figsize'] = (12,12)\n",
-    "\n",
-    "\n",
-    "# download MNIST dataset\n",
-    "digits = datasets.load_digits()\n",
-    "\n",
-    "# define inputs and labels\n",
-    "inputs = digits.images\n",
-    "labels = digits.target\n",
-    "\n",
-    "# RGB images have a depth of 3\n",
-    "# our images are grayscale so they should have a depth of 1\n",
-    "inputs = inputs[:,:,:,np.newaxis]\n",
-    "\n",
-    "print(\"inputs = (n_inputs, pixel_width, pixel_height, depth) = \" + str(inputs.shape))\n",
-    "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
-    "\n",
-    "\n",
-    "# choose some random images to display\n",
-    "n_inputs = len(inputs)\n",
-    "indices = np.arange(n_inputs)\n",
-    "random_indices = np.random.choice(indices, size=5)\n",
-    "\n",
-    "for i, image in enumerate(digits.images[random_indices]):\n",
-    "    plt.subplot(1, 5, i+1)\n",
-    "    plt.axis('off')\n",
-    "    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
-    "    plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Importing Keras and Tensorflow"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from tensorflow.keras import datasets, layers, models\n",
-    "from tensorflow.keras.layers import Input\n",
-    "from tensorflow.keras.models import Sequential      #This allows appending layers to existing models\n",
-    "from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer\n",
-    "from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n",
-    "from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)\n",
-    "from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function\n",
-<<<<<<< HEAD
-    "#from tensorflow.keras import Conv2D\n",
-=======
-    "#rt Cofrom tensorflow.keras imponv2D\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "#from tensorflow.keras import MaxPooling2D\n",
-    "#from tensorflow.keras import Flatten\n",
-    "\n",
-    "from sklearn.model_selection import train_test_split\n",
-    "\n",
-    "# representation of labels\n",
-    "labels = to_categorical(labels)\n",
-    "\n",
-    "# split into train and test data\n",
-    "# one-liner from scikit-learn library\n",
-    "train_size = 0.8\n",
-    "test_size = 1 - train_size\n",
-    "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
-    "                                                    test_size=test_size)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<!-- !split  -->\n",
-    "## Running with Keras"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def create_convolutional_neural_network_keras(input_shape, receptive_field,\n",
-    "                                              n_filters, n_neurons_connected, n_categories,\n",
-    "                                              eta, lmbd):\n",
-    "    model = Sequential()\n",
-    "    model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',\n",
-    "              activation='relu', kernel_regularizer=regularizers.l2(lmbd)))\n",
-    "    model.add(layers.MaxPooling2D(pool_size=(2, 2)))\n",
-    "    model.add(layers.Flatten())\n",
-    "    model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))\n",
-    "    model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))\n",
-    "    \n",
-    "    sgd = optimizers.SGD(lr=eta)\n",
-    "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
-    "    \n",
-    "    return model\n",
-    "\n",
-    "epochs = 100\n",
-    "batch_size = 100\n",
-    "input_shape = X_train.shape[1:4]\n",
-    "receptive_field = 3\n",
-    "n_filters = 10\n",
-    "n_neurons_connected = 50\n",
-    "n_categories = 10\n",
-    "\n",
-    "eta_vals = np.logspace(-5, 1, 7)\n",
-    "lmbd_vals = np.logspace(-5, 1, 7)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Final part"
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "12/12 [==============================] - 0s 2ms/step - loss: 2.8826 - accuracy: 0.2444\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  1e-05\n",
-      "Test accuracy: 0.244\n",
-      "\n",
-      "12/12 [==============================] - 0s 2ms/step - loss: 3.3143 - accuracy: 0.0528\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  0.0001\n",
-      "Test accuracy: 0.053\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 2.6159 - accuracy: 0.1611\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  0.001\n",
-      "Test accuracy: 0.161\n",
-      "\n",
-      "12/12 [==============================] - 0s 2ms/step - loss: 4.6617 - accuracy: 0.1278\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  0.01\n",
-      "Test accuracy: 0.128\n",
-      "\n",
-      "12/12 [==============================] - 0s 2ms/step - loss: 12.1948 - accuracy: 0.1139\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  0.1\n",
-      "Test accuracy: 0.114\n",
-      "\n",
-      "12/12 [==============================] - 0s 2ms/step - loss: 91.3207 - accuracy: 0.0917\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  1.0\n",
-      "Test accuracy: 0.092\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 517.6693 - accuracy: 0.1250\n",
-      "Learning rate =  1e-05\n",
-      "Lambda =  10.0\n",
-      "Test accuracy: 0.125\n",
-      "\n",
-      "12/12 [==============================] - 0s 2ms/step - loss: 1.3215 - accuracy: 0.6111\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  1e-05\n",
-      "Test accuracy: 0.611\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 1.2700 - accuracy: 0.5889\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  0.0001\n",
-      "Test accuracy: 0.589\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 1.4245 - accuracy: 0.5806\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  0.001\n",
-      "Test accuracy: 0.581\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 2.6471 - accuracy: 0.4556\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  0.01\n",
-      "Test accuracy: 0.456\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 10.4180 - accuracy: 0.5139\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  0.1\n",
-      "Test accuracy: 0.514\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 54.1625 - accuracy: 0.2583\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  1.0\n",
-      "Test accuracy: 0.258\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 4.5475 - accuracy: 0.0889\n",
-      "Learning rate =  0.0001\n",
-      "Lambda =  10.0\n",
-      "Test accuracy: 0.089\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 0.2355 - accuracy: 0.9306\n",
-      "Learning rate =  0.001\n",
-      "Lambda =  1e-05\n",
-      "Test accuracy: 0.931\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 0.2488 - accuracy: 0.9333\n",
-      "Learning rate =  0.001\n",
-      "Lambda =  0.0001\n",
-      "Test accuracy: 0.933\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 0.3576 - accuracy: 0.9194\n",
-      "Learning rate =  0.001\n",
-      "Lambda =  0.001\n",
-      "Test accuracy: 0.919\n",
-      "\n",
-      "12/12 [==============================] - 0s 1ms/step - loss: 1.2576 - accuracy: 0.8778\n",
-      "Learning rate =  0.001\n",
-      "Lambda =  0.01\n",
-      "Test accuracy: 0.878\n",
-      "\n",
-      "12/12 [==============================] - 0s 2ms/step - loss: 5.8163 - accuracy: 0.9167\n",
-      "Learning rate =  0.001\n",
-      "Lambda =  0.1\n",
-      "Test accuracy: 0.917\n",
-      "\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
-    "        \n",
-    "for i, eta in enumerate(eta_vals):\n",
-    "    for j, lmbd in enumerate(lmbd_vals):\n",
-    "        CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,\n",
-    "                                              n_filters, n_neurons_connected, n_categories,\n",
-    "                                              eta, lmbd)\n",
-    "        CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n",
-    "        scores = CNN.evaluate(X_test, Y_test)\n",
-    "        \n",
-    "        CNN_keras[i][j] = CNN\n",
-    "        \n",
-    "        print(\"Learning rate = \", eta)\n",
-    "        print(\"Lambda = \", lmbd)\n",
-    "        print(\"Test accuracy: %.3f\" % scores[1])\n",
-    "        print()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Final visualization"
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1437/1437 [==============================] - 0s 43us/sample - loss: 3.3022 - accuracy: 0.1872\n",
-      "360/360 [==============================] - 0s 121us/sample - loss: 3.4180 - accuracy: 0.1778\n",
-      "1437/1437 [==============================] - 0s 86us/sample - loss: 3.3955 - accuracy: 0.1093\n",
-      "360/360 [==============================] - 0s 142us/sample - loss: 3.4203 - accuracy: 0.0917\n",
-      "1437/1437 [==============================] - 0s 80us/sample - loss: 2.7250 - accuracy: 0.1587\n",
-      "360/360 [==============================] - 0s 216us/sample - loss: 2.7661 - accuracy: 0.1556\n",
-      "1437/1437 [==============================] - 0s 66us/sample - loss: 3.5698 - accuracy: 0.1343\n",
-      "360/360 [==============================] - 0s 46us/sample - loss: 3.5947 - accuracy: 0.1167\n",
-      "1437/1437 [==============================] - 0s 63us/sample - loss: 12.5837 - accuracy: 0.0946\n",
-      "360/360 [==============================] - 0s 60us/sample - loss: 12.5511 - accuracy: 0.1111\n",
-      "1437/1437 [==============================] - 0s 59us/sample - loss: 91.5210 - accuracy: 0.2408\n",
-      "360/360 [==============================] - 0s 53us/sample - loss: 91.5551 - accuracy: 0.2222\n",
-      "1437/1437 [==============================] - 0s 64us/sample - loss: 518.1178 - accuracy: 0.1969\n",
-      "360/360 [==============================] - 0s 48us/sample - loss: 518.1064 - accuracy: 0.1889\n",
-      "1437/1437 [==============================] - 0s 66us/sample - loss: 1.4465 - accuracy: 0.5623\n",
-      "360/360 [==============================] - 0s 37us/sample - loss: 1.4667 - accuracy: 0.5444\n",
-      "1437/1437 [==============================] - 0s 63us/sample - loss: 1.0335 - accuracy: 0.7015\n",
-      "360/360 [==============================] - 0s 75us/sample - loss: 1.0560 - accuracy: 0.6806\n",
-      "1437/1437 [==============================] - 0s 62us/sample - loss: 1.9454 - accuracy: 0.3730\n",
-      "360/360 [==============================] - 0s 48us/sample - loss: 2.0023 - accuracy: 0.3611\n",
-      "1437/1437 [==============================] - 0s 92us/sample - loss: 2.4747 - accuracy: 0.5080\n",
-      "360/360 [==============================] - 0s 49us/sample - loss: 2.5625 - accuracy: 0.4722\n",
-      "1437/1437 [==============================] - 0s 65us/sample - loss: 10.2878 - accuracy: 0.5887\n",
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sqfMEhPjjH5TH0O694R/z3ZLMw34vtp9M1O4/bnuct0PBonmJPX3BuR13Jp6A4Dz4B/oZ2s0c+zmbVu2+/u4ULxNG3gKBvP7JAN7/5nkeG9Gayxfv3I7A9UKL5SP2r6v5x56+QECwP/5Bxvzff34Rm5bvuP7uANisNp77oC+zfnyVfT9GcepI9G2N+b8ILVGQ2FNXh65iT53LdK7frM2hHb/zQI9GWLws+AX4Ub/zveQvkheAhHOXiJz1Df2rj2LeC58xbsUoChbL77rk/qHQQsHExiQ4t2NjEwgI9MPf38e572z0RXZs/d25/fSQFvz0fRQZGTbyFwxkwPCWTBq3Cps1Z1+Cr2DhEOP7wNmETO8DMafj2bn5sHP7qecfZPt3B8lIt7o0VsleLukILViwgMWLF/PMM8/QtWtXunbtyjPPPMOiRYtYunSpK0K4KbPZBPbMU+Sttr/3wp4zKRI7dt5dNZSX3+/J3q1HyEjPOfNDwPE7sGf1O8jhf9z+DrPJRFZftPx3c7d4m6neMJyJ/eczpM0UgvL688TzbbM5ytvHZDZny7Gf3H8eD5cbTlC+AB59LvPQ4p3Cca5n3n/tG/nN2sx69mOw25m5ZzKvrhzFnm9/cc4He7XLFL5f/hMAB348xIGth6nZPOK25JEdTDd43duyWDLk5+fN2AkPUbR4PqZOXIPFYuaF1zoza/p6Z7UoJzObTWT1hyCr9wHfPN68MO1RipYqwNsvrXBBdK5ns5tc9uNuLukIeXl5kZGRuWOQkpKCt7e3K0K4qZjT8eQPu1rBKVgomEvxSaQmp/+t+/sH+jFv8loGtJ3GC0/MxWQyOcurOUXMyXMUKJLPuV2wWH4unb9MalLWE8Zzk5jTF8hfKMS5XbBwCJfiE0lNTrvJva46fzaBrV/9QtLlFDLSrWxcsZPwmnfdpmizX+ypcxQonNe5XbBIXi5dSCQ16e/lX7NpJfIXdvz+UhJT2bR8B2UjSt6WWLNDzIm4TOd6wvnLpFxzrt+sjX+wP3Oe+4SnIp7l+RavO17vR6MJCPGn+5hOhucymUx3dLUgNjqBAgWDnNsFQ4NJSEgmJcX4ty+0UDDTZvfGZrUzatBCEi+nUr5iEYoUzcvTQ5oz8+N+PNipJo2a3cPwMTnnQ8C1Ys7EGyr5N3ofCC0SwtTPBmCz2Xi+1xwSb7CoQHIOl3SE+vfvT8eOHRk7dizTp0/nnXfeYezYsXTt2pX+/fu7IoSb2vNDFOHVSlK0VAEA2nS/l20bfvvb92/TvS49hrYAIG+BQFp2rZ3lENqdbPe3+wmvU5aidxcC4MF+zdgWmXkYKDfas/kQ4TVKUbR0KABtetRn29d/f/7aD1/+TIO21fHxc3Tq67WKIOqXE7cl1tth93e/EV6rDEXLhAHwYO9GbPvq75+/DTvW4vErFSBvHy8adKzFL98fui2xZofd63+h4r3lKFa2MABt+7dg2+qdf7tNu/7N6fWaYyFB3rAQWvdtxsbPfiD5Ugrtn2lF/c6O+VV3V7uLCnXKsnPdnfu3YPeOo1SsXIyixR3Dd2071WTblsOGNnn8fZjyXk9+3HSIN15eQVqq40PtwV//4rGO7zCg1xwG9JrDlyt3s3nDb0ybGOnyPLLDnh+PEF61xNX3gUfqsm2j8X0gj78P//v4KX785gCTnl3s/F1IzuaS5fPt2rWjTp06bNu2jZiYGGw2G7Vq1WLw4MEUKlTIFSHc1MXziUwbs4wXZzyOl7cXZ06cY8pzSyhXuRhDJ3RhUIfpN73/0lnfMfLNbsyMHI7JZGLh9G+I2n/KRdFnj4uxCbz11CxeWjQULx8vzvwRw5t9Z1KuRmmGz+zHM3VfcHeIt83Fc5eZ9uxnvDirD17eFs78GceUYZ9QLqIEQ9/szqCWk296/8iPvycwrz8z1o7CbDHx+/5TzH1tlYui/+8uxl1i6qD5jP2ov+PYH4vlzQHzKFetFMOm92Jgo9duev/ZY5cyeOrjfPDjOAC2frmXVR9scEHk/058bAJT+rzPS8uexdvHi9NHzzK517uUr1mGEXMG0L/GqBu2AVg0cSXPLxjM7H1vYTKZ+PiVJUTtOgrAKx3/x8B3+tJz3MPYMmxM6DaNhHOX3JnuTcVfSGLK+DW89EYXvL0tnP7rPG++tppy4UUYMaYtA3rNoUOX2oQVDuH+RhW4v1EF532fG/wJl+7gSfH/1MXziUx7cTkvvv2Y4+/AyfNMGb2UcpWKMfT1zgzqPIN2j9UjrGhe7nvgHu574B7nfcf0mcel+CQ3Rp/97oRJzK5ismc1QHyHa13+eXeH4Da2Ezmrg5XdzAULuDsEt7In5Z43nn/KGp/zViRmJ1PdO3eukStYcllH45/66uBElz7fnhOuG96uUdK9FXRdUFFEREQMrB50mUHPyVRERETkOqoIiYiIiMGdsKzdVVQREhEREY+lipCIiIgYeNKqMVWERERExGOpIiQiIiIGVrvn1Ek8J1MRERGR66giJCIiIgY2D6qTeE6mIiIiItdRRUhEREQMtGpMRERExAOoIiQiIiIGWjUmIiIi4gHUERIRERGPpaExERERMbBpsrSIiIhI7qeKkIiIiBhYPahO4jmZioiIiFxHFSEREREx0PJ5EREREQ+gipCIiIgY6EtXRURERDyAKkIiIiJiYLXrOkIiIiIiuZ4qQiIiImKg6wiJiIiIeABVhERERMTApusIiYiIiOR+qgiJiIiIgeYIiYiIiHgAdYRERETEY2loTERERAx0QUURERERD5AjK0IHh4a5OwS3KVzWs/uu1iWh7g7BrS6W9ZxPaddLDctwdwhu5Zc/2d0huFWpbn+6OwSPoi9dFREREfEAObIiJCIiIrePVRdUFBEREcn9VBESERERAxueMx9RFSERERHxWKoIiYiIiIHmCImIiIh4AFWERERExEBfuioiIiLiAVQREhEREQObvmtMREREJPdTRUhEREQMNEdIRERExAOoIyQiIiIeS0NjIiIiYmDTBRVFREREcj9VhERERMTAqi9dFREREcn9VBESERERA80REhEREfEAqgiJiIiIgeYIiYiIiHgAVYRERETEQHOERERERDyAKkIiIiJiYFVFSERERCT3U0VIREREDGxaNSYiIiKS+6kiJCIiIgaaIyQiIiLiAVQREhEREQObXXOERERERHI9dYRERETEY2loTERERAysHlQnUUfoiialSvPcvQ3wsVg4dC6W5zeu53J6mqHNi/c3os3d5bmYmgLAHxcuMGh9JACPV65Kt3uq4GfxYn/sWZ7fuJ40m9XleWSX+wpW4JnyLfE2e/H7pWgm/LqcJGuq8/bWRavTvVR953aglx9hfiG03zyJ82mX3RHyf3J/RGkGPlQfH28LR07GMX7+ehJTjMe/a9NqdGkSgd0Op2LjmfDRN1y4lMykZ9pSIiyvs13RgiHsOXyKZ2esdnUa/1rju0szosn9+FgsHI6J44UvvyExzZj/6GYNaRVejospjvP/2LkLDFu11nl74aBAlj3RnfZzF3IhOcWl8f9XTUuU4bnaDfExWzh0Ppbnvl+X6fU/tm5j2pSuQPz/v/4vnmfQxjWE+Pox4f7m3JM/jOSMdJZF7eej3/a6I41/pVHhcjxbqSk+ZguHL8bwwp4vSMww5l4+OIyxVVsR5O2LzW7n5b1fciD+DAA/PTiS6OQEZ9t5R7ay5uSvLs3hv6rTuhp9xnfD29eLY/tPMvWp2SRdSs6y7ah5/Tn260k+n/alc19AiD9vbXyZt/rN4sieY64KW7KJOkJAfr88vNm0FV1WLOL4xXhG12vA8/Ua8NKWDYZ2NQsXZfD6L9kTfdqwv2WZsjxRpToPrVhMQmoK77dqR99qNZm5Z4cr08g2eb0DGFu5C0/v+ICTSecYWL4VA8u34s2DV9/Yvzq9l69OO/7YW0xmPqjzNAuObc6RnaC8QXl4uU9LnnxjMSdj4hnUpQGDutTnf59sdLYJLxXG461q8ugrC0lMTmPoww3p3+l+Ji74ltHvRzrb3XNXISY9047Jn2zI6qnuSPn88zCxbQu6LVjCnxfiGdmkPiOb1OfVrzca2lUvVoThq9ay968zmR6jY+WKDG5Yj0JBga4KO9vk98vDmw1b8dCazzieEM/o2g0ZXbshY7d+a2hXM6wYgzeuYXeM8fX/ct0mJKWn8cDyD7GYTMxp3okTly6y8eQfrkzjX8nn48/EGu3pvnk+fyaeZ2SlZoys3IxXf/7K2cbP4sW8+o/x4u41bDn7O82KlGdK7U60/uZ9SgcWID4tmY4bZ7sxi/8mpGAQI+c8zbDGr3L692j6vtGNvhO6MWPIfEO7EuFFGTy9N+F17ubYryed+2u3qkb/KY9TqFSoq0O/rTRZ2sM0KFmKfTHRHL8YD8Anv/5Ch/IVDW18zBYqFQyjf/XarOvWk5mt2lE0MAiAhypUYs7Pu7mYmoIdeHHTt6w4/Jur08g2dQuW42DCKU4mnQNgxYmfaFmk2g3b9yzdiAtpl1l1Kmd2/O6tVIrfjkVzMsZx/Jd/9wut7jUe/0N/xtB5zHwSk9Pw8bIQmi+Qi5eNnxi9LGZeebIVUxdv4uyFnNMhrF+6FPvPRPPnBUf+i/bso32lcEMbb4uFewqH0e/eWqx5sgczOrelSLDj/A8LDOCBCnfTd/EKl8eeHRoWu4t9sdEcT7jy+j/4Mx3K3mNo42O2cE+BMJ6OqMPXnZ/gg2YdKBrgyL9KwUKs+P03bHY76TYbG0/8QZvSFVyex79Rv1AZ9sef5s/E8wAsOraLdiWqGNrcH3Y3Jy9fYMvZ3wHYcCaKYds/B6B6geLY7DY+bfgEXzR7moHhDTHnsCsS12weweFdf3D692gAImd9S9Pu92dq175/C76a/x1blm837O84sCX/6/U+58/EuyReyX7qCAFFA4M5c/mSc/vM5UsE+/oS6O3j3BcWEMDWv04wZfsPtFq8gL1nzzCnTUcASufNRwH/PHzctjNfPdKTYXXuIyE1Zw0NXCvML4SzKRed2zGpCQR6++Fv8c3UNsTbn+53NeDtQ5GZbsspCuUP4uz5q8c/5sIlAv19CfDzMbSzWm00qn43X771FNXLF2fNDwcMt3doUJm4+Mts2vO7S+LOLkWCgziTcLXjFp1wiSA/XwJ8ruZfKDCAn46fZNqWrbSbu5Cf/zrDzC7tAYi5nMig5ZEcP58z3wiKBARxOvGa13/iJYJ9jK//Qv6BbDtzgim7f6Dlio/YG3Oauc07AfBz7Bk6l70HL5MZfy9vWpcuR5h/gMvz+DcK5wkhOunqaz06OYEgbz8CvK7mXjqwALGpl5lQox3LmzzJ/PqPYzE73josJjNbY4/x5I+f8tiWj6hf6G563F3H5Xn8F6HF8xN76pxzO/bUeQJC/PEPymNo996wj/hu8dZM93+x3f+I2n3nV//+KRtml/24m0siOH369E1/3M1kAjv2TPutdpvz/6cuJdA7ciVR5x0vmNl7d1EyJITiQcF4mc00KF6KgV9H0n7ZJ+T19WPUvfUzPV5OYcYE9sy/Dxu2TPs6Fq/D9zG/cTr5gitCuy1MJlMWRx+stsz5bt57lOZDZzJn9TZmPNsZ0zUffru3qMm8Ndsz3edOZ77B+W+79vy/mEC/pas4Eus4/+dt303JfCEUDwl2WZy3i/lGx/+a18DJyxd54uvlRF2IA2DW/p2UDM5LicAQxm/fhB1Y26knc5p34vu//iQ9h8wPvFHutmty9zKbaVSoHEuO7eGh7+byydEdzL7vUbzNFpYd38v4X9aRbE3nUnoq849s44Gi4Vk84p3LZDZn9ecOmzXz61/cb82aNbRp04YWLVrw6aefZrr9wIEDPPTQQ7Rv356nn36ahISELB7FyCVzhJ5++mmOHz9OWFgY9uvOOJPJxIYN7p1PcfrSJaoXKuLcLhwYSHxKMskZGc594QUKUrFAKCujDjr3mTCRYbMRk3iZdX/87pxcuTLqN4bWrue6BLLZ2ZR4KuUt4dwO9Q3mYnoSKdb0TG0fKBLB1INrXBletjt77hKVyxR2bjuGvVJISbt6/IuH5aVAiD+/HHF03L/4/ldG92xGsL8fFxNTKF8yFC+LiT2HT7k8/v/q9MVLRBS9evZ7te0AACAASURBVP4XCgokPjmF5PSr+VcILUh4oVBW/3rwmnuaSM+is5jTnE68RLWwa17/AUFXXv9Xz/fw/KFUzB/Kyt+vDnmbMJFusxLo7cMbOzY7F1EMrFrXOcx+pzuTdJGq+Yo5twv5BROflkzyNa/1mJRLHL0Uy74LfwGOobHxNUyUCMhHlbxFOHTxLIcTYoArfxPtOaMT+P9iT8YRXudu53bBYvlJOH+ZlKTUm9wr97PegXOEzp49y7Rp01ixYgU+Pj5069aNunXrUrZsWWebCRMmMGTIEBo1asSkSZOYN28ew4cPv+njuqQitGjRIkqXLs3kyZPZuHGj4cfdnSCA708ep1qhItwV4lj581ilqnxz7Kihjc1uZ1yDphQPcnwCfrxyVQ6diyU68TJrjx7hwbLl8bU4+pUtSpfll7PRrk0iG20/d4TKISUo4V8AgE4l6vJ9TOY5T0FefhTPU4B98X+6OsRs9dOB41QuU8S58uuhxlXZ8rNxeKtgSAATnn6QkEA/AFrVC+foX+e4mOh486tZoTg7D54kJ/rh2J9UK1aYUvkc+XevEcGGqOvOf+yMbd7YWQF6tEYEh2PiOHsp58yFupEtp45TPawodwVfef2HV2X9CePxt9ntvFqvGSUCQwDoUbEahy7EEp10mccqVuPZGo45JQXz+NOtQgSrjx4kJ/gh5ihV8xejVEB+ALqVqcmGM4cNbbZE/07xgHxUyuvoLNYqUNKxcjLxAuWCwxhyT2PMmPA1e/HY3bVZe+pApue5k+3+Zj8V65SjaFnHh6G2TzVj25rdbo5KsrJ161buvfde8ubNi7+/Py1btmTdunWGNjabjcTERACSk5Px8/O75eO6pCIUGBjI+PHjWbZsGTVr1nTFU/4j55KTGbXxa2a2aoe32cKfCfGM+HYdVUIL8b+mLWizZCFR58/xyvcbmfdgJywmE2cSLzNkvWP55MJffyavnx+RDz+O2WTiQGwME378xs1Z/XsX0hJ5/dflvFHtMbxNFk4lnee1X5cSHlyMFyp1pue2GQAU9y9IXNolwxBiTnThUjKvfbieSQPb4W0xcyr2IuPmrqPiXYUY+0RzHhv3CT8f+Yv5kduZ9dzDWG02YuMTGXXN8vgShfJxJu7WJdg70fmkZMZErmdG57Z4W8ycuHCR59aso3LhQkx48AE6zPuUI7HneH39d3zwcAcsJhPRly4zYvXaWz94DnAuJYlRm79iZrMO+Fgcr//hm9dSpWAh/tegFW1WfkzUhThe2baBeS06YTGbOZN4icEbHZXQ93/5iWmNHmR95ycwmUxM3fMj++Jyxgeh86lJjNn9Be/U7YK32cKJxAs8v2sVlfMWYXyNdnTcOJu41EQGblvCK9XakMfiTZotg8Hbl5Jms/Luoc28XLU1ax7oj5fZzLq/DrLseM65dABAfGwCU/rN4qXFQ/H28eL00bO82Wcm5WqUZsSsfgyo/YK7Q3QLV64aS0hIyHIIKzg4mODgq8PvMTExhIZeXZ0XFhbGvn37DPcZPXo0ffr04Y033iBPnjwsXbr0ls9vsl8/VpUD3PXeW+4OwW0Kl41zdwhuZV2Su5ao/lMXy9555WpXSQ3LuHWjXMwvf9bXtfEUpbodcncIbrU+7TOXPt/Qvd1d9lxlf7iPd999N9P+QYMGMXjwYOf2zJkzSU1NZdiwYQAsXbqUX3/9lddeew2AlJQUHnroISZOnEhERATz589n27ZtzJ5988s76DpCIiIiYmCzu241V69evejUqVOm/ddWgwAKFy7Mrl27nNuxsbGEhYU5t6OiovD19SUiIgKARx55hOnTp9/y+d2/bk1EREQ8VnBwMMWLF8/0c31H6L777mPbtm2cP3+e5ORk1q9fT8OGDZ23lypViujoaP74w3E5gw0bNlClivG6WFlRRUhEREQMrHfghTELFSrE8OHD6dmzJ+np6XTp0oWIiAj69evHkCFDqFKlChMnTmTYsGHY7XYKFCjAG2+8ccvHVUdIREREcoR27drRrl07w745c+Y4/9+oUSMaNWr0jx5THSEREREx0HeNiYiIiHgAdYRERETEY2loTERERAxcuXze3TwnUxEREZHrqCIkIiIiBrY7cPn87aKKkIiIiHgsVYRERETEwKrl8yIiIiK5nypCIiIiYqBVYyIiIiIeQBUhERERMdBXbIiIiIh4AFWERERExEDXERIRERHxAKoIiYiIiIHmCImIiIh4AFWERERExEDXERIRERHxAOoIiYiIiMfS0JiIiIgYaLK0iIiIiAdQRUhEREQMdEFFEREREQ+gipCIiIgYaI6QiIiIiAdQRUhEREQMVBESERER8QCqCImIiIiBKkIiIiIiHiBHVoS+bv+Wu0NwmyAP77qmVLK7OwS3snrQtT2uZ8Gzj/3Apj3dHYJbWe02d4fgUVQREhEREfEAObIiJCIiIrePriwtIiIi4gFUERIREREDzRESERER8QDqCImIiIjH0tCYiIiIGGhoTERERMQDqCIkIiIiBqoIiYiIiHgAVYRERETEQBUhEREREQ+gipCIiIgY2FUREhEREcn9VBESERERA33pqoiIiIgHUEVIREREDLRqTERERMQDqCIkIiIiBlo1JiIiIuIBVBESERERA80REhEREfEA6giJiIiIx9LQmIiIiBhosrSIiIiIB1BFSERERAw0WVpERETEA6giJCIiIgZ2u7sjcB1VhERERMRjqSIkIiIiBjY0R0hEREQk11NFSERERAx0HSERERERD6CK0BU7f7KwYJ4vGekmSpWxMuTZFPwDjG0iV3rz5WoffHztFC9po//gFIKCHbc91jmAgqFXp9l3ejiNxs0yXJjBf7PtJwtz5/qSnmaiTBkro0alEHBd/itWeLNqlSP/UiVtDB2aQvCV/Fet9mbtl96kpkH58jZGjUzBx8f1efxbO37yYv5cX9LToXQZG8NGJmfKf/VKb9as8sHXF0qUtDFwSLLz+D/SKdBw/B96OJWmD+Sc47/zJwsfz/UlPd3EXWWsDB2Z+fxfs9KbyCvHv0RJGwOGXD3/H+0UQIFr8u/8cBpNclD+nnz8azcOp/eIVnj7eHHs8BnefuFzkhJTs2z77P8e5vjhaJZ/uAWAwJA8DHq1E3eHFyUlOY1vVuzii4VbXRl+tqrTujp9JnTD28ebY/tPMPWpWSRdSs6y7agPB3Bs/0k+nxbp4ihdQ9cR8jAX4028M8WPMa8kM/OjRAoXsfHxXF9Dm30/W1i+xIfX30xi+qwkatXJ4L1pfgCcOmkiKAimz0py/uSkTlB8vInJk/14dVwyCxYkUqSojdlzjPnv3Wth0WIf3noriblzkqhbN4O3pjry37LFi5UrvZkyJYn5HyaRmgqff55zekHx8SamvunH2HHJzP3Ycfznz/UztPllr4Vli32ZOCWJ92YnUrtuBtOn5gHg1EkzQUF23pud6PzJKW+C4Dj/337TjzHjkpl1Jf+Prj//91r4fLEPE6YkMWN2ErXqZjBj6tXzPzAIZsxOcv7kpE6QJx//kHwBjJjYlfGDF9Kv1RSiT56n98jWmdqVuDuMiR/3o37LKob9T7/QjpTENJ5u8xbDH36PWg0rUKdxuKvCz1YhBYMYObc/rz08jb6VR3DmWAx93+ieqV2J8KJMXj+WBp3ruiFKuR1c1hH69ttvWbhwISdOnDDsX7JkiatCuKG9uy2UK2+jaHHHJ7rW7dLZvMHbcB2Fo1FmqtawOj/11aufwY6fvEhPh0MHLJgtdkYPy8Pgfv4sXuiD1eqOTP6dnbssVKhgo/iV/Du0T2fDdflHRZmpWdNK6JX8GzTIYNs2R/7rv/Hi4a7pBAeD2QwjhqfSvHm6O1L5V/bsslC+gpVixW0AtG2fxnfX5X/kiIXqNTKc+d9fP53tV47/bwcsmC0wcqg/A54M4NMFOev479lloVwFG8WuHP827dPZdF3+vx8xU+2a8/++a87/g1fO/+eG5mHQk/4syoH5e+rxr1G/HFH7T3L6z3MARC76iSbtq2dq1/axeny9bCffr9tn2F+2UjE2rN6DzWYnI93Kjk2HqN+qSqb75wQ1m0dweNdRTv8eDUDkrG9o2r1+pnbtB7Tkqw+/Y8vy7a4O0aXsdtf9uJtLOkJTpkzhk08+4fjx43Tv3p3Vq1c7b1u8eLErQripuBgzBcNszu2CoXaSkkwkJ11tU76ijX17LcScdZQLv/3am4x0E5cSTFitJqpWtzJuYjITpyWxZ5cXkau8XZ3GvxYbYybsmvxDQ+0kJppIuib/ihVt7N1rITrakf+6dd6kp5tISDBx6pSZC/Emnns+D32f9Oejj30IDLwDzu6/KS7W7HyDgyvH/7r8w8Ot/PKzF2evHP/1huMP1WpYGT8piTffTmTPLi++WJVzKmJxsWYKhl53/ided/6H29j389Xz/5vrzv9qNay8NimZSW/nvPPfk49/wSJ5iT1z0bkdF32RgCA//AOMFcGZr61mU+TPme5/+JeTNOtQA4uXGT9/H+5vUZn8ocG3Pe7bIbR4AWJPnXNux546R0CIP/5BeQzt3hs6n+8W/+jq8OQ2cskcoc2bN7Ny5Uq8vLzo0aMHffr0wcfHh9atW2O/A7qDthuEYL6mm1ipipVuPdN445U8mM3wQMt0goLseHnZafmgsfrR8aE01qzypsNDOaMqYrOT5RUjrs0/IsJKz55pvPxyHkxmaN06neBgR/4ZGSZ277Yw/vVkfHxg0iQ/5s3zZdCgrOcZ3GlsNrL8BViuyb9yhJXHeqTy+sv+mM3QolUaQUE2vLyg9YPpwNVj3alLGqtX+tDpobTbHnt2sNvAlEX+5uvy794jjQlXjn/zVlfP/1bXn/9d0lizMged/x58/M1mU5Yfya02WxatM5szKZInRz/Iu6uGciHuEnu3HuGe6qWyO0yXMJnNWVYnbNa/97vIbTxp1ZhLOkJ2ux3Tlb+0d911F7NmzaJ3797kz5/fud+dQsNsRB28+qs4F2ciMMiO3zUfBJKSoHJEBi1apzvbfPqRL0HB8N03Xtx1t43SZRwvGDvgZXFlBv9NoTAbB6/JPzbWRFCQnTzX5V+tagYPtkl3tpk/35fgYChQwEaD+hnOyaUPNE9nwQLjJ8o7WViYncOHrp6HcTc4/lWqZtDySv5xsSYWzPclKNjOhm+8KVPGSum7rxx/O3jloGUIoWE2Dh/6G+d/1QxaXJP/J/Md5//Gb7woXcZmyN+Sg/L35OMfczqeChElnNsFCwVzKT6J1OS/14n1D/Rj3uS1XL7omFD8SP8mzmG2nCb2ZBzhdco6twsWy0/C+cukJOWMD3Ty77lkaKxVq1b06NGDffsc48vlypVj+vTpDBs2LNOcIXeoXtPK4YMWTp9y/DH8ao03de8zTnY8f87Ei8/6k5To2F76qQ8NmqZjMsGfx8189pFjXkBqKny5ypv6jXPGZEmAWrWsHDxo4dSV/Nes8eb+6/KPizMxbLg/iVfy/+RTH5o2ceTfqGEGmzZ7kZrqeBP48QcvwivkkEkSQI1aGRz6zcJfpxwvh7VrfKh3n/GN4Pw5M8+NCHDmv/gzXxo3zcBkguPHzCz8yNd5/Nes9qFh45xRDQGoXsvK4d8s/HXl+K9d4829WZz/Y0Zcc/5/5kPD/z//j5n59JrzP3K1Nw1y0Pnvycd/zw9RhFcrSdFSBQBo0/1etm347W/fv033uvQY2gKAvAUCadm1dpZDaDnB7m/2UbFuWYqWLQxA26ceYNuaXW6OSlzBZHfR2NS2bdsICwvj7rvvdu47c+YMH374IS+++OI/eqzDJ4tmd3js2n5l+XwGFC5iZ/jzyUSfMfPuVD+mz3JMFohc5c3aL7yx20xUrJzB04NT8fWF1BT4YIYfUQfNZFhN3N8wnR590rIcbvivgm5T1/WnnyzMmevIv2hRO2NGJ3PmjJk3p/gxd44j/5UrvVm12pF/5SoZDB3iyN9qhU8+8eG7TV7YrCbKlbMyYkTm5ffZIeU2na47tnvx0ZX8ixSxMfJK/tPfysN7sx3vfl+s8iZytQ82G1SqbOWZISn4+kJKCrw/w49Dv1mwWqFBwwx69U29Lcffepsue79zu2P5vCN/OyNGO87/d97yY8Zsx/Ffs8qbL68c/3sqZ9D/yvFPuXL+H/7Ncf7Xb5hOz77Zf/5buH1/qnLC8R/YtGf2PuAVtRtV4IlnW+Hl7cWZE+eY8twSipTIz9AJXRjUYbqh7YhJXfkz6qxz+XyeAB9GvtmNoiULYDKZWDLrO777Yu9tidN67M/b8rjXqt2qGn0mdMfb24vTf5zlzd7vUbhMIUbMeooBtUYb2o6cN4Djv7pu+fz6dNfOp63yxSsue6797V912XNlxWUdoex0OzpCOcXt6gjlFLerI5RT3K6OUE5wOztCOcHt6gjlFK7oCN3J1BG6fXLISLaIiIi4ii6oKCIiIuIBVBESERERA0+ahaCKkIiIiHgsVYRERETEwJMuqKiKkIiIiHgsVYRERETEQBUhEREREQ+gipCIiIgYeNCiMVWERERExHOpIiQiIiIGmiMkIiIi4gFUERIREREjD5okpIqQiIiIeCx1hERERMRjaWhMREREDDRZWkRERMQDqCIkIiIiBnZNlhYRERHJ/VQREhEREQPNERIRERHxAKoIiYiIiJEqQiIiIiK5nypCIiIiYqBVYyIiIiIeQBUhERERMVJFSERERCT3U0VIREREDHQdIREREREPoIqQiIiIGGmOkIiIiEjup46QiIiIeCwNjYmIiIiBJkuLiIiIeIAcWREq5x3o7hDETWzY3B2CW5k9+LNLtPWyu0NwK+uxP90dgngSTZYWERERyf1yZEVIREREbifNERIRERHJ9dQREhERESO7C3/+gTVr1tCmTRtatGjBp59+mun2P/74gx49etC+fXv69u3LxYsXb/mY6giJiIjIHe/s2bNMmzaNzz77jFWrVrFkyRJ+//135+12u50BAwbQr18/vvjiCypWrMjs2bNv+bjqCImIiIjRHVgR2rp1K/feey958+bF39+fli1bsm7dOuftBw4cwN/fn4YNGwLQv39/HnvssVs+riZLi4iIiNskJCSQkJCQaX9wcDDBwcHO7ZiYGEJDQ53bYWFh7Nu3z7l94sQJChYsyAsvvMDBgwcpU6YML7300i2fXxUhERERMbKbXPbz8ccf06xZs0w/H3/8sSEkm82GyXR1NZvdbjdsZ2RksGPHDrp3787KlSspUaIEkyZNumWqqgiJiIiI2/Tq1YtOnTpl2n9tNQigcOHC7Nq1y7kdGxtLWFiYczs0NJRSpUpRpUoVANq2bcuQIUNu+fzqCImIiIiB3YVXlr5+COxG7rvvPmbMmMH58+fJkycP69ev5/XXX3feXr16dc6fP8+hQ4cIDw9n48aNVKpU6ZaPq46QiIiI3PEKFSrE8OHD6dmzJ+np6XTp0oWIiAj69evHkCFDqFKlCu+99x5jx44lOTmZwoULM3ny5Fs+rslud2W/L3vYosu7OwRxE33XmOdO6/P07xp74q6G7g5B3Gh9+mKXPl+pebfuQGSXP/s+57Lnyorn/lUVERERj6eOkIiIiHgszRESERERI7u+dFVEREQk11NFSERERAxMOW4Z1b+nipCIiIh4LFWERERExEgVIREREZHcTxUhERERMdKqMREREZHcTxUhERERMdIcIREREZHcTxUhERERMVJFSERERCT3U0VIREREjFQREhEREcn9VBESERERI11HSERERCT3U0dIREREPJaGxkRERMTApMnSIiIiIrmfKkIiIiJi5EEVIXWE/iG7HcZMhPJloE83d0fjWrk5983b4O3ZZtLSHfm9/ryNwABjm0+Xm/hspQlfXyhT0s7Y4XbyBkN8Arw+1cSh303k8YNOre089lDu+yuSm4//tp8szJ3rS3qaiTJlrIwalULAdcd/xQpvVq3ywcfXTqmSNoYOTSE42HHbqtXerP3Sm9Q0KF/exqiRKfj4uD6P7FCndXX6TOiGt483x/afYOpTs0i6lJxl21EfDuDY/pN8Pi3SxVHeHp6cuyfT0Ng/cPQ49B4O6ze7OxLXy825n4+HsZPMvP26jS8/sVG8qJ2ps4xLR7fvgXmLTMybamPFPBsN74VxUxwvn/+9a8I/D3zxsY3PZtr4fruJTVvdkcntk5uPf3y8icmT/Xh1XDILFiRSpKiN2XN8DW327rWwaLEPb72VxNw5SdStm8FbU/0A2LLFi5UrvZkyJYn5HyaRmgqff54ze0EhBYMYObc/rz08jb6VR3DmWAx93+ieqV2J8KJMXj+WBp3ruiHK28OTc/d0LusIHT9+nLNnzwKwbNkyxo8fz9q1a1319Nnis1XQ5UFo2djdkbhebs59604TlcOhVHHHdrcOdr781oT9mqLOb1Em7q1pp3CYY/uBhnY2bYW0dMdt7VrYsVjAxxsa1rOzfnPuugZHbj7+O3dZqFDBRvHijgPeoX06GzZ4G45/VJSZmjWthIY6djZokMG2bV6kp8P6b7x4uGs6wcFgNsOI4ak0b57ujlT+s5rNIzi86yinf48GIHLWNzTtXj9Tu/YDWvLVh9+xZfl2V4d423hy7p7ulkNjH374Ie+++y5Wq5VixYpRvnx5KlSoQIUKFShfvjzFixe/5ZN89NFHLFy4EJvNxr333suZM2do3rw5y5cv59ixYwwcODBbkrndXhrm+PfHXe6Nwx1yc+5nYqBw2NV3vUKhcDnRRGISzuGxiIp2Pllu5nS0naKFYeVXJtLTTVxMcNy2Zr2J6lXspKXBN5tNeHlBbhpkz83HPzbGTFiYzbkdGmonMdFEUhLO4bGKFW2sWOlDdLSJwoXtrFvnTXq6iYQEE6dOmbkQb+O55/Nw7pyJKlWsPP1Uqpuy+W9Cixcg9tQ553bsqXMEhPjjH5THMET03tD5gKPzkFt4cu5Z8aRVY7fsCM2aNYvJkycTERHByZMniYqK4vDhw2zZsoUjR44AUK5cORYtWnTDx1i+fDlr164lLi6Otm3b8tNPP+Hr60vXrl3p0qVLjukISe5kt0FW9RvzNfXSmlXhmSfsDBlrxmx2zAMKCbbj7QWjnrEzZaaJLk+aKZgf7qtlZ++vuasilJvZ7Lc+/hERVnr2TOPll/NgMkPr1ukEB9vx8rKTkWFi924L419PxscHJk3yY948XwYNynmdIZPZbKiE/T+b1ZZ5Zy7jybl7ult2hAIDA2ncuDFeXl6EhYVRs2ZNw+2nTp1ydohuxGaz4ePjQ7FixejTpw++vlfH361W678MXSR7FCkE+w6a+P8KTkwcBAfZ8c9ztU1iEtSqauehBx1tzsbCjA9NhAQ7Kkoj+tvJG+y4bfZCEyWLe9DHqRyuUJiNgwev/imMjTURFGQnzzXHPykJqlXN4ME26c428+f7EhwMBQrYaFA/w1k9eqB5OgsWGOcY5RSxJ+MIr1PWuV2wWH4Szl8mJSnnder+KU/OPUv6io2rnnrqKZYtW3bD24sXL06TJk1u+hgtWrTg8ccfx2q1MnjwYAAOHTrEo48+SuvWrf9hyCLZ677advb9Bn+ecmwv+cJE0/uNHZmYOOg9zMzlRMf2rIUm2jSzYzLB0tUm3v3Q8Ucj7jws/9LEg83UEcopatWycvCghVOnHMdwzRpv7r8vw9AmLs7EsOH+JF45/p986kPTJumYTNCoYQabNnuRmupYWffjD16EV8iZH/B2f7OPinXLUrRsYQDaPvUA29bkwvHQLHhy7p7ulhWhSZMmkZ6ezvfff0+DBg2oWLEiFSpUIM+1H5duYejQoezcuROLxeLc5+Pjw+DBg2nUqNG/i1wkmxTIB+NH2xj2spmMdChRDN54wcavh+DlN82smGejdEno+6id7v3N2OxQo4qdF4c5Ojv9HrczeoKZDk84JlgP6mOnSkU3JyV/W758dp4blcIr4/KQkQFFi9oZMzqZw4fNvDnFj7lzkihZ0s6j3dN4ZqA/dpuJylUyGDrEUSno0CGdS5dMPN3fH5vVRLlyVgYMSHFzVv9OfGwCU578gJeWDMfb24vTf5zlzd7vUa5mGUbMeooBtUa7O8TbxpNzz5IHfZYz2e1ZjYpedeLECQ4fPuz8OXToEKdPn6Z48eJ8/fXXrorTwBZd3i3PK+5nw7PH680efMWLaOtld4fgVk/c1dDdIYgbrU9f7NLnK/P2VJc91x/DRrjsubJyy4pQyZIlKVmyJM2bN3fuS0pKIioq6rYGJiIiIm7iQRWhf/Xx0t/fn2rVqmV3LCIiIiIupa/YEBEREQNPuo6Q5044EBEREY+nipCIiIgYqSIkIiIikvupIyQiIiIeS0NjIiIiYqShMREREZHcTxUhERERMdDyeREREREPoIqQiIiIGNlN7o7AZVQREhEREY+lipCIiIgYaY6QiIiISO6nipCIiIgYaNWYiIiIiAdQRUhERESMVBESERERyf1UERIREREDzRESERER8QCqCImIiIiRKkIiIiIiuZ86QiIiIuKxNDQmIiIiRhoaExEREcn9VBESERERAy2fFxEREfEA6giJiIiIx1JHSERERDyW5giJiIiIkeYIiYiIiOR+qgiJiIiIgVaNiYiIiHgAVYQkRzF7eN/9xxSbu0Nwm21JVd0dgojnUEVIREREJPdTRUhERESMVBESERERyf1UERIREREDrRoTERER8QDqCImIiIjH0tCYiIiIGGloTERERCT3U0VIREREDDRZWkRERMQDqCIkIiIiRqoIiYiIiOR+qgiJiIiIkSpCIiIiIrmfKkIiIiJioFVjIiIiIh5AFSERERExUkVIREREJPdTRUhERESMVBESERERyf1UERIREREDrRoTERER8QDqCImIiIjH0tCYiIiIGGloTERERCT3U0VIREREDDRZWkRERMQDqCIkIiIiRqoIiYiIiOR+qgiJiIiIUQxg+wAAHNNJREFUkSpCIiIiIrmfKkIiIiJiYHJ3AC6kipCIiIh4LFWERERExMiD5gipI/QP2e0wZiKULwN9urk7Gtfy5Nwhd+e/bzssn28mIx2Kl4YnhtvIE2Bss2G1iY1fmPDxgSIl7Tw60E5gMKSlwv+1d+9hVZVpH8d/G4EUU1E5eWimTBM7eIh5Ra08lahoHpK31Bl1UjM8RGEnx9EsS1OyyNRJa9S01NRKUycVTHMqscYO0tuMWp6SREAdwwMYstf7BxO2BlI0WEv38/1c175ibR72uu/2Au99P89aa9FMj/bu9EiWdE2kpd+PshR4hTu5XIzvtp3StjeOyltgqeZvA3XbqFAFBtkb5vu2ntTnb/5bHo90xZV+unVEqKrXCbCN2TDlkIJq+avNsBAnwy9XLbu20OBJfRUQGKC9X32nF4bN0anjeaWOfXTecO396oDeSl7jcJQVw+TcTcbU2AXYvU+6N1FK2ex2JM4zOXfJt/M/fkya/7yfRoz3atJcr0IjLL09z75CYMeX0rplHj08xasJL3t10/9Ir08v+vPxtyUeeQulJ2d79eRsrwp+lN578/JZYZD3Q6E+nJGt2x8LV9ysq1Qtwl//eP2obcyZ015tfjFbdzwert7J9fWb/wlS2tzDtjHpK44p61/5ToZe7mqEVNMjf43XxLuTNeTG0crcm60hk/uVGHdVZF0lpYzTbXdFuxBlxTA599J4LOcebnOlEJoyZYobu/3VFq+U4rpJndu7HYnzTM5d8u38v/7co6sbS+H1irbbd7f0yUaPrJ/9gdr/jUdNWliqFVq0ffOtlrZ/Ip0pkK67yVK3/pb8/CS/StJV10pHsp3P42J9/+UphTS6QjXqFnV3mnSprt1/Py7rZ/8DLG9RR/DHU15JUkG+Jf+As8Ve5v/lKePzU4rsXN3Z4MtZVKem2rlttw5+e0iStGZOqjr2u7XEuB7DO2vtvE36+9ufOB1ihTE5d9NV+NTYn/70pxLPbdy4UT/88IMk6dlnn63oEMrN+IeK/vvxNnfjcIPJuUu+nf/RHKlWyNl/9GuGSnmnPMo/peLpsWsiLb3/rp+OZFmqHS59vN6jMwUenciVbog6+1pHsqQNKzwa+KDX4Swu3snDhbqy9tk/hVVr+6vglKWCPEuBQUXFTkAVP90SH6LVY75X5WqV5PVKdz5bt+jnj57R1rlH1Hl8hHak5LqSQ3kJrV9bORlHirdzMo6oao0gBVWrYpsimvXgfElFxYOvMDn3Ul0CnRqnVHghFBwcrJUrVyo+Pl7Vqxd9Wtq6datatmxZ0bsGUAaWV6WeK+tX6ezX190k3fkHS7Mm+snjkW7tbKlqNUv+P1sis+8b6S9P+aljD0vNWlV42OXGsqxS8/f8rF9+dP+P+mLZv9XnpatUvU6Avl7zg95PylLP5+rpg+ezFX1vbQXVuvyXXHr8/GydwJ94Cy+fwvZimZy76Sr8N/fxxx9X27Zt9eKLL2r06NGKjo7WggUL1Lt374reNYAyqBUm7d3h0U8fAY8dloKutHRF5bNj8k8VTYHd1qVozL8PSysXeFS1WtH3P/3AozdmePT7kZaiO15eHyWvDPFXzq7Txdsnj5xR4JV+Cqh8thL6/otTCo+sXLw4uknX6vpk/hFl78rX8awCfTK/qJOQd6xQltdSYYGl20aGOptIOcg5cFiRLRsWb4fUq6XcoyeUf+r0OX7KN5icu+kcWSPUunVrzZkzR4sXL9bUqVNVWFjoxG4BlMENUZZ275Cyvi/a/uBvHjVvbS9mjh2Rpj3mp7yTRdt/W+JRy/aWPB7py63Skr94NPpZ72VXBElSveZByt51Wj8cLJAk7Vh/XL9tGWQbU7vBFTr0db7yjp2RJO3/9KSuDPNXxPVV1Pevv1Xv5PrqnVxfkZ2r6ZpbrrwsiyBJ+iw1XU2iG6puwwhJUvdhdyhttQ/OB5fC5NxLZTn4cJljvdzg4GBNnz5dy5cv186dO53aLYDzqB4s3fuwVy8/7aczZ6SwOtLgR73at0takOynCS97FXGV1PVuS5MeLJo+aHRD0enzkrT8VT9ZKhr7k4Y3FJ1CfzmoElxJbR8I1cbnslRYYKl6RIDaPRiqnG9P66NZOeqdXF91m1bRTb1q6G/jMlUpwKMrrvRTpz9FuB16uTuWk6tpQ2dr/NJEBQT46+CeLD137yw1imqg0XOGafjvxrgdYoUxOXfTeSyrtFnRS5v30HVuhwC44uN8c9crpJ1q5HYIrtrQrIbbIcBFKQVvOrq/5g8kO7avL2ckOrav0nAdIQAAYKzL/zQHAABQvi67uaKLR0cIAABcFlavXq3Y2FjFxMRo0aJFvzjugw8+UMeOHcv0mnSEAACAzaVw64v/lpWVpeTkZL3zzjsKDAxU3759FR0drYYNG9rGHT58WFOnTi3z69IRAgAAl7wtW7aoVatWCg4OVlBQkDp37qx169aVGDdu3DiNGjWqzK9LRwgAANg52BHKzc1Vbm7J29NUr169+I4UkpSdna3Q0LPX6AoLC1N6errtZxYuXKjrr79ezZo1K/P+KYQAAIBrFixYoJkzZ5Z4ftSoUXrggQeKt71erzyes/fDsSzLtr1r1y6lpKTotdde06FDh8q8fwohAABg4+QaoUGDBpV6262fd4MkKSIiQtu2nb3ad05OjsLCwoq3161bp5ycHPXp00cFBQXKzs5W//79tXjx4nPun0IIAAC45r+nwH5JmzZtNGPGDB09elRVqlRRSkqKnn766eLvJyQkKCEhQZKUkZGhgQMHnrcIklgsDQAA/tsleK+x8PBwJSYmauDAgerVq5e6d++upk2b6r777tNXX3110anSEQIAAJeFO++8U3feeaftuVdffbXEuPr162vjxo1lek0KIQAAYHcJXkeoojA1BgAAjEUhBAAAjMXUGAAAsLkUb7FRUegIAQAAY9ERAgAAdnSEAAAAfB8dIQAAYOOxzGkJ0RECAADGoiMEAADszGkI0RECAADmoiMEAABsuI4QAACAAegIAQAAOzpCAAAAvo+OEAAAsGGNEAAAgAHoCAEAADs6QgAAAL6PQggAABiLqTEAAGDDYmkAAAADXJYdoc71Wrgdgms8fh63Q4CLLK9BH9Ng4+FjK5xk0J8afrUAAICxLsuOEAAAqDisEQIAADAAHSEAAGBnmdMSoiMEAACMRUcIAADYsEYIAADAAHSEAACAHR0hAAAA30dHCAAA2Hi8bkfgHDpCAADAWHSEAACAHWuEAAAAfB+FEAAAMBZTYwAAwIYLKgIAABiAjhAAALDjpqsAAAC+j44QAACwYY0QAACAAegIAQAAOzpCAAAAvo+OEAAAsGGNEAAAgAHoCAEAADuuIwQAAOD76AgBAAAb1ggBAAAYgI4QAACwoyMEAADg+yiEAACAsZgaAwAANiyWBgAAMAAdIQAAYOc1pyVER+gXtIxtoTlfJGneP5M1fmmigqpV+cWxj84fobjR3R2MruK17NpCsz+fqrn/94LGLXno3PnPG664RN/J3+TcJY594/M3+Pg3OXeTUQiVokZINT0yd7gm/u8LGnx9ojL3ZGnIs/1LjPtNZD0lpY7XbX2iXYiy4tQIqaZH/hqviXcna8iNo5W5N1tDJvcrMe6qyLpKShmn2+7ynfxNzl3i2Cd/c49/k3MvleXgw2WOFELp6enFX6elpWnKlCmaNm2atm/f7sTuL1hUTDPt2rZb3397SJK0enaqbu9/a4lxPUbEaO28jfrwra1Oh1ihojo11c5tu3XwP/mvmZOqjv1KyX94Z62dt0l/f/sTp0OsMCbnLnHsG5+/wce/ybmbzpFCaMKECZKkRYsWafLkyYqIiFBISIieeOIJvfHGG06EcEFC69dWzoEjxds5GUdUtUZQiTbpzIT52rTkY6fDq3Ch9WsrJ+P8+c96cL42velb+Zucu8SxT/7mHv8m514aj+Xcw22OLpZetmyZFi5cqJo1a0qS4uLiFBcXpz/84Q9OhnFefn4eWaXceddb6HUhGud5/PxKvfGwCfmbnLvEsW96/iYf/ybnbjpHOkJnzpyR1+tVcHCwAgMDi58PDAyUn9+lt0wp+8Bh1a5bs3g7pF4t5R49ofxTp12Myjk5Bw6rdh0z8zc5d4lj3/T8TT7+Tc69VJbl3MNljlQhwcHBat++vfbu3aunn35aUtFaob59+6pLly5OhHBBPktJV5PoRqrXMEKS1P3+Tkpbtc3lqJzzWWq6mkQ3VN2f8h92h9JWm5G/yblLHPvG52/w8W9y7qZzZGrs9ddflyTt2bNHubm5koq6QQkJCWrfvr0TIVyQYzm5mjbkZY1fNloBgf46uOeQkgbN0nVRDTT6lfsVH/W42yFWqGM5uZo2dLbGL01UQIC/Du7J0nP3zlKjqAYaPWeYhv9ujNshVhiTc5c49snf3OPf5NxLcyms3XGKxyptQvwS16nSPW6H4BqPn8ftEOAiy6CLnMGO332zpRS86ej+OnSe6ti+Nq139wMGV5YGAAB2Bn3muvRWKgMAADiEjhAAALDxXH6rZi4aHSEAAGAsCiEAAGAspsYAAICdQRfUpiMEAACMRUcIAADYsFgaAADAAHSEAACAnTkNITpCAADAXHSEAACAHWuEAAAAfB8dIQAAYOMxpyFERwgAAJiLjhAAALBjjRAAAIDvoyMEAABsPNxrDAAAwPfREQIAAHasEQIAAPB9dIQAAICdOQ0hOkIAAMBcFEIAAMBYTI0BAAAbD4ulAQAAfB8dIQAAYEdHCAAAwPfREQIAAHbcYgMAAMD30RECAAA2nDUGAABgADpCAADAjo4QAACA76MjdJmxvOZU6aWyDDqVoTQecz+7ePw8bocAmIOOEAAAgO+jIwQAAOwMar7TEQIAAMaiIwQAAGy4jhAAAIABKIQAAICxmBoDAAB2TI0BAAD4PjpCAADAjo4QAACA76MjBAAA7OgIAQAAXFpWr16t2NhYxcTEaNGiRSW+v2HDBvXs2VM9evTQiBEj9MMPP5z3NSmEAACAndfBRxllZWUpOTlZixcv1sqVK7V06VJ9++23xd8/ceKEnnzySb3yyitatWqVGjdurBkzZpz3dSmEAACAa3Jzc5WRkVHikZubaxu3ZcsWtWrVSsHBwQoKClLnzp21bt264u8XFBRowoQJCg8PlyQ1btxYmZmZ590/a4QAAICNk7fYWLBggWbOnFni+VGjRumBBx4o3s7OzlZoaGjxdlhYmNLT04u3a9asqU6dOkmS8vPz9corr2jAgAHn3T+FEAAAcM2gQYPUu3fvEs9Xr17dtu31euXxeIq3Lcuybf/k+PHjGjlypCIjI0t93f9GIQQAAOwc7AhVr169RNFTmoiICG3btq14OycnR2FhYbYx2dnZGjJkiFq1aqWxY8eWaf+sEQIAAJe8Nm3aKC0tTUePHlVeXp5SUlLUtm3b4u8XFhYqPj5eXbt21Z///OdSu0WloSMEAADsvJfedYTCw8OVmJiogQMHqqCgQHFxcWratKnuu+8+JSQk6NChQ/rnP/+pwsJCrV+/XpJ04403atKkSed8XY9lXX5XTepU6R63Q4BbrAs419IXecxt4nr8yvbpDvBFKQVvOrq/ro3HOLavtTunOLav0tARAgAAdpdfj+SimfvxEgAAGI9CCAAAGIupMQAAYMfUGAAAgO+jIwQAAOzoCAEAAPg+OkIAAMDuErygYkWhIwQAAIxFRwgAANgZdBV/OkIAAMBYdIQAAIAdZ40BAAD4PjpCAADAzqCzxiiEfkHL2BYaMqmfAq4I0N6vvtPzQ2fr1PG8Usc+On+E9n71nd56YY3DUVYcE/JvGXuzhkzuX5Rj+n49P/TlEjn+0phqNa9Uwl/u07XNr1b+yXytf22T3p25TpLUqnuUHn1tlHK+O1z8OoltxyvvRL6j+V0sE977c2nZtYUGT+qrgMCi/F8YNueX8583XHu/OqC3ksnfF5icu8mYGitFjZBqemTucE383xc0+PpEZe7J0pBn+5cY95vIekpKHa/b+kS7EGXFMSH/GiHV9ci8EZoYN02DmzyozL1ZGjLl92UeE//CIOWdzNfQGxKV0PrPatmlhaK73SxJur5NY731/CrF3/xo8eNyKYJMeO/PpUZINT3y13hNvDtZQ24crcy92RoyuV+JcVdF1lVSyjjddhf5+wqTcy+VZTn3cJljhdCHH36o3NxcSdLKlSs1ceJEvf32207t/oJExTTTrm279f23hyRJq2en6vb+t5YY12NEjNbO26gP39rqdIgVyoT8o2Kaatc/fpbjyym6vf9tZR7TKKqBNry+WV6vV2cKzuiT9z5X2z6tJUk3tG6s5h1u1OwvntMLmyfqptuaOJjZr2PCe38uUZ2aaue23Tr4n/zXzElVx36l5D+8s9bO26S/v/2J0yFWKJPzNzl30zlSCE2aNElz5szR6dOn9eKLL2rVqlVq2LChUlNT9cwzzzgRwgUJrV9bOQeOFG/nZBxR1RpBCqpWxTZuZsJ8bVrysdPhVTgT8g+9KkQ5GWenrkrL8Vxjdnz6re4Y0E6V/CupctXKuvWuVqpVJ1iSlHvkuNbMSVV8i0c1d+xiPfnOowqpV8u55H4FE977cwmtX1s5GefPf9aD87XpTfL3JSbnXiqDOkKOrBHasmWLVq1apUqVKmnz5s1aunSpAgMDdc8996h79+5OhHBB/Pw8skp5c7yFZlxgyoT8i3Is+fzPczzXmDkPL9D90wbq5c+T9O9Dx/T5hu26vnVjSdJTcdOKx3798Q59vWWnojo11frXPijvNMqdCe/9uXj8/M57XPgyk/M3OXfTOdIRqly5so4cKaq0IyIidOrUKUlSXl6e/P0vvfXa2QcOq3bdmsXbIfVqKffoCeWfOu1iVM4xIf/s7w6rdp1z53iuMUHVg/TqY29oWNOH9XjM0/J4PDq4+5Cq1ghSvz/1tu3L4/HoTEFhxSdVDkx4788l58D5jwtfZnL+JuduOkcKoZEjRyouLk5Tp05V/fr1NWDAAE2ePFl333237r33XidCuCCfpaSrSXQj1WsYIUnqfn8npa3a5nJUzjEh/89StqtJq5/lGB+jtHf/UeYxd8Z30qCJ90iSgsNqqOuQ27Vx8UfKO56vHiO66Nb/LKS8tvnVatyyof6x7kunUvtVTHjvz+Wz1HQ1iW6ouj/lP+wOpa0mfxOYnHupmBorXx07dlSjRo20YcMG7d+/X82bN1fVqlU1ZcoUNW3a1IkQLsixnFxNG/Kyxi8brYBAfx3cc0hJg2bpuqgGGv3K/YqPetztECuUCfkfy8nVtMF/0fjlDxfluDtLSYNmFuX46nDF3/zoL46RpCXPrtDjCx/QK+nPy+PxaMGEpdq1bbckaUKvqRr50hANfPJuec94NalvsnKPHHcz3TIz4b0/l2M5uZo2dLbGL01UQIC/Du7J0nP3zlKjqAYaPWeYhv9ujNshViiT8zc5d9N5rNIWBFziOlW6x+0Q4BaDbgRYKo+5V7zw+HncDgFwTUrBm47ur2udkY7ta23mLMf2VRpz/6oCAADjXXorlQEAgLsuv8mii0ZHCAAAGIuOEAAAsKMjBAAA4PvoCAEAADsvHSEAAACfR0cIAADYWAZds42OEAAAMBYdIQAAYMcaIQAAAN9HRwgAANhxHSEAAADfRyEEAACMxdQYAACw83L6PAAAgM+jIwQAAOxYLA0AAOD76AgBAAAbizVCAAAAvo+OEAAAsGONEAAAgO+jIwQAAOy46SoAAIDvoyMEAADsLM4aAwAA8Hl0hAAAgI3FGiEAAADfR0cIAADYsUYIAADA91EIAQAAYzE1BgAAbFgsDQAAYAA6QgAAwM6gxdIeyzLoFrMAAAA/w9QYAAAwFoUQAAAwFoUQAAAwFoUQAAAwFoUQAAAwFoUQAAAwFoUQAAAwFoUQAAAwFoUQAAAwFoXQBVi9erViY2MVExOjRYsWuR2O406cOKHu3bsrIyPD7VAcN3PmTHXr1k3dunVTUlKS2+E4bvr06YqNjVW3bt00f/58t8NxzdSpUzVmzBi3w3DcgAED1K1bN/Xs2VM9e/bU9u3b3Q7JURs3btRdd92lrl276plnnnE7HJQz7jVWRllZWUpOTtY777yjwMBA9e3bV9HR0WrYsKHboTli+/btGjdunPbt2+d2KI7bsmWLPvroI61YsUIej0dDhw5VamqqOnXq5HZojvj000+1detWrVq1SmfOnFFsbKzatWunBg0auB2ao9LS0rRixQq1b9/e7VAcZVmW9u3bp02bNsnf37x/Mg4cOKAJEyZo+fLlql27tgYNGqTNmzerXbt2boeGckJHqIy2bNmiVq1aKTg4WEFBQercubPWrVvndliOWbZsmSZMmKCwsDC3Q3FcaGioxowZo8DAQAUEBOjaa6/VwYMH3Q7LMS1bttTChQvl7++vI0eOqLCwUEFBQW6H5ahjx44pOTlZ8fHxbofiuD179kiSBg8erB49euiNN95wOSJnpaamKjY2VhEREQoICFBycrKaNWvmdlgoR+aV9xcpOztboaGhxdthYWFKT093MSJnTZo0ye0QXNOoUaPir/ft26e1a9dqyZIlLkbkvICAAL300kuaN2+eunTpovDwcLdDctQTTzyhxMREZWZmuh2K43Jzc9W6dWuNHz9eBQUFGjhwoK655hrdcsstbofmiP379ysgIEDx8fHKzMxU+/bt9dBDD7kdFsoRHaEy8nq98ng8xduWZdm24fu++eYbDR48WI899piuvvpqt8NxXEJCgtLS0pSZmally5a5HY5jli9frjp16qh169Zuh+KKFi1aKCkpSdWqVVOtWrUUFxenzZs3ux2WYwoLC5WWlqbJkydr6dKlSk9P14oVK9wOC+WIQqiMIiIilJOTU7ydk5Nj5DSRqT777DP98Y9/1MMPP6zevXu7HY6jdu/erX/961+SpCpVqigmJkY7d+50OSrnvPfee/r444/Vs2dPvfTSS9q4caMmT57sdliO2bZtm9LS0oq3Lcsyaq1QSEiIWrdurVq1aqly5cq64447jJoNMAGFUBm1adNGaWlpOnr0qPLy8pSSkqK2bdu6HRYckJmZqZEjR2ratGnq1q2b2+E4LiMjQ+PGjdOPP/6oH3/8Ue+//76ioqLcDssx8+fP15o1a/Tuu+8qISFBHTt21NixY90OyzHHjx9XUlKSTp8+rRMnTmjFihXGnCggSR06dNBHH32k3NxcFRYW6sMPP9QNN9zgdlgoR+aU9b9SeHi4EhMTNXDgQBUUFCguLk5NmzZ1Oyw4YO7cuTp9+rSmTJlS/Fzfvn3Vr18/F6NyTrt27ZSenq5evXqpUqVKiomJMbIgNFWHDh20fft29erVS16vV/3791eLFi3cDssxzZo109ChQ9W/f38VFBTolltuUZ8+fdwOC+XIY1mW5XYQAAAAbmBqDAAAGItCCAAAGItCCAAAGItCCAAAGItCCAAAGItCCAAAGItCCAAAGItCCECZdO3aVW3bttU333zjdigAUG4ohACUyZo1a3T11Vdr/fr1bocCAOWGQghAmVSqVElRUVFG3XAVgO/jXmMAyiQ/P1/vvfeeuCsPAF9CRwhAmSQnJyssLEzfffedTp486XY4AFAuKIQAnNcXX3yhtWvXasaMGapWrRoLpgH4DAohAOd0+vRpjR07Vk899ZSCg4MVGRmpHTt2uB0WAJQLCiEA5zR9+nQ1b95cHTp0kCRFRkayYBqAz6AQAvCL0tPTtW7dOo0dO7b4uSZNmtARAuAzPBangAAAAEPREQIAAMaiEAIAAMaiEAIAAMaiEAIAAMaiEAIAAMaiEAIAAMaiEAIAAMaiEAIAAMb6fyr6WSBpNFEzAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 720x720 with 2 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 720x720 with 2 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "# visual representation of grid search\n",
-    "# uses seaborn heatmap, could probably do this in matplotlib\n",
-    "import seaborn as sns\n",
-    "\n",
-    "sns.set()\n",
-    "\n",
-    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "\n",
-    "for i in range(len(eta_vals)):\n",
-    "    for j in range(len(lmbd_vals)):\n",
-    "        CNN = CNN_keras[i][j]\n",
-    "\n",
-    "        train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]\n",
-    "        test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]\n",
-    "\n",
-    "        \n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Training Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Test Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The CIFAR01 data set\n",
-    "\n",
-    "The CIFAR10 dataset contains 60,000 color images in 10 classes, with\n",
-    "6,000 images in each class. The dataset is divided into 50,000\n",
-    "training images and 10,000 testing images. The classes are mutually\n",
-    "exclusive and there is no overlap between them."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Downloading data from https://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz\n",
-      "170500096/170498071 [==============================] - 35s 0us/step\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "import tensorflow as tf\n",
-    "\n",
-    "from tensorflow.keras import datasets, layers, models\n",
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "# We import the data set\n",
-    "(train_images, train_labels), (test_images, test_labels) = datasets.cifar10.load_data()\n",
-    "\n",
-    "# Normalize pixel values to be between 0 and 1 by dividing by 255. \n",
-    "train_images, test_images = train_images / 255.0, test_images / 255.0"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Verifying the data set\n",
-    "\n",
-    "To verify that the dataset looks correct, let's plot the first 25 images from the training set and display the class name below each image."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class_names = ['airplane', 'automobile', 'bird', 'cat', 'deer',\n",
-    "               'dog', 'frog', 'horse', 'ship', 'truck']\n",
-    "​\n",
-=======
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 720x720 with 25 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "class_names = ['airplane', 'automobile', 'bird', 'cat', 'deer',\n",
-    "               'dog', 'frog', 'horse', 'ship', 'truck']\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "plt.figure(figsize=(10,10))\n",
-    "for i in range(25):\n",
-    "    plt.subplot(5,5,i+1)\n",
-    "    plt.xticks([])\n",
-    "    plt.yticks([])\n",
-    "    plt.grid(False)\n",
-    "    plt.imshow(train_images[i], cmap=plt.cm.binary)\n",
-    "    # The CIFAR labels happen to be arrays, \n",
-    "    # which is why you need the extra index\n",
-    "    plt.xlabel(class_names[train_labels[i][0]])\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Set up  the model\n",
-    "\n",
-    "The 6 lines of code below define the convolutional base using a common pattern: a stack of Conv2D and MaxPooling2D layers.\n",
-    "\n",
-    "As input, a CNN takes tensors of shape (image_height, image_width, color_channels), ignoring the batch size. If you are new to these dimensions, color_channels refers to (R,G,B). In this example, you will configure our CNN to process inputs of shape (32, 32, 3), which is the format of CIFAR images. You can do this by passing the argument input_shape to our first layer."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Model: \"sequential_49\"\n",
-      "_________________________________________________________________\n",
-      "Layer (type)                 Output Shape              Param #   \n",
-      "=================================================================\n",
-      "conv2d_49 (Conv2D)           (None, 30, 30, 32)        896       \n",
-      "_________________________________________________________________\n",
-      "max_pooling2d_49 (MaxPooling (None, 15, 15, 32)        0         \n",
-      "_________________________________________________________________\n",
-      "conv2d_50 (Conv2D)           (None, 13, 13, 64)        18496     \n",
-      "_________________________________________________________________\n",
-      "max_pooling2d_50 (MaxPooling (None, 6, 6, 64)          0         \n",
-      "_________________________________________________________________\n",
-      "conv2d_51 (Conv2D)           (None, 4, 4, 64)          36928     \n",
-      "=================================================================\n",
-      "Total params: 56,320\n",
-      "Trainable params: 56,320\n",
-      "Non-trainable params: 0\n",
-      "_________________________________________________________________\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "model = models.Sequential()\n",
-    "model.add(layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)))\n",
-    "model.add(layers.MaxPooling2D((2, 2)))\n",
-    "model.add(layers.Conv2D(64, (3, 3), activation='relu'))\n",
-    "model.add(layers.MaxPooling2D((2, 2)))\n",
-    "model.add(layers.Conv2D(64, (3, 3), activation='relu'))\n",
-    "\n",
-    "# Let's display the architecture of our model so far.\n",
-    "\n",
-    "model.summary()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You can see that the output of every Conv2D and MaxPooling2D layer is a 3D tensor of shape (height, width, channels). The width and height dimensions tend to shrink as you go deeper in the network. The number of output channels for each Conv2D layer is controlled by the first argument (e.g., 32 or 64). Typically, as the width and height shrink, you can afford (computationally) to add more output channels in each Conv2D layer.\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Add Dense layers on top\n",
-    "\n",
-    "To complete our model, you will feed the last output tensor from the\n",
-    "convolutional base (of shape (4, 4, 64)) into one or more Dense layers\n",
-    "to perform classification. Dense layers take vectors as input (which\n",
-    "are 1D), while the current output is a 3D tensor. First, you will\n",
-    "flatten (or unroll) the 3D output to 1D, then add one or more Dense\n",
-    "layers on top. CIFAR has 10 output classes, so you use a final Dense\n",
-    "layer with 10 outputs and a softmax activation."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Model: \"sequential_49\"\n",
-      "_________________________________________________________________\n",
-      "Layer (type)                 Output Shape              Param #   \n",
-      "=================================================================\n",
-      "conv2d_49 (Conv2D)           (None, 30, 30, 32)        896       \n",
-      "_________________________________________________________________\n",
-      "max_pooling2d_49 (MaxPooling (None, 15, 15, 32)        0         \n",
-      "_________________________________________________________________\n",
-      "conv2d_50 (Conv2D)           (None, 13, 13, 64)        18496     \n",
-      "_________________________________________________________________\n",
-      "max_pooling2d_50 (MaxPooling (None, 6, 6, 64)          0         \n",
-      "_________________________________________________________________\n",
-      "conv2d_51 (Conv2D)           (None, 4, 4, 64)          36928     \n",
-      "_________________________________________________________________\n",
-      "flatten_49 (Flatten)         (None, 1024)              0         \n",
-      "_________________________________________________________________\n",
-      "dense_98 (Dense)             (None, 64)                65600     \n",
-      "_________________________________________________________________\n",
-      "dense_99 (Dense)             (None, 10)                650       \n",
-      "=================================================================\n",
-      "Total params: 122,570\n",
-      "Trainable params: 122,570\n",
-      "Non-trainable params: 0\n",
-      "_________________________________________________________________\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "model.add(layers.Flatten())\n",
-    "model.add(layers.Dense(64, activation='relu'))\n",
-    "model.add(layers.Dense(10))\n",
-<<<<<<< HEAD
-    "Here's the complete architecture of our model.\n",
-=======
-    "#Here's the complete architecture of our model.\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "model.summary()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As you can see, our (4, 4, 64) outputs were flattened into vectors of shape (1024) before going through two Dense layers.\n",
-    "\n",
-    "## Compile and train the model"
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Train on 50000 samples, validate on 10000 samples\n",
-      "Epoch 1/10\n",
-      "50000/50000 [==============================] - 40s 793us/sample - loss: 1.5115 - accuracy: 0.4515 - val_loss: 1.2411 - val_accuracy: 0.5545\n",
-      "Epoch 2/10\n",
-      "50000/50000 [==============================] - 41s 826us/sample - loss: 1.1297 - accuracy: 0.6006 - val_loss: 1.0419 - val_accuracy: 0.6307\n",
-      "Epoch 3/10\n",
-      "50000/50000 [==============================] - 43s 870us/sample - loss: 0.9842 - accuracy: 0.6534 - val_loss: 1.0402 - val_accuracy: 0.6314\n",
-      "Epoch 4/10\n",
-      "50000/50000 [==============================] - 43s 869us/sample - loss: 0.8824 - accuracy: 0.6894 - val_loss: 0.9944 - val_accuracy: 0.6599\n",
-      "Epoch 5/10\n",
-      "50000/50000 [==============================] - 40s 803us/sample - loss: 0.8098 - accuracy: 0.7171 - val_loss: 0.9176 - val_accuracy: 0.6829\n",
-      "Epoch 6/10\n",
-      "50000/50000 [==============================] - 46s 925us/sample - loss: 0.7469 - accuracy: 0.7370 - val_loss: 0.8683 - val_accuracy: 0.7072\n",
-      "Epoch 7/10\n",
-      "50000/50000 [==============================] - 43s 857us/sample - loss: 0.6939 - accuracy: 0.7546 - val_loss: 0.8628 - val_accuracy: 0.7055\n",
-      "Epoch 8/10\n",
-      "50000/50000 [==============================] - 38s 770us/sample - loss: 0.6492 - accuracy: 0.7719 - val_loss: 0.8725 - val_accuracy: 0.7120\n",
-      "Epoch 9/10\n",
-      "50000/50000 [==============================] - 37s 743us/sample - loss: 0.6064 - accuracy: 0.7881 - val_loss: 0.8604 - val_accuracy: 0.7144\n",
-      "Epoch 10/10\n",
-      "50000/50000 [==============================] - 36s 715us/sample - loss: 0.5675 - accuracy: 0.8003 - val_loss: 0.8882 - val_accuracy: 0.7137\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "model.compile(optimizer='adam',\n",
-    "              loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),\n",
-    "              metrics=['accuracy'])\n",
-<<<<<<< HEAD
-    "​\n",
-=======
-    "\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "history = model.fit(train_images, train_labels, epochs=10, \n",
-    "                    validation_data=(test_images, test_labels))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Finally, evaluate the model"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.plot(history.history['accuracy'], label='accuracy')\n",
-    "plt.plot(history.history['val_accuracy'], label = 'val_accuracy')\n",
-    "plt.xlabel('Epoch')\n",
-    "plt.ylabel('Accuracy')\n",
-    "plt.ylim([0.5, 1])\n",
-    "plt.legend(loc='lower right')\n",
-    "\n",
-    "test_loss, test_acc = model.evaluate(test_images,  test_labels, verbose=2)\n",
-    "\n",
-    "print(test_acc)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Recurrent neural networks: Overarching view\n",
-    "\n",
-    "Till now our focus has been, including convolutional neural networks\n",
-    "as well, on feedforward neural networks. The output or the activations\n",
-    "flow only in one direction, from the input layer to the output layer.\n",
-    "\n",
-    "A recurrent neural network (RNN) looks very much like a feedforward\n",
-    "neural network, except that it also has connections pointing\n",
-    "backward. \n",
-    "\n",
-    "RNNs are used to analyze time series data such as stock prices, and\n",
-    "tell you when to buy or sell. In autonomous driving systems, they can\n",
-    "anticipate car trajectories and help avoid accidents. More generally,\n",
-    "they can work on sequences of arbitrary lengths, rather than on\n",
-    "fixed-sized inputs like all the nets we have discussed so far. For\n",
-    "example, they can take sentences, documents, or audio samples as\n",
-    "input, making them extremely useful for natural language processing\n",
-    "systems such as automatic translation and speech-to-text.\n",
-    "\n",
-    "\n",
-    "## A simple example"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Start importing packages\n",
-    "import pandas as pd\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "import tensorflow as tf\n",
-    "from tensorflow.keras import datasets, layers, models\n",
-    "from tensorflow.keras.layers import Input\n",
-    "from tensorflow.keras.models import Model, Sequential \n",
-    "from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU\n",
-    "from tensorflow.keras import optimizers     \n",
-    "from tensorflow.keras import regularizers           \n",
-    "from tensorflow.keras.utils import to_categorical \n",
-    "\n",
-    "\n",
-    "\n",
-    "# convert into dataset matrix\n",
-    "def convertToMatrix(data, step):\n",
-    " X, Y =[], []\n",
-    " for i in range(len(data)-step):\n",
-    "  d=i+step  \n",
-    "  X.append(data[i:d,])\n",
-    "  Y.append(data[d,])\n",
-    " return np.array(X), np.array(Y)\n",
-    "\n",
-    "step = 4\n",
-    "N = 1000    \n",
-    "Tp = 800    \n",
-    "\n",
-    "t=np.arange(0,N)\n",
-    "x=np.sin(0.02*t)+2*np.random.rand(N)\n",
-    "df = pd.DataFrame(x)\n",
-    "df.head()\n",
-    "\n",
-    "plt.plot(df)\n",
-    "plt.show()\n",
-    "\n",
-    "values=df.values\n",
-    "train,test = values[0:Tp,:], values[Tp:N,:]\n",
-    "\n",
-    "# add step elements into train and test\n",
-    "test = np.append(test,np.repeat(test[-1,],step))\n",
-    "train = np.append(train,np.repeat(train[-1,],step))\n",
-    " \n",
-    "trainX,trainY =convertToMatrix(train,step)\n",
-    "testX,testY =convertToMatrix(test,step)\n",
-    "trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))\n",
-    "testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))\n",
-    "\n",
-    "model = Sequential()\n",
-    "model.add(SimpleRNN(units=32, input_shape=(1,step), activation=\"relu\"))\n",
-    "model.add(Dense(8, activation=\"relu\")) \n",
-    "model.add(Dense(1))\n",
-    "model.compile(loss='mean_squared_error', optimizer='rmsprop')\n",
-    "model.summary()\n",
-    "\n",
-    "model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2)\n",
-    "trainPredict = model.predict(trainX)\n",
-    "testPredict= model.predict(testX)\n",
-    "predicted=np.concatenate((trainPredict,testPredict),axis=0)\n",
-    "\n",
-    "trainScore = model.evaluate(trainX, trainY, verbose=0)\n",
-    "print(trainScore)\n",
-    "\n",
-    "index = df.index.values\n",
-    "plt.plot(index,df)\n",
-    "plt.plot(index,predicted)\n",
-    "plt.axvline(df.index[Tp], c=\"r\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Set up of an RNN\n",
-    "\n",
-    "The figure here displays a simple example of an RNN, with inputs $x_t$\n",
-    "at a given time $t$ and outputs $y_t$.  Introducing time as a variable\n",
-    "offers an intutitive way of understanding these networks. In addition\n",
-    "to the inputs $x_t$, the layer at a time $t$ receives also as input\n",
-    "the output from the previous layer $t-1$, that is $y_{t1}$.\n",
-    "\n",
-    "This means also that we need to have weights that link both the inputs\n",
-    "$x_t$ to the outputs $y_t$ as well as weights that link the output\n",
-    "from the previous time $y_{t-1}$ and $y_t$.  The figure here shows an\n",
-    "example of a simple RNN.\n",
-    "\n",
-    "More material will be added here.\n",
-    "\n",
-    "\n",
-    "## Solving differential equations and eigenvalue problems with RNNs\n",
-    "\n",
-    "\n",
-    "\n",
-    "In our discussions of ordinary differential equations and partial\n",
-    "differential equations using neural networks. Here we will discuss how\n",
-    "we can solve say ordinary differential equations and eigenvalue\n",
-    "problems using RNNs. Eigenvalue problems can be solved using RNNs by\n",
-    "rewriting such a problems as a non-linear differential equation.\n",
-    "\n",
-    "Instead of starting with a well-known ordinary differential equation,\n",
-    "we start directly with an eigenvaule problem.\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Long-Short Time Memory\n",
-    "\n",
-    "Discussions about dynamic unrolling through time. discuss memory cells, input and output\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Autoencoders: Overarching view\n",
-    "\n",
-    "Autoencoders are artificial neural networks capable of learning\n",
-    "efficient representations of the input data (these representations are called codings)  without\n",
-    "any supervision (i.e., the training set is unlabeled). These codings\n",
-    "typically have a much lower dimensionality than the input data, making\n",
-    "autoencoders useful for dimensionality reduction. \n",
-    "\n",
-    "More importantly, autoencoders act as powerful feature detectors, and\n",
-    "they can be used for unsupervised pretraining of deep neural networks.\n",
-    "\n",
-    "Lastly, they are capable of randomly generating new data that looks\n",
-    "very similar to the training data; this is called a generative\n",
-    "model. For example, you could train an autoencoder on pictures of\n",
-    "faces, and it would then be able to generate new faces.  Surprisingly,\n",
-    "autoencoders work by simply learning to copy their inputs to their\n",
-    "outputs. This may sound like a trivial task, but we will see that\n",
-    "constraining the network in various ways can make it rather\n",
-    "difficult. For example, you can limit the size of the internal\n",
-    "representation, or you can add noise to the inputs and train the\n",
-    "network to recover the original inputs. These constraints prevent the\n",
-    "autoencoder from trivially copying the inputs directly to the outputs,\n",
-    "which forces it to learn efficient ways of representing the data. In\n",
-    "short, the codings are byproducts of the autoencoder’s attempt to\n",
-    "learn the identity function under some constraints.\n",
-    "\n",
-    "## Simple examples of Autoencoders"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-<<<<<<< HEAD
-   "version": "3.6.8"
-=======
-   "version": "3.8.3"
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
diff --git a/doc/pub/week42/ipynb/week42.ipynb b/doc/pub/week42/ipynb/week42.ipynb
deleted file mode 100644
index 45a126e79..000000000
--- a/doc/pub/week42/ipynb/week42.ipynb
+++ /dev/null
@@ -1,5952 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "d231eeee",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
-    "doconce format html week42.do.txt --no_mako -->\n",
-    "<!-- dom:TITLE: Week 42 Constructing a Neural Network code with examples -->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5e782cb1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "# Week 42 Constructing a Neural Network code with examples\n",
-    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway\n",
-    "\n",
-    "Date: **October 13-17, 2025**"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "53309290",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Lecture October 13, 2025\n",
-    "1. Building our own Feed-forward Neural Network and discussion of project 2\n",
-    "\n",
-    "2. Project 2 is available at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/2025/Project2/ipynb/Project2.ipynb>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "71367514",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Readings and videos\n",
-    "1. These lecture notes\n",
-    "\n",
-    "2. Video of lecture at <https://youtu.be/eqyNrEYRXnY>\n",
-    "\n",
-    "3. Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek42.pdf>\n",
-    "\n",
-    "4. For a more in depth discussion on  neural networks we recommend Goodfellow et al chapters 6 and 7. For the optimization part, see chapter 8.    \n",
-    "\n",
-    "5. Neural Networks demystified at <https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs>\n",
-    "\n",
-    "6. Building Neural Networks from scratch at <https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex>\n",
-    "\n",
-    "7. Video on Neural Networks at <https://www.youtube.com/watch?v=CqOfi41LfDw>\n",
-    "\n",
-    "8. Video on the back propagation algorithm at <https://www.youtube.com/watch?v=Ilg3gGewQ5U>\n",
-    "\n",
-    "I also  recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at <http://neuralnetworksanddeeplearning.com/chap4.html>."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c7be87be",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Material for the lab sessions on Tuesday and Wednesday\n",
-    "1. Exercises on writing a code for neural networks, back propagation part, see exercises for week 42 at <https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/exercisesweek42.html> \n",
-    "\n",
-    "2. Discussion of project 2"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8e0567a2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Lecture material: Writing a code which implements a feed-forward neural network\n",
-    "\n",
-    "Last week we discussed the basics of neural networks and deep learning\n",
-    "and the basics of automatic differentiation.  We looked also at\n",
-    "examples on how compute the parameters of a simple network with scalar\n",
-    "inputs and ouputs and no or just one hidden layers.\n",
-    "\n",
-    "We ended our discussions with the derivation of the equations for a\n",
-    "neural network with one hidden layers and two input variables and two\n",
-    "hidden nodes but only one output node. We did almost finish the derivation of the back propagation algorithm."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "549dcc05",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Mathematics of deep learning\n",
-    "\n",
-    "**Two recent books online.**\n",
-    "\n",
-    "1. [The Modern Mathematics of Deep Learning, by Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen](https://arxiv.org/abs/2105.04026), published as [Mathematical Aspects of Deep Learning, pp. 1-111. Cambridge University Press, 2022](https://doi.org/10.1017/9781009025096.002)\n",
-    "\n",
-    "2. [Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory, Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger](https://doi.org/10.48550/arXiv.2310.20360)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "21203bae",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Reminder on books with hands-on material and codes\n",
-    "* [Sebastian Rashcka et al, Machine learning with Sickit-Learn and PyTorch](https://sebastianraschka.com/blog/2022/ml-pytorch-book.html)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1c102a30",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Reading recommendations\n",
-    "\n",
-    "1. Rashkca et al., chapter 11, jupyter-notebook sent separately, from [GitHub](https://github.com/rasbt/machine-learning-book)\n",
-    "\n",
-    "2. Goodfellow et al, chapter 6 and 7 contain most of the neural network background."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "53f11afe",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Reminder from last week: First network example, simple percepetron with one input\n",
-    "\n",
-    "As yet another example we define now a simple perceptron model with\n",
-    "all quantities given by scalars. We consider only one input variable\n",
-    "$x$ and one target value $y$.  We define an activation function\n",
-    "$\\sigma_1$ which takes as input"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "afa8c42a",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z_1 = w_1x+b_1,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "cb5c959f",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where $w_1$ is the weight and $b_1$ is the bias. These are the\n",
-    "parameters we want to optimize.  The output is $a_1=\\sigma(z_1)$ (see\n",
-    "graph from whiteboard notes). This output is then fed into the\n",
-    "**cost/loss** function, which we here for the sake of simplicity just\n",
-    "define as the squared error"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0083ae15",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "C(x;w_1,b_1)=\\frac{1}{2}(a_1-y)^2.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f4931203",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Layout of a simple neural network with no hidden layer\n",
-    "\n",
-    "<!-- dom:FIGURE: [figures/simplenn1.png, width=900 frac=1.0] -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<img src=\"figures/simplenn1.png\" width=\"900\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
-    "<!-- end figure -->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d3a3754d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Optimizing the parameters\n",
-    "\n",
-    "In setting up the feed forward and back propagation parts of the\n",
-    "algorithm, we need now the derivative of the various variables we want\n",
-    "to train.\n",
-    "\n",
-    "We need"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bcd5dbab",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_1} \\hspace{0.1cm}\\mathrm{and}\\hspace{0.1cm}\\frac{\\partial C}{\\partial b_1}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2cbc30f1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Using the chain rule we find"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1a1d803d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_1}=\\frac{\\partial C}{\\partial a_1}\\frac{\\partial a_1}{\\partial z_1}\\frac{\\partial z_1}{\\partial w_1}=(a_1-y)\\sigma_1'x,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "776735c7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c1a2e5af",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial b_1}=\\frac{\\partial C}{\\partial a_1}\\frac{\\partial a_1}{\\partial z_1}\\frac{\\partial z_1}{\\partial b_1}=(a_1-y)\\sigma_1',\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9e603df9",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "which we later will just define as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "533212cd",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial a_1}\\frac{\\partial a_1}{\\partial z_1}=\\delta_1.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "09d91067",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Adding a hidden layer\n",
-    "\n",
-    "We change our simple model to (see graph)\n",
-    "a network with just one hidden layer but with scalar variables only.\n",
-    "\n",
-    "Our output variable changes to $a_2$ and $a_1$ is now the output from the hidden node and $a_0=x$.\n",
-    "We have then"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f767afe7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z_1 = w_1a_0+b_1 \\hspace{0.1cm} \\wedge a_1 = \\sigma_1(z_1),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f38ded54",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z_2 = w_2a_1+b_2 \\hspace{0.1cm} \\wedge a_2 = \\sigma_2(z_2),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f3f03bc3",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and the cost function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9062730e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "C(x;\\boldsymbol{\\Theta})=\\frac{1}{2}(a_2-y)^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "75bbc32c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $\\boldsymbol{\\Theta}=[w_1,w_2,b_1,b_2]$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "fcf02dbf",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Layout of a simple neural network with one hidden layer\n",
-    "\n",
-    "<!-- dom:FIGURE: [figures/simplenn2.png, width=900 frac=1.0] -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<img src=\"figures/simplenn2.png\" width=\"900\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
-    "<!-- end figure -->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "aa97678f",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The derivatives\n",
-    "\n",
-    "The derivatives are now, using the chain rule again"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "98f68e27",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_2}=\\frac{\\partial C}{\\partial a_2}\\frac{\\partial a_2}{\\partial z_2}\\frac{\\partial z_2}{\\partial w_2}=(a_2-y)\\sigma_2'a_1=\\delta_2a_1,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c4528178",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial b_2}=\\frac{\\partial C}{\\partial a_2}\\frac{\\partial a_2}{\\partial z_2}\\frac{\\partial z_2}{\\partial b_2}=(a_2-y)\\sigma_2'=\\delta_2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d6304298",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_1}=\\frac{\\partial C}{\\partial a_2}\\frac{\\partial a_2}{\\partial z_2}\\frac{\\partial z_2}{\\partial a_1}\\frac{\\partial a_1}{\\partial z_1}\\frac{\\partial z_1}{\\partial w_1}=(a_2-y)\\sigma_2'a_1\\sigma_1'a_0,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "dfc47ba6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial b_1}=\\frac{\\partial C}{\\partial a_2}\\frac{\\partial a_2}{\\partial z_2}\\frac{\\partial z_2}{\\partial a_1}\\frac{\\partial a_1}{\\partial z_1}\\frac{\\partial z_1}{\\partial b_1}=(a_2-y)\\sigma_2'\\sigma_1'=\\delta_1.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8834c3dc",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Can you generalize this to more than one hidden layer?"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "40956770",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Important observations\n",
-    "\n",
-    "From the above equations we see that the derivatives of the activation\n",
-    "functions play a central role. If they vanish, the training may\n",
-    "stop. This is called the vanishing gradient problem, see discussions below. If they become\n",
-    "large, the parameters $w_i$ and $b_i$ may simply go to infinity. This\n",
-    "is referenced as  the exploding gradient problem."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "69e7fdcf",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The training\n",
-    "\n",
-    "The training of the parameters is done through various gradient descent approximations with"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "726d4c90",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{i}\\leftarrow w_{i}- \\eta \\delta_i a_{i-1},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0ee83d1c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f5b3b5a5",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "b_i \\leftarrow b_i-\\eta \\delta_i,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b2746792",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $\\eta$ is the learning rate.\n",
-    "\n",
-    "One iteration consists of one feed forward step and one back-propagation step. Each back-propagation step does one update of the parameters $\\boldsymbol{\\Theta}$.\n",
-    "\n",
-    "For the first hidden layer $a_{i-1}=a_0=x$ for this simple model."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "76e2e41a",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Code example\n",
-    "\n",
-    "The code here implements the above model with one hidden layer and\n",
-    "scalar variables for the same function we studied in the previous\n",
-    "example.  The code is however set up so that we can add multiple\n",
-    "inputs $x$ and target values $y$. Note also that we have the\n",
-    "possibility of defining a feature matrix $\\boldsymbol{X}$ with more than just\n",
-    "one column for the input values. This will turn useful in our next example. We have also defined matrices and vectors for all of our operations although it is not necessary here."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "1c4719c1",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "# We use the Sigmoid function as activation function\n",
-    "def sigmoid(z):\n",
-    "    return 1.0/(1.0+np.exp(-z))\n",
-    "\n",
-    "def forwardpropagation(x):\n",
-    "    # weighted sum of inputs to the hidden layer\n",
-    "    z_1 = np.matmul(x, w_1) + b_1\n",
-    "    # activation in the hidden layer\n",
-    "    a_1 = sigmoid(z_1)\n",
-    "    # weighted sum of inputs to the output layer\n",
-    "    z_2 = np.matmul(a_1, w_2) + b_2\n",
-    "    a_2 = z_2\n",
-    "    return a_1, a_2\n",
-    "\n",
-    "def backpropagation(x, y):\n",
-    "    a_1, a_2 = forwardpropagation(x)\n",
-    "    # parameter delta for the output layer, note that a_2=z_2 and its derivative wrt z_2 is just 1\n",
-    "    delta_2 = a_2 - y\n",
-    "    print(0.5*((a_2-y)**2))\n",
-    "    # delta for  the hidden layer\n",
-    "    delta_1 = np.matmul(delta_2, w_2.T) * a_1 * (1 - a_1)\n",
-    "    # gradients for the output layer\n",
-    "    output_weights_gradient = np.matmul(a_1.T, delta_2)\n",
-    "    output_bias_gradient = np.sum(delta_2, axis=0)\n",
-    "    # gradient for the hidden layer\n",
-    "    hidden_weights_gradient = np.matmul(x.T, delta_1)\n",
-    "    hidden_bias_gradient = np.sum(delta_1, axis=0)\n",
-    "    return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient\n",
-    "\n",
-    "\n",
-    "# ensure the same random numbers appear every time\n",
-    "np.random.seed(0)\n",
-    "# Input variable\n",
-    "x = np.array([4.0],dtype=np.float64)\n",
-    "# Target values\n",
-    "y = 2*x+1.0 \n",
-    "\n",
-    "# Defining the neural network, only scalars here\n",
-    "n_inputs = x.shape\n",
-    "n_features = 1\n",
-    "n_hidden_neurons = 1\n",
-    "n_outputs = 1\n",
-    "\n",
-    "# Initialize the network\n",
-    "# weights and bias in the hidden layer\n",
-    "w_1 = np.random.randn(n_features, n_hidden_neurons)\n",
-    "b_1 = np.zeros(n_hidden_neurons) + 0.01\n",
-    "\n",
-    "# weights and bias in the output layer\n",
-    "w_2 = np.random.randn(n_hidden_neurons, n_outputs)\n",
-    "b_2 = np.zeros(n_outputs) + 0.01\n",
-    "\n",
-    "eta = 0.1\n",
-    "for i in range(50):\n",
-    "    # calculate gradients\n",
-    "    derivW2, derivB2, derivW1, derivB1 = backpropagation(x, y)\n",
-    "    # update weights and biases\n",
-    "    w_2 -= eta * derivW2\n",
-    "    b_2 -= eta * derivB2\n",
-    "    w_1 -= eta * derivW1\n",
-    "    b_1 -= eta * derivB1"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "debaaadc",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "We see that after some few iterations (the results do depend on the learning rate however), we get an error which is rather small."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7d576f19",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Simple neural network and the  back propagation equations\n",
-    "\n",
-    "Let us now try to increase our level of ambition and attempt at setting \n",
-    "up the equations for a neural network with two input nodes, one hidden\n",
-    "layer with two hidden nodes and one output layer with one output node/neuron only (see graph)..\n",
-    "\n",
-    "We need to define the following parameters and variables with the input layer (layer $(0)$) \n",
-    "where we label the  nodes $x_1$ and $x_2$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "582b3b43",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "x_1 = a_1^{(0)} \\wedge x_2 = a_2^{(0)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c8eace47",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "The  hidden layer (layer $(1)$) has  nodes which yield the outputs $a_1^{(1)}$ and $a_2^{(1)}$) with  weight $\\boldsymbol{w}$ and bias $\\boldsymbol{b}$ parameters"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "81ec9945",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{ij}^{(1)}=\\left\\{w_{11}^{(1)},w_{12}^{(1)},w_{21}^{(1)},w_{22}^{(1)}\\right\\} \\wedge b^{(1)}=\\left\\{b_1^{(1)},b_2^{(1)}\\right\\}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c35e1f69",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Layout of a simple neural network with two input nodes, one  hidden layer with two hidden noeds and one output node\n",
-    "\n",
-    "<!-- dom:FIGURE: [figures/simplenn3.png, width=900 frac=1.0] -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<img src=\"figures/simplenn3.png\" width=\"900\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
-    "<!-- end figure -->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "05b8eea9",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The ouput layer\n",
-    "\n",
-    "We have the ouput layer given by layer label $(2)$ with output $a^{(2)}$ and weights and biases to be determined given by the variables"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7ef9cb55",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{i}^{(2)}=\\left\\{w_{1}^{(2)},w_{2}^{(2)}\\right\\} \\wedge b^{(2)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1eb5c5ac",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Our output is $\\tilde{y}=a^{(2)}$ and we define a generic cost function $C(a^{(2)},y;\\boldsymbol{\\Theta})$ where $y$ is the target value (a scalar here).\n",
-    "The parameters we need to optimize are given by"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "00492358",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\boldsymbol{\\Theta}=\\left\\{w_{11}^{(1)},w_{12}^{(1)},w_{21}^{(1)},w_{22}^{(1)},w_{1}^{(2)},w_{2}^{(2)},b_1^{(1)},b_2^{(1)},b^{(2)}\\right\\}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "45cca5aa",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Compact expressions\n",
-    "\n",
-    "We can define the inputs to the activation functions for the various layers in terms of various matrix-vector multiplications and vector additions.\n",
-    "The inputs to the first hidden layer are"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "22cfb40b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\begin{bmatrix}z_1^{(1)} \\\\ z_2^{(1)} \\end{bmatrix}=\\left(\\begin{bmatrix}w_{11}^{(1)} & w_{12}^{(1)}\\\\ w_{21}^{(1)} &w_{22}^{(1)} \\end{bmatrix}\\right)^{T}\\begin{bmatrix}a_1^{(0)} \\\\ a_2^{(0)} \\end{bmatrix}+\\begin{bmatrix}b_1^{(1)} \\\\ b_2^{(1)} \\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "45b30d06",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with outputs"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ebd6a7a5",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\begin{bmatrix}a_1^{(1)} \\\\ a_2^{(1)} \\end{bmatrix}=\\begin{bmatrix}\\sigma^{(1)}(z_1^{(1)}) \\\\ \\sigma^{(1)}(z_2^{(1)}) \\end{bmatrix}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "659dd686",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Output layer\n",
-    "\n",
-    "For the final output layer we have the inputs to the final activation function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "34a1d4ca",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z^{(2)} = w_{1}^{(2)}a_1^{(1)} +w_{2}^{(2)}a_2^{(1)}+b^{(2)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "34471712",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "resulting in the  output"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0b3a74fd",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "a^{(2)}=\\sigma^{(2)}(z^{(2)}).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1a5bdab3",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Explicit derivatives\n",
-    "\n",
-    "In total we have nine parameters which we need to train.  Using the\n",
-    "chain rule (or just the back-propagation algorithm) we can find all\n",
-    "derivatives. Since we will use automatic differentiation in reverse\n",
-    "mode, we start with the derivatives of the cost function with respect\n",
-    "to the parameters of the output layer, namely"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "37f19e78",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_{i}^{(2)}}=\\frac{\\partial C}{\\partial a^{(2)}}\\frac{\\partial a^{(2)}}{\\partial z^{(2)}}\\frac{\\partial z^{(2)}}{\\partial w_{i}^{(2)}}=\\delta^{(2)}a_i^{(1)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5505aab8",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d55d045c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta^{(2)}=\\frac{\\partial C}{\\partial a^{(2)}}\\frac{\\partial a^{(2)}}{\\partial z^{(2)}}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "04f101e7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and finally"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bfab2e91",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial b^{(2)}}=\\frac{\\partial C}{\\partial a^{(2)}}\\frac{\\partial a^{(2)}}{\\partial z^{(2)}}\\frac{\\partial z^{(2)}}{\\partial b^{(2)}}=\\delta^{(2)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "77f35b7e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Derivatives of the hidden layer\n",
-    "\n",
-    "Using the chain rule we have the following expressions for say one of the weight parameters (it is easy to generalize to the other weight parameters)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8cf4a606",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_{11}^{(1)}}=\\frac{\\partial C}{\\partial a^{(2)}}\\frac{\\partial a^{(2)}}{\\partial z^{(2)}}\n",
-    "\\frac{\\partial z^{(2)}}{\\partial z_1^{(1)}}\\frac{\\partial z_1^{(1)}}{\\partial w_{11}^{(1)}}=    \\delta^{(2)}\\frac{\\partial z^{(2)}}{\\partial z_1^{(1)}}\\frac{\\partial z_1^{(1)}}{\\partial w_{11}^{(1)}},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "86951351",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "which, noting that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "73414e65",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z^{(2)} =w_1^{(2)}a_1^{(1)}+w_2^{(2)}a_2^{(1)}+b^{(2)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8f0aaa15",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "allows us to rewrite"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "730c5415",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial z^{(2)}}{\\partial z_1^{(1)}}\\frac{\\partial z_1^{(1)}}{\\partial w_{11}^{(1)}}=w_1^{(2)}\\frac{\\partial a_1^{(1)}}{\\partial z_1^{(1)}}a_1^{(1)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1afcb5a1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Final expression\n",
-    "Defining"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7f30cb44",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_1^{(1)}=w_1^{(2)}\\frac{\\partial a_1^{(1)}}{\\partial z_1^{(1)}}\\delta^{(2)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "14c045ce",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "we have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0c1a2c68",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_{11}^{(1)}}=\\delta_1^{(1)}a_1^{(1)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a3385222",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Similarly, we obtain"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "18ee3804",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_{12}^{(1)}}=\\delta_1^{(1)}a_2^{(1)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ad741d56",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Completing the list\n",
-    "\n",
-    "Similarly, we find"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "65870a70",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_{21}^{(1)}}=\\delta_2^{(1)}a_1^{(1)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f7807fdc",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9af4a759",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial w_{22}^{(1)}}=\\delta_2^{(1)}a_2^{(1)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "dc548cb7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where we have defined"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "83b75e94",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_2^{(1)}=w_2^{(2)}\\frac{\\partial a_2^{(1)}}{\\partial z_2^{(1)}}\\delta^{(2)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1c2be559",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Final expressions for the biases of the hidden layer\n",
-    "\n",
-    "For the sake of completeness, we list the derivatives of the biases, which are"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "18b85f86",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial b_{1}^{(1)}}=\\delta_1^{(1)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "63e39eb4",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a55371c1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial C}{\\partial b_{2}^{(1)}}=\\delta_2^{(1)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "fa31a9b3",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "As we will see below, these expressions can be generalized in a more compact form."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "580df891",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Gradient expressions\n",
-    "\n",
-    "For this specific model, with just one output node and two hidden\n",
-    "nodes, the gradient descent equations take the following form for output layer"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c10bf2ce",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{i}^{(2)}\\leftarrow w_{i}^{(2)}- \\eta \\delta^{(2)} a_{i}^{(1)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0bae11f8",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ed4a8b93",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "b^{(2)} \\leftarrow b^{(2)}-\\eta \\delta^{(2)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2d582987",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5fa760a1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{ij}^{(1)}\\leftarrow w_{ij}^{(1)}- \\eta \\delta_{i}^{(1)} a_{j}^{(0)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bc9de8bf",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f00e3ace",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "b_{i}^{(1)} \\leftarrow b_{i}^{(1)}-\\eta \\delta_{i}^{(1)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7ac96362",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where $\\eta$ is the learning rate."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9c46f966",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Setting up the equations for a neural network\n",
-    "\n",
-    "The questions we want to ask are how do changes in the biases and the\n",
-    "weights in our network change the cost function and how can we use the\n",
-    "final output to modify the weights and biases?\n",
-    "\n",
-    "To derive these equations let us start with a plain regression problem\n",
-    "and define our cost function as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ea509b11",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "{\\cal C}(\\boldsymbol{\\Theta})  =  \\frac{1}{2}\\sum_{i=1}^n\\left(y_i - \\tilde{y}_i\\right)^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e08ff771",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where the $y_i$s are our $n$ targets (the values we want to\n",
-    "reproduce), while the outputs of the network after having propagated\n",
-    "all inputs $\\boldsymbol{x}$ are given by $\\boldsymbol{\\tilde{y}}_i$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6f476983",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Layout of a neural network with three hidden layers (last layer = $l=L=4$, first layer $l=0$)\n",
-    "\n",
-    "<!-- dom:FIGURE: [figures/nn2.png, width=900 frac=1.0] -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<img src=\"figures/nn2.png\" width=\"900\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
-    "<!-- end figure -->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0535d087",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Definitions\n",
-    "\n",
-    "With our definition of the targets $\\boldsymbol{y}$, the outputs of the\n",
-    "network $\\boldsymbol{\\tilde{y}}$ and the inputs $\\boldsymbol{x}$ we\n",
-    "define now the activation $z_j^l$ of node/neuron/unit $j$ of the\n",
-    "$l$-th layer as a function of the bias, the weights which add up from\n",
-    "the previous layer $l-1$ and the forward passes/outputs\n",
-    "$\\boldsymbol{a}^{l-1}$ from the previous layer as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5e024ec1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z_j^l = \\sum_{i=1}^{M_{l-1}}w_{ij}^la_i^{l-1}+b_j^l,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "239fb4c6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where $b_k^l$ are the biases from layer $l$.  Here $M_{l-1}$\n",
-    "represents the total number of nodes/neurons/units of layer $l-1$. The\n",
-    "figure in the whiteboard notes illustrates this equation.  We can rewrite this in a more\n",
-    "compact form as the matrix-vector products we discussed earlier,"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7e4fa6c5",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\boldsymbol{z}^l = \\left(\\boldsymbol{W}^l\\right)^T\\boldsymbol{a}^{l-1}+\\boldsymbol{b}^l.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c47cc3c6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Inputs to the activation function\n",
-    "\n",
-    "With the activation values $\\boldsymbol{z}^l$ we can in turn define the\n",
-    "output of layer $l$ as $\\boldsymbol{a}^l = \\sigma(\\boldsymbol{z}^l)$ where $\\sigma$ is our\n",
-    "activation function. In the examples here we will use the sigmoid\n",
-    "function discussed in our logistic regression lectures. We will also use the same activation function $\\sigma$ for all layers\n",
-    "and their nodes.  It means we have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4eb89f11",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "a_j^l = \\sigma(z_j^l) = \\frac{1}{1+\\exp{-(z_j^l)}}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "92744a90",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Layout of input to first hidden layer $l=1$ from input layer $l=0$\n",
-    "\n",
-    "<!-- dom:FIGURE: [figures/structure.png, width=900 frac=1.0] -->\n",
-    "<!-- begin figure -->\n",
-    "\n",
-    "<img src=\"figures/structure.png\" width=\"900\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
-    "<!-- end figure -->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "35424d45",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Derivatives and the chain rule\n",
-    "\n",
-    "From the definition of the input variable to the activation function, that is $z_j^l$ we have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b8502930",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial z_j^l}{\\partial w_{ij}^l} = a_i^{l-1},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "81ad45a5",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "11bb8afb",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial z_j^l}{\\partial a_i^{l-1}} = w_{ji}^l.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b53ec752",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "With our definition of the activation function we have that (note that this function depends only on $z_j^l$)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b7519a84",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial a_j^l}{\\partial z_j^{l}} = a_j^l(1-a_j^l)=\\sigma(z_j^l)(1-\\sigma(z_j^l)).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c57689db",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Derivative of the cost function\n",
-    "\n",
-    "With these definitions we can now compute the derivative of the cost function in terms of the weights.\n",
-    "\n",
-    "Let us specialize to the output layer $l=L$. Our cost function is"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a9f83b15",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "{\\cal C}(\\boldsymbol{\\Theta}^L)  =  \\frac{1}{2}\\sum_{i=1}^n\\left(y_i - \\tilde{y}_i\\right)^2=\\frac{1}{2}\\sum_{i=1}^n\\left(a_i^L - y_i\\right)^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "067c2583",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "The derivative of this function with respect to the weights is"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "43545710",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial{\\cal C}(\\boldsymbol{\\Theta}^L)}{\\partial w_{ij}^L}  =  \\left(a_j^L - y_j\\right)\\frac{\\partial a_j^L}{\\partial w_{ij}^{L}},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1eb33717",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "The last partial derivative can easily be computed and reads (by applying the chain rule)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e09a8734",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial a_j^L}{\\partial w_{ij}^{L}} = \\frac{\\partial a_j^L}{\\partial z_{j}^{L}}\\frac{\\partial z_j^L}{\\partial w_{ij}^{L}}=a_j^L(1-a_j^L)a_i^{L-1}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3dc0f5a3",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The  back propagation equations for a neural network\n",
-    "\n",
-    "We have thus"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bb58784b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial{\\cal C}((\\boldsymbol{\\Theta}^L)}{\\partial w_{ij}^L}  =  \\left(a_j^L - y_j\\right)a_j^L(1-a_j^L)a_i^{L-1},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "10aea094",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Defining"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b7cc2db8",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^L = a_j^L(1-a_j^L)\\left(a_j^L - y_j\\right) = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6cce9a62",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and using the Hadamard product of two vectors we can write this as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "43e5a84b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\boldsymbol{\\delta}^L = \\sigma'(\\boldsymbol{z}^L)\\circ\\frac{\\partial {\\cal C}}{\\partial (\\boldsymbol{a}^L)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d5c607a7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Analyzing the last results\n",
-    "\n",
-    "This is an important expression. The second term on the right handside\n",
-    "measures how fast the cost function is changing as a function of the $j$th\n",
-    "output activation.  If, for example, the cost function doesn't depend\n",
-    "much on a particular output node $j$, then $\\delta_j^L$ will be small,\n",
-    "which is what we would expect. The first term on the right, measures\n",
-    "how fast the activation function $f$ is changing at a given activation\n",
-    "value $z_j^L$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a51b3b58",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## More considerations\n",
-    "\n",
-    "Notice that everything in the above equations is easily computed.  In\n",
-    "particular, we compute $z_j^L$ while computing the behaviour of the\n",
-    "network, and it is only a small additional overhead to compute\n",
-    "$\\sigma'(z^L_j)$.  The exact form of the derivative with respect to the\n",
-    "output depends on the form of the cost function.\n",
-    "However, provided the cost function is known there should be little\n",
-    "trouble in calculating"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4cd9d058",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c80b630d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "With the definition of $\\delta_j^L$ we have a more compact definition of the derivative of the cost function in terms of the weights, namely"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "dc0c1a06",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial{\\cal C}}{\\partial w_{ij}^L}  =  \\delta_j^La_i^{L-1}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8f2065b7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Derivatives in terms of $z_j^L$\n",
-    "\n",
-    "It is also easy to see that our previous equation can be written as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7f89b9d8",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^L =\\frac{\\partial {\\cal C}}{\\partial z_j^L}= \\frac{\\partial {\\cal C}}{\\partial a_j^L}\\frac{\\partial a_j^L}{\\partial z_j^L},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "49c2cd3f",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "which can also be interpreted as the partial derivative of the cost function with respect to the biases $b_j^L$, namely"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "517b1a37",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^L = \\frac{\\partial {\\cal C}}{\\partial b_j^L}\\frac{\\partial b_j^L}{\\partial z_j^L}=\\frac{\\partial {\\cal C}}{\\partial b_j^L},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "65c8107f",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "That is, the error $\\delta_j^L$ is exactly equal to the rate of change of the cost function as a function of the bias."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2a10f902",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Bringing it together\n",
-    "\n",
-    "We have now three equations that are essential for the computations of the derivatives of the cost function at the output layer. These equations are needed to start the algorithm and they are"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b2ebf9c2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "<!-- Equation labels as ordinary links -->\n",
-    "<div id=\"_auto1\"></div>\n",
-    "\n",
-    "$$\n",
-    "\\begin{equation}\n",
-    "\\frac{\\partial{\\cal C}(\\boldsymbol{W^L})}{\\partial w_{ij}^L}  =  \\delta_j^La_i^{L-1},\n",
-    "\\label{_auto1} \\tag{1}\n",
-    "\\end{equation}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "90336322",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f25ff166",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "<!-- Equation labels as ordinary links -->\n",
-    "<div id=\"_auto2\"></div>\n",
-    "\n",
-    "$$\n",
-    "\\begin{equation}\n",
-    "\\delta_j^L = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)},\n",
-    "\\label{_auto2} \\tag{2}\n",
-    "\\end{equation}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4cf11d5e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2670748d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "<!-- Equation labels as ordinary links -->\n",
-    "<div id=\"_auto3\"></div>\n",
-    "\n",
-    "$$\n",
-    "\\begin{equation}\n",
-    "\\delta_j^L = \\frac{\\partial {\\cal C}}{\\partial b_j^L},\n",
-    "\\label{_auto3} \\tag{3}\n",
-    "\\end{equation}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "18c29f71",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Final back propagating equation\n",
-    "\n",
-    "We have that (replacing $L$ with a general layer $l$)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c593470c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^l =\\frac{\\partial {\\cal C}}{\\partial z_j^l}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "28e8caef",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "We want to express this in terms of the equations for layer $l+1$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "516de9d7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Using the chain rule and summing over all $k$ entries\n",
-    "\n",
-    "We obtain"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "004c0bf4",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^l =\\sum_k \\frac{\\partial {\\cal C}}{\\partial z_k^{l+1}}\\frac{\\partial z_k^{l+1}}{\\partial z_j^{l}}=\\sum_k \\delta_k^{l+1}\\frac{\\partial z_k^{l+1}}{\\partial z_j^{l}},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d62a3b1f",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and recalling that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e9af770e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z_j^{l+1} = \\sum_{i=1}^{M_{l}}w_{ij}^{l+1}a_i^{l}+b_j^{l+1},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "eca56f17",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $M_l$ being the number of nodes in layer $l$, we obtain"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bb0e4414",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^l =\\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a4b190fc",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "This is our final equation.\n",
-    "\n",
-    "We are now ready to set up the algorithm for back propagation and learning the weights and biases."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ec0f87c0",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations\n",
-    "\n",
-    "**The architecture (our model).**\n",
-    "\n",
-    "1. Set up your inputs and outputs (scalars, vectors, matrices or higher-order arrays)\n",
-    "\n",
-    "2. Define the number of hidden layers and hidden nodes\n",
-    "\n",
-    "3. Define activation functions for hidden layers and output layers\n",
-    "\n",
-    "4. Define optimizer (plan learning rate, momentum, ADAgrad, RMSprop, ADAM etc) and array of initial learning rates\n",
-    "\n",
-    "5. Define cost function and possible regularization terms with hyperparameters\n",
-    "\n",
-    "6. Initialize weights and biases\n",
-    "\n",
-    "7. Fix number of iterations for the feed forward part and back propagation part"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2fb45155",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Setting up the back propagation algorithm, part 1\n",
-    "\n",
-    "The four equations  provide us with a way of computing the gradients of the cost function. Let us write this out in the form of an algorithm.\n",
-    "\n",
-    "**First**, we set up the input data $\\boldsymbol{x}$ and the activations\n",
-    "$\\boldsymbol{z}_1$ of the input layer and compute the activation function and\n",
-    "the pertinent outputs $\\boldsymbol{a}^1$.\n",
-    "\n",
-    "**Secondly**, we perform then the feed forward till we reach the output\n",
-    "layer and compute all $\\boldsymbol{z}_l$ of the input layer and compute the\n",
-    "activation function and the pertinent outputs $\\boldsymbol{a}^l$ for\n",
-    "$l=1,2,3,\\dots,L$.\n",
-    "\n",
-    "**Notation**: The first hidden layer has $l=1$ as label and the final output layer has $l=L$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3d5c2a0e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Setting up the back propagation algorithm, part 2\n",
-    "\n",
-    "Thereafter we compute the ouput error $\\boldsymbol{\\delta}^L$ by computing all"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9183bbd0",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^L = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "32ece956",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "466d6bda",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9f31b228",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Setting up the Back propagation algorithm, part 3\n",
-    "\n",
-    "Finally, we update the weights and the biases using gradient descent\n",
-    "for each $l=L-1,L-2,\\dots,1$ (the first hidden layer) and update the weights and biases\n",
-    "according to the rules"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "fbeac005",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bc6ae984",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "65f3133d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $\\eta$ being the learning rate."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5d27bbe1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Updating the gradients\n",
-    "\n",
-    "With the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5e5d0aa0",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ea32e5bb",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,1$ and update the weights and biases according to the rules"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3a9bb5a6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9008dcf8",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "89aba7d6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Activation functions\n",
-    "\n",
-    "A property that characterizes a neural network, other than its\n",
-    "connectivity, is the choice of activation function(s).  The following\n",
-    "restrictions are imposed on an activation function for an FFNN to\n",
-    "fulfill the universal approximation theorem\n",
-    "\n",
-    "  * Non-constant\n",
-    "\n",
-    "  * Bounded\n",
-    "\n",
-    "  * Monotonically-increasing\n",
-    "\n",
-    "  * Continuous"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ea0cdce2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### Activation functions, Logistic and Hyperbolic ones\n",
-    "\n",
-    "The second requirement excludes all linear functions. Furthermore, in\n",
-    "a MLP with only linear activation functions, each layer simply\n",
-    "performs a linear transformation of its inputs.\n",
-    "\n",
-    "Regardless of the number of layers, the output of the NN will be\n",
-    "nothing but a linear function of the inputs. Thus we need to introduce\n",
-    "some kind of non-linearity to the NN to be able to fit non-linear\n",
-    "functions Typical examples are the logistic *Sigmoid*"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "91342c80",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\sigma(x) = \\frac{1}{1 + e^{-x}},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bd6eb22a",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and the *hyperbolic tangent* function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4e75b2ab",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\sigma(x) = \\tanh(x)\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1626d9b7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Relevance\n",
-    "\n",
-    "The *sigmoid* function are more biologically plausible because the\n",
-    "output of inactive neurons are zero. Such activation function are\n",
-    "called *one-sided*. However, it has been shown that the hyperbolic\n",
-    "tangent performs better than the sigmoid for training MLPs.  has\n",
-    "become the most popular for *deep neural networks*"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "4ac7c23c",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "%matplotlib inline\n",
-    "\n",
-    "\"\"\"The sigmoid function (or the logistic curve) is a \n",
-    "function that takes any real number, z, and outputs a number (0,1).\n",
-    "It is useful in neural networks for assigning weights on a relative scale.\n",
-    "The value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\n",
-    "\n",
-    "import numpy\n",
-    "import matplotlib.pyplot as plt\n",
-    "import math as mt\n",
-    "\n",
-    "z = numpy.arange(-5, 5, .1)\n",
-    "sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))\n",
-    "sigma = sigma_fn(z)\n",
-    "\n",
-    "fig = plt.figure()\n",
-    "ax = fig.add_subplot(111)\n",
-    "ax.plot(z, sigma)\n",
-    "ax.set_ylim([-0.1, 1.1])\n",
-    "ax.set_xlim([-5,5])\n",
-    "ax.grid(True)\n",
-    "ax.set_xlabel('z')\n",
-    "ax.set_title('sigmoid function')\n",
-    "\n",
-    "plt.show()\n",
-    "\n",
-    "\"\"\"Step Function\"\"\"\n",
-    "z = numpy.arange(-5, 5, .02)\n",
-    "step_fn = numpy.vectorize(lambda z: 1.0 if z >= 0.0 else 0.0)\n",
-    "step = step_fn(z)\n",
-    "\n",
-    "fig = plt.figure()\n",
-    "ax = fig.add_subplot(111)\n",
-    "ax.plot(z, step)\n",
-    "ax.set_ylim([-0.5, 1.5])\n",
-    "ax.set_xlim([-5,5])\n",
-    "ax.grid(True)\n",
-    "ax.set_xlabel('z')\n",
-    "ax.set_title('step function')\n",
-    "\n",
-    "plt.show()\n",
-    "\n",
-    "\"\"\"Sine Function\"\"\"\n",
-    "z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n",
-    "t = numpy.sin(z)\n",
-    "\n",
-    "fig = plt.figure()\n",
-    "ax = fig.add_subplot(111)\n",
-    "ax.plot(z, t)\n",
-    "ax.set_ylim([-1.0, 1.0])\n",
-    "ax.set_xlim([-2*mt.pi,2*mt.pi])\n",
-    "ax.grid(True)\n",
-    "ax.set_xlabel('z')\n",
-    "ax.set_title('sine function')\n",
-    "\n",
-    "plt.show()\n",
-    "\n",
-    "\"\"\"Plots a graph of the squashing function used by a rectified linear\n",
-    "unit\"\"\"\n",
-    "z = numpy.arange(-2, 2, .1)\n",
-    "zero = numpy.zeros(len(z))\n",
-    "y = numpy.max([zero, z], axis=0)\n",
-    "\n",
-    "fig = plt.figure()\n",
-    "ax = fig.add_subplot(111)\n",
-    "ax.plot(z, y)\n",
-    "ax.set_ylim([-2.0, 2.0])\n",
-    "ax.set_xlim([-2.0, 2.0])\n",
-    "ax.grid(True)\n",
-    "ax.set_xlabel('z')\n",
-    "ax.set_title('Rectified linear unit')\n",
-    "\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6aeb0ee4",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Vanishing gradients\n",
-    "\n",
-    "The Back propagation algorithm we derived above works by going from\n",
-    "the output layer to the input layer, propagating the error gradient on\n",
-    "the way. Once the algorithm has computed the gradient of the cost\n",
-    "function with regards to each parameter in the network, it uses these\n",
-    "gradients to update each parameter with a Gradient Descent (GD) step.\n",
-    "\n",
-    "Unfortunately for us, the gradients often get smaller and smaller as\n",
-    "the algorithm progresses down to the first hidden layers. As a result,\n",
-    "the GD update leaves the lower layer connection weights virtually\n",
-    "unchanged, and training never converges to a good solution. This is\n",
-    "known in the literature as **the vanishing gradients problem**."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ea47d1d6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Exploding gradients\n",
-    "\n",
-    "In other cases, the opposite can happen, namely the the gradients can\n",
-    "grow bigger and bigger. The result is that many of the layers get\n",
-    "large updates of the weights the algorithm diverges. This is the\n",
-    "**exploding gradients problem**, which is mostly encountered in\n",
-    "recurrent neural networks. More generally, deep neural networks suffer\n",
-    "from unstable gradients, different layers may learn at widely\n",
-    "different speeds"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1947aa95",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Is the Logistic activation function (Sigmoid)  our choice?\n",
-    "\n",
-    "Although this unfortunate behavior has been empirically observed for\n",
-    "quite a while (it was one of the reasons why deep neural networks were\n",
-    "mostly abandoned for a long time), it is only around 2010 that\n",
-    "significant progress was made in understanding it.\n",
-    "\n",
-    "A paper titled [Understanding the Difficulty of Training Deep\n",
-    "Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio](http://proceedings.mlr.press/v9/glorot10a.html) found that\n",
-    "the problems with the popular logistic\n",
-    "sigmoid activation function and the weight initialization technique\n",
-    "that was most popular at the time, namely random initialization using\n",
-    "a normal distribution with a mean of 0 and a standard deviation of\n",
-    "1."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d024119f",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Logistic function as the root of problems\n",
-    "\n",
-    "They showed that with this activation function and this\n",
-    "initialization scheme, the variance of the outputs of each layer is\n",
-    "much greater than the variance of its inputs. Going forward in the\n",
-    "network, the variance keeps increasing after each layer until the\n",
-    "activation function saturates at the top layers. This is actually made\n",
-    "worse by the fact that the logistic function has a mean of 0.5, not 0\n",
-    "(the hyperbolic tangent function has a mean of 0 and behaves slightly\n",
-    "better than the logistic function in deep networks)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c9178132",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The derivative of the Logistic funtion\n",
-    "\n",
-    "Looking at the logistic activation function, when inputs become large\n",
-    "(negative or positive), the function saturates at 0 or 1, with a\n",
-    "derivative extremely close to 0. Thus when backpropagation kicks in,\n",
-    "it has virtually no gradient to propagate back through the network,\n",
-    "and what little gradient exists keeps getting diluted as\n",
-    "backpropagation progresses down through the top layers, so there is\n",
-    "really nothing left for the lower layers.\n",
-    "\n",
-    "In their paper, Glorot and Bengio propose a way to significantly\n",
-    "alleviate this problem. We need the signal to flow properly in both\n",
-    "directions: in the forward direction when making predictions, and in\n",
-    "the reverse direction when backpropagating gradients. We don’t want\n",
-    "the signal to die out, nor do we want it to explode and saturate. For\n",
-    "the signal to flow properly, the authors argue that we need the\n",
-    "variance of the outputs of each layer to be equal to the variance of\n",
-    "its inputs, and we also need the gradients to have equal variance\n",
-    "before and after flowing through a layer in the reverse direction."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "756185f5",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Insights from the paper by Glorot and Bengio\n",
-    "\n",
-    "One of the insights in the 2010 paper by Glorot and Bengio was that\n",
-    "the vanishing/exploding gradients problems were in part due to a poor\n",
-    "choice of activation function. Until then most people had assumed that\n",
-    "if Nature had chosen to use roughly sigmoid activation functions in\n",
-    "biological neurons, they must be an excellent choice. But it turns out\n",
-    "that other activation functions behave much better in deep neural\n",
-    "networks, in particular the ReLU activation function, mostly because\n",
-    "it does not saturate for positive values (and also because it is quite\n",
-    "fast to compute)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3d92cad4",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The RELU function family\n",
-    "\n",
-    "The ReLU activation function suffers from a problem known as the dying\n",
-    "ReLUs: during training, some neurons effectively die, meaning they\n",
-    "stop outputting anything other than 0.\n",
-    "\n",
-    "In some cases, you may find that half of your network’s neurons are\n",
-    "dead, especially if you used a large learning rate. During training,\n",
-    "if a neuron’s weights get updated such that the weighted sum of the\n",
-    "neuron’s inputs is negative, it will start outputting 0. When this\n",
-    "happen, the neuron is unlikely to come back to life since the gradient\n",
-    "of the ReLU function is 0 when its input is negative."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "cbc6f721",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## ELU function\n",
-    "\n",
-    "To solve this problem, nowadays practitioners use a variant of the\n",
-    "ReLU function, such as the leaky ReLU discussed above or the so-called\n",
-    "exponential linear unit (ELU) function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9249dc7b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\  z & z \\ge 0.\\end{array}\\right.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e59de3af",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Which activation function should we use?\n",
-    "\n",
-    "In general it seems that the ELU activation function is better than\n",
-    "the leaky ReLU function (and its variants), which is better than\n",
-    "ReLU. ReLU performs better than $\\tanh$ which in turn performs better\n",
-    "than the logistic function.\n",
-    "\n",
-    "If runtime performance is an issue, then you may opt for the leaky\n",
-    "ReLU function over the ELU function If you don’t want to tweak yet\n",
-    "another hyperparameter, you may just use the default $\\alpha$ of\n",
-    "$0.01$ for the leaky ReLU, and $1$ for ELU. If you have spare time and\n",
-    "computing power, you can use cross-validation or bootstrap to evaluate\n",
-    "other activation functions."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e2da998c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## More on activation functions, output layers\n",
-    "\n",
-    "In most cases you can use the ReLU activation function in the hidden\n",
-    "layers (or one of its variants).\n",
-    "\n",
-    "It is a bit faster to compute than other activation functions, and the\n",
-    "gradient descent optimization does in general not get stuck.\n",
-    "\n",
-    "**For the output layer:**\n",
-    "\n",
-    "* For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).\n",
-    "\n",
-    "* For regression tasks, you can simply use no activation function at all."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e1abf01e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Fine-tuning neural network hyperparameters\n",
-    "\n",
-    "The flexibility of neural networks is also one of their main\n",
-    "drawbacks: there are many hyperparameters to tweak. Not only can you\n",
-    "use any imaginable network topology (how neurons/nodes are\n",
-    "interconnected), but even in a simple FFNN you can change the number\n",
-    "of layers, the number of neurons per layer, the type of activation\n",
-    "function to use in each layer, the weight initialization logic, the\n",
-    "stochastic gradient optmized and much more. How do you know what\n",
-    "combination of hyperparameters is the best for your task?\n",
-    "\n",
-    "* You can use grid search with cross-validation to find the right hyperparameters.\n",
-    "\n",
-    "However,since there are many hyperparameters to tune, and since\n",
-    "training a neural network on a large dataset takes a lot of time, you\n",
-    "will only be able to explore a tiny part of the hyperparameter space.\n",
-    "\n",
-    "* You can use randomized search.\n",
-    "\n",
-    "* Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a8ded7cd",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Hidden layers\n",
-    "\n",
-    "For many problems you can start with just one or two hidden layers and\n",
-    "it will work just fine.  For the MNIST data set discussed below you can easily get a\n",
-    "high accuracy using just one hidden layer with a few hundred neurons.\n",
-    "You can reach for this data set above 98% accuracy using two hidden\n",
-    "layers with the same total amount of neurons, in roughly the same\n",
-    "amount of training time.\n",
-    "\n",
-    "For more complex problems, you can gradually ramp up the number of\n",
-    "hidden layers, until you start overfitting the training set. Very\n",
-    "complex tasks, such as large image classification or speech\n",
-    "recognition, typically require networks with dozens of layers and they\n",
-    "need a huge amount of training data. However, you will rarely have to\n",
-    "train such networks from scratch: it is much more common to reuse\n",
-    "parts of a pretrained state-of-the-art network that performs a similar\n",
-    "task."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "96da4f48",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Batch Normalization\n",
-    "\n",
-    "Batch Normalization aims to address the vanishing/exploding gradients\n",
-    "problems, and more generally the problem that the distribution of each\n",
-    "layer’s inputs changes during training, as the parameters of the\n",
-    "previous layers change.\n",
-    "\n",
-    "The technique consists of adding an operation in the model just before\n",
-    "the activation function of each layer, simply zero-centering and\n",
-    "normalizing the inputs, then scaling and shifting the result using two\n",
-    "new parameters per layer (one for scaling, the other for shifting). In\n",
-    "other words, this operation lets the model learn the optimal scale and\n",
-    "mean of the inputs for each layer.  In order to zero-center and\n",
-    "normalize the inputs, the algorithm needs to estimate the inputs’ mean\n",
-    "and standard deviation. It does so by evaluating the mean and standard\n",
-    "deviation of the inputs over the current mini-batch, from this the\n",
-    "name batch normalization."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "395346a7",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Dropout\n",
-    "\n",
-    "It is a fairly simple algorithm: at every training step, every neuron\n",
-    "(including the input neurons but excluding the output neurons) has a\n",
-    "probability $p$ of being temporarily dropped out, meaning it will be\n",
-    "entirely ignored during this training step, but it may be active\n",
-    "during the next step.\n",
-    "\n",
-    "The hyperparameter $p$ is called the dropout rate, and it is typically\n",
-    "set to 50%. After training, the neurons are not dropped anymore.  It\n",
-    "is viewed as one of the most popular regularization techniques."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9c712bbb",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Gradient Clipping\n",
-    "\n",
-    "A popular technique to lessen the exploding gradients problem is to\n",
-    "simply clip the gradients during backpropagation so that they never\n",
-    "exceed some threshold (this is mostly useful for recurrent neural\n",
-    "networks).\n",
-    "\n",
-    "This technique is called Gradient Clipping.\n",
-    "\n",
-    "In general however, Batch\n",
-    "Normalization is preferred."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2b66ea72",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## A top-down perspective on Neural networks\n",
-    "\n",
-    "The first thing we would like to do is divide the data into two or\n",
-    "three parts. A training set, a validation or dev (development) set,\n",
-    "and a test set. The test set is the data on which we want to make\n",
-    "predictions. The dev set is a subset of the training data we use to\n",
-    "check how well we are doing out-of-sample, after training the model on\n",
-    "the training dataset. We use the validation error as a proxy for the\n",
-    "test error in order to make tweaks to our model. It is crucial that we\n",
-    "do not use any of the test data to train the algorithm. This is a\n",
-    "cardinal sin in ML. Then:\n",
-    "\n",
-    "1. Estimate optimal error rate\n",
-    "\n",
-    "2. Minimize underfitting (bias) on training data set.\n",
-    "\n",
-    "3. Make sure you are not overfitting."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5acbc082",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## More top-down perspectives\n",
-    "\n",
-    "If the validation and test sets are drawn from the same distributions,\n",
-    "then a good performance on the validation set should lead to similarly\n",
-    "good performance on the test set. \n",
-    "\n",
-    "However, sometimes\n",
-    "the training data and test data differ in subtle ways because, for\n",
-    "example, they are collected using slightly different methods, or\n",
-    "because it is cheaper to collect data in one way versus another. In\n",
-    "this case, there can be a mismatch between the training and test\n",
-    "data. This can lead to the neural network overfitting these small\n",
-    "differences between the test and training sets, and a poor performance\n",
-    "on the test set despite having a good performance on the validation\n",
-    "set. To rectify this, Andrew Ng suggests making two validation or dev\n",
-    "sets, one constructed from the training data and one constructed from\n",
-    "the test data. The difference between the performance of the algorithm\n",
-    "on these two validation sets quantifies the train-test mismatch. This\n",
-    "can serve as another important diagnostic when using DNNs for\n",
-    "supervised learning."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "31825b65",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Limitations of supervised learning with deep networks\n",
-    "\n",
-    "Like all statistical methods, supervised learning using neural\n",
-    "networks has important limitations. This is especially important when\n",
-    "one seeks to apply these methods, especially to physics problems. Like\n",
-    "all tools, DNNs are not a universal solution. Often, the same or\n",
-    "better performance on a task can be achieved by using a few\n",
-    "hand-engineered features (or even a collection of random\n",
-    "features)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c76d9af9",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Limitations of NNs\n",
-    "\n",
-    "Here we list some of the important limitations of supervised neural network based models. \n",
-    "\n",
-    "* **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).\n",
-    "\n",
-    "* **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bdc93363",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Homogeneous data\n",
-    "\n",
-    "* **Homogeneous data.** Almost all DNNs deal with homogeneous data of one type. It is very hard to design architectures that mix and match data types (i.e. some continuous variables, some discrete variables, some time series). In applications beyond images, video, and language, this is often what is required. In contrast, ensemble models like random forests or gradient-boosted trees have no difficulty handling mixed data types."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a1d6ff64",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## More limitations\n",
-    "\n",
-    "* **Many problems are not about prediction.** In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a *wrong* model. The model might or might not be useful for understanding the underlying science.\n",
-    "\n",
-    "Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0c2e5742",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Setting up a Multi-layer perceptron model for classification\n",
-    "\n",
-    "We are now gong to develop an example based on the MNIST data\n",
-    "base. This is a classification problem and we need to use our\n",
-    "cross-entropy function we discussed in connection with logistic\n",
-    "regression. The cross-entropy defines our cost function for the\n",
-    "classificaton problems with neural networks.\n",
-    "\n",
-    "In binary classification with two classes $(0, 1)$ we define the\n",
-    "logistic/sigmoid function as the probability that a particular input\n",
-    "is in class $0$ or $1$.  This is possible because the logistic\n",
-    "function takes any input from the real numbers and inputs a number\n",
-    "between 0 and 1, and can therefore be interpreted as a probability. It\n",
-    "also has other nice properties, such as a derivative that is simple to\n",
-    "calculate.\n",
-    "\n",
-    "For an input $\\boldsymbol{a}$ from the hidden layer, the probability that the input $\\boldsymbol{x}$\n",
-    "is in class 0 or 1 is just. We let $\\theta$ represent the unknown weights and biases to be adjusted by our equations). The variable $x$\n",
-    "represents our activation values $z$. We have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d4da3f02",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "01ea2e0b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9c1c7bec",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9238ff2d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where $y \\in \\{0, 1\\}$  and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
-    "of our network."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3be74bd1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Defining the cost function\n",
-    "\n",
-    "Our cost function is given as (see the Logistic regression lectures)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2e2fd39c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
-    "y_i \\ln[P(y_i = 0)] + (1 - y_i) \\ln [1 - P(y_i = 0)] = \\sum_{i=1}^n \\mathcal{L}_i(\\boldsymbol{\\theta}) .\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "42b1d26b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n",
-    "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$.  \n",
-    "The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather\n",
-    "than maximizing a negative number.  \n",
-    "\n",
-    "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  \n",
-    "\n",
-    "$y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n",
-    "\n",
-    "$y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n",
-    "\n",
-    "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$)..  \n",
-    "\n",
-    "If $\\boldsymbol{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n",
-    "output vector $\\boldsymbol{y}_i$.  \n",
-    "The probability of $\\boldsymbol{x}_i$ being in class $c$ will be given by the softmax function:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f740a484",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
-    "{\\sum_{c'=0}^{C-1} \\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_{c'})}} ,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "19189bfc",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "which reduces to the logistic function in the binary case.  \n",
-    "The likelihood of this $C$-class classifier\n",
-    "is now given as:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "aeb3ef60",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "dbf419a1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Again we take the negative log-likelihood to define our cost function:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9e345753",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3b13095e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "See the logistic regression lectures for a full definition of the cost function.\n",
-    "\n",
-    "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "96501a91",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Example: binary classification problem\n",
-    "\n",
-    "As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\\beta$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "48cf79fe",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3243c0b1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where we had defined the logistic (sigmoid) function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "bb312a09",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "484cf2b4",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2b9c5483",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5ca21f09",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "The parameters $\\boldsymbol{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n",
-    "\n",
-    "Now we replace $x_i$ with the activation $z_i^l$ for a given layer $l$ and the outputs as $y_i=a_i^l=f(z_i^l)$, with $z_i^l$ now being a function of the weights $w_{ij}^l$ and biases $b_i^l$. \n",
-    "We have then"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4852e4d2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e3b7cbef",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0c1e69a1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e71df7f4",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n",
-    "Our cost function at the final layer $l=L$ is now"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "50d6fecc",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e145e461",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "97f13260",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4361ce3b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "In case we use another activation function than the logistic one, we need to evaluate other derivatives."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "52a16654",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## The Softmax function\n",
-    "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3bfb321e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n",
-    "\\frac{\\partial f(z_i^l)}{\\partial z_j^l} \\frac{\\partial z_j^l}{\\partial w_{jk}^l}= \\frac{\\partial f(z_i^l)}{\\partial z_j^l}a_k^{l-1}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "eccac6c9",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "For the Softmax function we have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "23634198",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7a2e75ba",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Its derivative with respect to $z_j^l$ gives"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2dad2d14",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "46415917",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "which in case of the simply binary model reduces to  having $i=j$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6adc7c1e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Developing a code for doing neural networks with back propagation\n",
-    "\n",
-    "One can identify a set of key steps when using neural networks to solve supervised learning problems:  \n",
-    "\n",
-    "1. Collect and pre-process data  \n",
-    "\n",
-    "2. Define model and architecture  \n",
-    "\n",
-    "3. Choose cost function and optimizer  \n",
-    "\n",
-    "4. Train the model  \n",
-    "\n",
-    "5. Evaluate model performance on test data  \n",
-    "\n",
-    "6. Adjust hyperparameters (if necessary, network architecture)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4110d83e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Collect and pre-process data\n",
-    "\n",
-    "Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**\n",
-    "package. You may also find it for example [here](http://yann.lecun.com/exdb/mnist/).  \n",
-    "The *MNIST* (Modified National Institute of Standards and Technology) database is a large database\n",
-    "of handwritten digits that is commonly used for training various image processing systems.  \n",
-    "The MNIST dataset consists of 70 000 images of size $28\\times 28$ pixels, each labeled from 0 to 9.  \n",
-    "The scikit-learn dataset we will use consists of a selection of 1797 images of size $8\\times 8$ collected and processed from this database.  \n",
-    "\n",
-    "To feed data into a feed-forward neural network we need to represent\n",
-    "the inputs as a design/feature matrix $X = (n_{inputs}, n_{features})$.  Each\n",
-    "row represents an *input*, in this case a handwritten digit, and\n",
-    "each column represents a *feature*, in this case a pixel.  The\n",
-    "correct answers, also known as *labels* or *targets* are\n",
-    "represented as a 1D array of integers \n",
-    "$Y = (n_{inputs}) = (5, 3, 1, 8,...)$.\n",
-    "\n",
-    "As an example, say we want to build a neural network using supervised learning to predict Body-Mass Index (BMI) from\n",
-    "measurements of height (in m)  \n",
-    "and weight (in kg). If we have measurements of 5 people the design/feature matrix could be for example:  \n",
-    "\n",
-    "$$ X = \\begin{bmatrix}\n",
-    "1.85 & 81\\\\\n",
-    "1.71 & 65\\\\\n",
-    "1.95 & 103\\\\\n",
-    "1.55 & 42\\\\\n",
-    "1.63 & 56\n",
-    "\\end{bmatrix} ,$$  \n",
-    "\n",
-    "and the targets would be:  \n",
-    "\n",
-    "$$ Y = (23.7, 22.2, 27.1, 17.5, 21.1) $$  \n",
-    "\n",
-    "Since each input image is a 2D matrix, we need to flatten the image\n",
-    "(i.e. \"unravel\" the 2D matrix into a 1D array) to turn the data into a\n",
-    "design/feature matrix. This means we lose all spatial information in the\n",
-    "image, such as locality and translational invariance. More complicated\n",
-    "architectures such as Convolutional Neural Networks can take advantage\n",
-    "of such information, and are most commonly applied when analyzing\n",
-    "images."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "070c610d",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# import necessary packages\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "from sklearn import datasets\n",
-    "\n",
-    "\n",
-    "# ensure the same random numbers appear every time\n",
-    "np.random.seed(0)\n",
-    "\n",
-    "# display images in notebook\n",
-    "%matplotlib inline\n",
-    "plt.rcParams['figure.figsize'] = (12,12)\n",
-    "\n",
-    "\n",
-    "# download MNIST dataset\n",
-    "digits = datasets.load_digits()\n",
-    "\n",
-    "# define inputs and labels\n",
-    "inputs = digits.images\n",
-    "labels = digits.target\n",
-    "\n",
-    "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
-    "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
-    "\n",
-    "\n",
-    "# flatten the image\n",
-    "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
-    "n_inputs = len(inputs)\n",
-    "inputs = inputs.reshape(n_inputs, -1)\n",
-    "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
-    "\n",
-    "\n",
-    "# choose some random images to display\n",
-    "indices = np.arange(n_inputs)\n",
-    "random_indices = np.random.choice(indices, size=5)\n",
-    "\n",
-    "for i, image in enumerate(digits.images[random_indices]):\n",
-    "    plt.subplot(1, 5, i+1)\n",
-    "    plt.axis('off')\n",
-    "    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
-    "    plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "28bb6085",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Train and test datasets\n",
-    "\n",
-    "Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.  \n",
-    "\n",
-    "We will reserve $80 \\%$ of our dataset for training and $20 \\%$ for testing.  \n",
-    "\n",
-    "It is important that the train and test datasets are drawn randomly from our dataset, to ensure\n",
-    "no bias in the sampling.  \n",
-    "Say you are taking measurements of weather data to predict the weather in the coming 5 days.\n",
-    "You don't want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data\n",
-    "collected from 12.00 to 24.00."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "5a6ae0b0",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "from sklearn.model_selection import train_test_split\n",
-    "\n",
-    "# one-liner from scikit-learn library\n",
-    "train_size = 0.8\n",
-    "test_size = 1 - train_size\n",
-    "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
-    "                                                    test_size=test_size)\n",
-    "\n",
-    "# equivalently in numpy\n",
-    "def train_test_split_numpy(inputs, labels, train_size, test_size):\n",
-    "    n_inputs = len(inputs)\n",
-    "    inputs_shuffled = inputs.copy()\n",
-    "    labels_shuffled = labels.copy()\n",
-    "    \n",
-    "    np.random.shuffle(inputs_shuffled)\n",
-    "    np.random.shuffle(labels_shuffled)\n",
-    "    \n",
-    "    train_end = int(n_inputs*train_size)\n",
-    "    X_train, X_test = inputs_shuffled[:train_end], inputs_shuffled[train_end:]\n",
-    "    Y_train, Y_test = labels_shuffled[:train_end], labels_shuffled[train_end:]\n",
-    "    \n",
-    "    return X_train, X_test, Y_train, Y_test\n",
-    "\n",
-    "#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)\n",
-    "\n",
-    "print(\"Number of training images: \" + str(len(X_train)))\n",
-    "print(\"Number of test images: \" + str(len(X_test)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "c26d604d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Define model and architecture\n",
-    "\n",
-    "Our simple feed-forward neural network will consist of an *input* layer, a single *hidden* layer and an *output* layer. The activation $y$ of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have \n",
-    "\n",
-    "$$ z = \\sum_{i=1}^n w_i a_i ,$$\n",
-    "\n",
-    "$$ y = f(z) ,$$\n",
-    "\n",
-    "where $f$ is the activation function, $a_i$ represents input from neuron $i$ in the preceding layer\n",
-    "and $w_i$ is the weight to input $i$.  \n",
-    "The activation of the neurons in the input layer is just the features (e.g. a pixel value).  \n",
-    "\n",
-    "The simplest activation function for a neuron is the *Heaviside* function:\n",
-    "\n",
-    "$$ f(z) = \n",
-    "\\begin{cases}\n",
-    "1,  &  z > 0\\\\\n",
-    "0,  & \\text{otherwise}\n",
-    "\\end{cases}\n",
-    "$$\n",
-    "\n",
-    "A feed-forward neural network with this activation is known as a *perceptron*.  \n",
-    "For a binary classifier (i.e. two classes, 0 or 1, dog or not-dog) we can also use this in our output layer.  \n",
-    "This activation can be generalized to $k$ classes (using e.g. the *one-against-all* strategy), \n",
-    "and we call these architectures *multiclass perceptrons*.  \n",
-    "\n",
-    "However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and  \n",
-    "Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function.  \n",
-    "\n",
-    "Typical choices for activation functions include the sigmoid function, hyperbolic tangent, and Rectified Linear Unit (ReLU).  \n",
-    "We will be using the sigmoid function $\\sigma(x)$:  \n",
-    "\n",
-    "$$ f(x) = \\sigma(x) = \\frac{1}{1 + e^{-x}} ,$$\n",
-    "\n",
-    "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2775283b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Layers\n",
-    "\n",
-    "* Input \n",
-    "\n",
-    "Since each input image has 8x8 = 64 pixels or features, we have an input layer of 64 neurons.  \n",
-    "\n",
-    "* Hidden layer\n",
-    "\n",
-    "We will use 50 neurons in the hidden layer receiving input from the neurons in the input layer.  \n",
-    "Since each neuron in the hidden layer is connected to the 64 inputs we have 64x50 = 3200 weights to the hidden layer.  \n",
-    "\n",
-    "* Output\n",
-    "\n",
-    "If we were building a binary classifier, it would be sufficient with a single neuron in the output layer,\n",
-    "which could output 0 or 1 according to the Heaviside function. This would be an example of a *hard* classifier, meaning it outputs the class of the input directly. However, if we are dealing with noisy data it is often beneficial to use a *soft* classifier, which outputs the probability of being in class 0 or 1.  \n",
-    "\n",
-    "For a soft binary classifier, we could use a single neuron and interpret the output as either being the probability of being in class 0 or the probability of being in class 1. Alternatively we could use 2 neurons, and interpret each neuron as the probability of being in each class.  \n",
-    "\n",
-    "Since we are doing multiclass classification, with 10 categories, it is natural to use 10 neurons in the output layer. We number the neurons $j = 0,1,...,9$. The activation of each output neuron $j$ will be according to the *softmax* function:  \n",
-    "\n",
-    "$$ P(\\text{class $j$} \\mid \\text{input $\\boldsymbol{a}$}) = \\frac{\\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_j)}}\n",
-    "{\\sum_{c=0}^{9} \\exp{(\\boldsymbol{a}^T \\boldsymbol{w}_c)}} ,$$  \n",
-    "\n",
-    "i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\\boldsymbol{a}$, with $\\boldsymbol{w}_j$ the weights of neuron $j$ to the inputs.  \n",
-    "The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  \n",
-    "The exponent is just the weighted sum of inputs as before:  \n",
-    "\n",
-    "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i+b_j.$$  \n",
-    "\n",
-    "Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500\n",
-    "weights to the output layer."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f7455c00",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Weights and biases\n",
-    "\n",
-    "Typically weights are initialized with small values distributed around zero, drawn from a uniform\n",
-    "or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless.  \n",
-    "\n",
-    "Adding a bias value to the weighted sum of inputs allows the neural network to represent a greater range\n",
-    "of values. Without it, any input with the value 0 will be mapped to zero (before being passed through the activation). The bias unit has an output of 1, and a weight to each neuron $j$, $b_j$:  \n",
-    "\n",
-    "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i + b_j.$$  \n",
-    "\n",
-    "The bias weights $\\boldsymbol{b}$ are often initialized to zero, but a small value like $0.01$ ensures all neurons have some output which can be backpropagated in the first training cycle."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "20b3c8c0",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# building our neural network\n",
-    "\n",
-    "n_inputs, n_features = X_train.shape\n",
-    "n_hidden_neurons = 50\n",
-    "n_categories = 10\n",
-    "\n",
-    "# we make the weights normally distributed using numpy.random.randn\n",
-    "\n",
-    "# weights and bias in the hidden layer\n",
-    "hidden_weights = np.random.randn(n_features, n_hidden_neurons)\n",
-    "hidden_bias = np.zeros(n_hidden_neurons) + 0.01\n",
-    "\n",
-    "# weights and bias in the output layer\n",
-    "output_weights = np.random.randn(n_hidden_neurons, n_categories)\n",
-    "output_bias = np.zeros(n_categories) + 0.01"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a41d9acd",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Feed-forward pass\n",
-    "\n",
-    "Denote $F$ the number of features, $H$ the number of hidden neurons and $C$ the number of categories.  \n",
-    "For each input image we calculate a weighted sum of input features (pixel values) to each neuron $j$ in the hidden layer $l$:  \n",
-    "\n",
-    "$$ z_{j}^{l} = \\sum_{i=1}^{F} w_{ij}^{l} x_i + b_{j}^{l},$$\n",
-    "\n",
-    "this is then passed through our activation function  \n",
-    "\n",
-    "$$ a_{j}^{l} = f(z_{j}^{l}) .$$  \n",
-    "\n",
-    "We calculate a weighted sum of inputs (activations in the hidden layer) to each neuron $j$ in the output layer:  \n",
-    "\n",
-    "$$ z_{j}^{L} = \\sum_{i=1}^{H} w_{ij}^{L} a_{i}^{l} + b_{j}^{L}.$$  \n",
-    "\n",
-    "Finally we calculate the output of neuron $j$ in the output layer using the softmax function:  \n",
-    "\n",
-    "$$ a_{j}^{L} = \\frac{\\exp{(z_j^{L})}}\n",
-    "{\\sum_{c=0}^{C-1} \\exp{(z_c^{L})}} .$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b2f64238",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Matrix multiplications\n",
-    "\n",
-    "Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden\n",
-    "layer have the dimensions  \n",
-    "$W_{hidden} = (n_{features}, n_{hidden})$,\n",
-    "we can easily feed the network all our training data in one go by taking the matrix product  \n",
-    "\n",
-    "$$ X W^{h} = (n_{inputs}, n_{hidden}),$$ \n",
-    "\n",
-    "and obtain a matrix that holds the weighted sum of inputs to the hidden layer\n",
-    "for each input image and each hidden neuron.    \n",
-    "We also add the bias to obtain a matrix of weighted sums to the hidden layer $Z^{h}$:  \n",
-    "\n",
-    "$$ \\boldsymbol{z}^{l} = \\boldsymbol{X} \\boldsymbol{W}^{l} + \\boldsymbol{b}^{l} ,$$\n",
-    "\n",
-    "meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.  \n",
-    "This is then passed through the activation:  \n",
-    "\n",
-    "$$ \\boldsymbol{a}^{l} = f(\\boldsymbol{z}^l) .$$  \n",
-    "\n",
-    "This is fed to the output layer:  \n",
-    "\n",
-    "$$ \\boldsymbol{z}^{L} = \\boldsymbol{a}^{L} \\boldsymbol{W}^{L} + \\boldsymbol{b}^{L} .$$\n",
-    "\n",
-    "Finally we receive our output values for each image and each category by passing it through the softmax function:  \n",
-    "\n",
-    "$$ output = softmax (\\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "id": "1f5589af",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# setup the feed-forward pass, subscript h = hidden layer\n",
-    "\n",
-    "def sigmoid(x):\n",
-    "    return 1/(1 + np.exp(-x))\n",
-    "\n",
-    "def feed_forward(X):\n",
-    "    # weighted sum of inputs to the hidden layer\n",
-    "    z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
-    "    # activation in the hidden layer\n",
-    "    a_h = sigmoid(z_h)\n",
-    "    \n",
-    "    # weighted sum of inputs to the output layer\n",
-    "    z_o = np.matmul(a_h, output_weights) + output_bias\n",
-    "    # softmax output\n",
-    "    # axis 0 holds each input and axis 1 the probabilities of each category\n",
-    "    exp_term = np.exp(z_o)\n",
-    "    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
-    "    \n",
-    "    return probabilities\n",
-    "\n",
-    "probabilities = feed_forward(X_train)\n",
-    "print(\"probabilities = (n_inputs, n_categories) = \" + str(probabilities.shape))\n",
-    "print(\"probability that image 0 is in category 0,1,2,...,9 = \\n\" + str(probabilities[0]))\n",
-    "print(\"probabilities sum up to: \" + str(probabilities[0].sum()))\n",
-    "print()\n",
-    "\n",
-    "# we obtain a prediction by taking the class with the highest likelihood\n",
-    "def predict(X):\n",
-    "    probabilities = feed_forward(X)\n",
-    "    return np.argmax(probabilities, axis=1)\n",
-    "\n",
-    "predictions = predict(X_train)\n",
-    "print(\"predictions = (n_inputs) = \" + str(predictions.shape))\n",
-    "print(\"prediction for image 0: \" + str(predictions[0]))\n",
-    "print(\"correct label for image 0: \" + str(Y_train[0]))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4518e911",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Choose cost function and optimizer\n",
-    "\n",
-    "To measure how well our neural network is doing we need to introduce a cost function.  \n",
-    "We will call the function that gives the error of a single sample output the *loss* function, and the function\n",
-    "that gives the total error of our network across all samples the *cost* function.\n",
-    "A typical choice for multiclass classification is the *cross-entropy* loss, also known as the negative log likelihood.  \n",
-    "\n",
-    "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  \n",
-    "\n",
-    "$$ y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  \n",
-    "\n",
-    "$$ y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  \n",
-    "\n",
-    "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset.  \n",
-    "\n",
-    "Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector.  \n",
-    "We define the cost function $\\mathcal{C}$ as a sum over the cross-entropy loss for each point $\\boldsymbol{x}_i$ in the dataset.\n",
-    "\n",
-    "In the one-hot representation only one of the terms in the loss function is non-zero, namely the\n",
-    "probability of the correct category $c'$  \n",
-    "(i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong\n",
-    "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\boldsymbol{\\theta}$ represents the parameters of our network, i.e. all the weights and biases."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d519516b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Optimizing the cost function\n",
-    "\n",
-    "The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent\n",
-    "is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a *local* minimum of the cost function.  \n",
-    "Each parameter $\\theta$ is iteratively adjusted according to the rule  \n",
-    "\n",
-    "$$ \\theta_{i+1} = \\theta_i - \\eta \\nabla \\mathcal{C}(\\theta_i) ,$$\n",
-    "\n",
-    "where $\\eta$ is known as the *learning rate*, which controls how big a step we take towards the minimum.  \n",
-    "This update can be repeated for any number of iterations, or until we are satisfied with the result.  \n",
-    "\n",
-    "A simple and effective improvement is a variant called *Batch Gradient Descent*.  \n",
-    "Instead of calculating the gradient on the whole dataset, we calculate an approximation of the gradient\n",
-    "on a subset of the data called a *minibatch*.  \n",
-    "If there are $N$ data points and we have a minibatch size of $M$, the total number of batches\n",
-    "is $N/M$.  \n",
-    "We denote each minibatch $B_k$, with $k = 1, 2,...,N/M$. The gradient then becomes:  \n",
-    "\n",
-    "$$ \\nabla \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\nabla \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
-    "\\frac{1}{M} \\sum_{i \\in B_k} \\nabla \\mathcal{L}_i(\\theta) ,$$\n",
-    "\n",
-    "i.e. instead of averaging the loss over the entire dataset, we average over a minibatch.  \n",
-    "\n",
-    "This has two important benefits:  \n",
-    "1. Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima.  \n",
-    "\n",
-    "2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient.  \n",
-    "\n",
-    "The various optmization  methods, with codes and algorithms,  are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "46b71202",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Regularization\n",
-    "\n",
-    "It is common to add an extra term to the cost function, proportional\n",
-    "to the size of the weights.  This is equivalent to constraining the\n",
-    "size of the weights, so that they do not grow out of control.\n",
-    "Constraining the size of the weights means that the weights cannot\n",
-    "grow arbitrarily large to fit the training data, and in this way\n",
-    "reduces *overfitting*.\n",
-    "\n",
-    "We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes:  \n",
-    "\n",
-    "$$  \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
-    "\\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}_i(\\theta) + \\lambda \\lvert \\lvert \\boldsymbol{w} \\rvert \\rvert_2^2 \n",
-    "= \\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}(\\theta) + \\lambda \\sum_{ij} w_{ij}^2,$$  \n",
-    "\n",
-    "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n",
-    "\n",
-    "In order to train the model, we need to calculate the derivative of\n",
-    "the cost function with respect to every bias and weight in the\n",
-    "network.  In total our network has $(64 + 1)\\times 50=3250$ weights in\n",
-    "the hidden layer and $(50 + 1)\\times 10=510$ weights to the output\n",
-    "layer ($+1$ for the bias), and the gradient must be calculated for\n",
-    "every parameter.  We use the *backpropagation* algorithm discussed\n",
-    "above. This is a clever use of the chain rule that allows us to\n",
-    "calculate the gradient efficently."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "129c39d3",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Matrix  multiplication\n",
-    "\n",
-    "To more efficently train our network these equations are implemented using matrix operations.  \n",
-    "The error in the output layer is calculated simply as, with $\\boldsymbol{t}$ being our targets,  \n",
-    "\n",
-    "$$ \\delta_L = \\boldsymbol{t} - \\boldsymbol{y} = (n_{inputs}, n_{categories}) .$$  \n",
-    "\n",
-    "The gradient for the output weights is calculated as  \n",
-    "\n",
-    "$$ \\nabla W_{L} = \\boldsymbol{a}^T \\delta_L   = (n_{hidden}, n_{categories}) ,$$\n",
-    "\n",
-    "where $\\boldsymbol{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input.  \n",
-    "Since we are going backwards we have to transpose the activation matrix.  \n",
-    "\n",
-    "The gradient with respect to the output bias is then  \n",
-    "\n",
-    "$$ \\nabla \\boldsymbol{b}_{L} = \\sum_{i=1}^{n_{inputs}} \\delta_L = (n_{categories}) .$$  \n",
-    "\n",
-    "The error in the hidden layer is  \n",
-    "\n",
-    "$$ \\Delta_h = \\delta_L W_{L}^T \\circ f'(z_{h}) = \\delta_L W_{L}^T \\circ a_{h} \\circ (1 - a_{h}) = (n_{inputs}, n_{hidden}) ,$$  \n",
-    "\n",
-    "where $f'(a_{h})$ is the derivative of the activation in the hidden layer. The matrix products mean\n",
-    "that we are summing up the products for each neuron in the output layer. The symbol $\\circ$ denotes\n",
-    "the *Hadamard product*, meaning element-wise multiplication.  \n",
-    "\n",
-    "This again gives us the gradients in the hidden layer:  \n",
-    "\n",
-    "$$ \\nabla W_{h} = X^T \\delta_h = (n_{features}, n_{hidden}) ,$$  \n",
-    "\n",
-    "$$ \\nabla b_{h} = \\sum_{i=1}^{n_{inputs}} \\delta_h = (n_{hidden}) .$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "id": "8abafb44",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# to categorical turns our integer vector into a onehot representation\n",
-    "from sklearn.metrics import accuracy_score\n",
-    "\n",
-    "# one-hot in numpy\n",
-    "def to_categorical_numpy(integer_vector):\n",
-    "    n_inputs = len(integer_vector)\n",
-    "    n_categories = np.max(integer_vector) + 1\n",
-    "    onehot_vector = np.zeros((n_inputs, n_categories))\n",
-    "    onehot_vector[range(n_inputs), integer_vector] = 1\n",
-    "    \n",
-    "    return onehot_vector\n",
-    "\n",
-    "#Y_train_onehot, Y_test_onehot = to_categorical(Y_train), to_categorical(Y_test)\n",
-    "Y_train_onehot, Y_test_onehot = to_categorical_numpy(Y_train), to_categorical_numpy(Y_test)\n",
-    "\n",
-    "def feed_forward_train(X):\n",
-    "    # weighted sum of inputs to the hidden layer\n",
-    "    z_h = np.matmul(X, hidden_weights) + hidden_bias\n",
-    "    # activation in the hidden layer\n",
-    "    a_h = sigmoid(z_h)\n",
-    "    \n",
-    "    # weighted sum of inputs to the output layer\n",
-    "    z_o = np.matmul(a_h, output_weights) + output_bias\n",
-    "    # softmax output\n",
-    "    # axis 0 holds each input and axis 1 the probabilities of each category\n",
-    "    exp_term = np.exp(z_o)\n",
-    "    probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
-    "    \n",
-    "    # for backpropagation need activations in hidden and output layers\n",
-    "    return a_h, probabilities\n",
-    "\n",
-    "def backpropagation(X, Y):\n",
-    "    a_h, probabilities = feed_forward_train(X)\n",
-    "    \n",
-    "    # error in the output layer\n",
-    "    error_output = probabilities - Y\n",
-    "    # error in the hidden layer\n",
-    "    error_hidden = np.matmul(error_output, output_weights.T) * a_h * (1 - a_h)\n",
-    "    \n",
-    "    # gradients for the output layer\n",
-    "    output_weights_gradient = np.matmul(a_h.T, error_output)\n",
-    "    output_bias_gradient = np.sum(error_output, axis=0)\n",
-    "    \n",
-    "    # gradient for the hidden layer\n",
-    "    hidden_weights_gradient = np.matmul(X.T, error_hidden)\n",
-    "    hidden_bias_gradient = np.sum(error_hidden, axis=0)\n",
-    "\n",
-    "    return output_weights_gradient, output_bias_gradient, hidden_weights_gradient, hidden_bias_gradient\n",
-    "\n",
-    "print(\"Old accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))\n",
-    "\n",
-    "eta = 0.01\n",
-    "lmbd = 0.01\n",
-    "for i in range(1000):\n",
-    "    # calculate gradients\n",
-    "    dWo, dBo, dWh, dBh = backpropagation(X_train, Y_train_onehot)\n",
-    "    \n",
-    "    # regularization term gradients\n",
-    "    dWo += lmbd * output_weights\n",
-    "    dWh += lmbd * hidden_weights\n",
-    "    \n",
-    "    # update weights and biases\n",
-    "    output_weights -= eta * dWo\n",
-    "    output_bias -= eta * dBo\n",
-    "    hidden_weights -= eta * dWh\n",
-    "    hidden_bias -= eta * dBh\n",
-    "\n",
-    "print(\"New accuracy on training data: \" + str(accuracy_score(predict(X_train), Y_train)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e95c7166",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Improving performance\n",
-    "\n",
-    "As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.  \n",
-    "In order to obtain a network that does something useful, we will have to do a bit more work.  \n",
-    "\n",
-    "The choice of *hyperparameters* such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a *grid-search* is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates $\\eta = 10^{-6}, 10^{-5},...,10^{-1}$ with different regularization parameters $\\lambda = 10^{-6},...,10^{-0}$.  \n",
-    "\n",
-    "Next, we haven't implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an *iteration*, and a full training period\n",
-    "going through the entire dataset ($n/M$ batches) an *epoch*.\n",
-    "\n",
-    "If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers.  \n",
-    "Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b4365471",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Full object-oriented implementation\n",
-    "\n",
-    "It is very natural to think of the network as an object, with specific instances of the network\n",
-    "being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "id": "5a0357b2",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "class NeuralNetwork:\n",
-    "    def __init__(\n",
-    "            self,\n",
-    "            X_data,\n",
-    "            Y_data,\n",
-    "            n_hidden_neurons=50,\n",
-    "            n_categories=10,\n",
-    "            epochs=10,\n",
-    "            batch_size=100,\n",
-    "            eta=0.1,\n",
-    "            lmbd=0.0):\n",
-    "\n",
-    "        self.X_data_full = X_data\n",
-    "        self.Y_data_full = Y_data\n",
-    "\n",
-    "        self.n_inputs = X_data.shape[0]\n",
-    "        self.n_features = X_data.shape[1]\n",
-    "        self.n_hidden_neurons = n_hidden_neurons\n",
-    "        self.n_categories = n_categories\n",
-    "\n",
-    "        self.epochs = epochs\n",
-    "        self.batch_size = batch_size\n",
-    "        self.iterations = self.n_inputs // self.batch_size\n",
-    "        self.eta = eta\n",
-    "        self.lmbd = lmbd\n",
-    "\n",
-    "        self.create_biases_and_weights()\n",
-    "\n",
-    "    def create_biases_and_weights(self):\n",
-    "        self.hidden_weights = np.random.randn(self.n_features, self.n_hidden_neurons)\n",
-    "        self.hidden_bias = np.zeros(self.n_hidden_neurons) + 0.01\n",
-    "\n",
-    "        self.output_weights = np.random.randn(self.n_hidden_neurons, self.n_categories)\n",
-    "        self.output_bias = np.zeros(self.n_categories) + 0.01\n",
-    "\n",
-    "    def feed_forward(self):\n",
-    "        # feed-forward for training\n",
-    "        self.z_h = np.matmul(self.X_data, self.hidden_weights) + self.hidden_bias\n",
-    "        self.a_h = sigmoid(self.z_h)\n",
-    "\n",
-    "        self.z_o = np.matmul(self.a_h, self.output_weights) + self.output_bias\n",
-    "\n",
-    "        exp_term = np.exp(self.z_o)\n",
-    "        self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
-    "\n",
-    "    def feed_forward_out(self, X):\n",
-    "        # feed-forward for output\n",
-    "        z_h = np.matmul(X, self.hidden_weights) + self.hidden_bias\n",
-    "        a_h = sigmoid(z_h)\n",
-    "\n",
-    "        z_o = np.matmul(a_h, self.output_weights) + self.output_bias\n",
-    "        \n",
-    "        exp_term = np.exp(z_o)\n",
-    "        probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n",
-    "        return probabilities\n",
-    "\n",
-    "    def backpropagation(self):\n",
-    "        error_output = self.probabilities - self.Y_data\n",
-    "        error_hidden = np.matmul(error_output, self.output_weights.T) * self.a_h * (1 - self.a_h)\n",
-    "\n",
-    "        self.output_weights_gradient = np.matmul(self.a_h.T, error_output)\n",
-    "        self.output_bias_gradient = np.sum(error_output, axis=0)\n",
-    "\n",
-    "        self.hidden_weights_gradient = np.matmul(self.X_data.T, error_hidden)\n",
-    "        self.hidden_bias_gradient = np.sum(error_hidden, axis=0)\n",
-    "\n",
-    "        if self.lmbd > 0.0:\n",
-    "            self.output_weights_gradient += self.lmbd * self.output_weights\n",
-    "            self.hidden_weights_gradient += self.lmbd * self.hidden_weights\n",
-    "\n",
-    "        self.output_weights -= self.eta * self.output_weights_gradient\n",
-    "        self.output_bias -= self.eta * self.output_bias_gradient\n",
-    "        self.hidden_weights -= self.eta * self.hidden_weights_gradient\n",
-    "        self.hidden_bias -= self.eta * self.hidden_bias_gradient\n",
-    "\n",
-    "    def predict(self, X):\n",
-    "        probabilities = self.feed_forward_out(X)\n",
-    "        return np.argmax(probabilities, axis=1)\n",
-    "\n",
-    "    def predict_probabilities(self, X):\n",
-    "        probabilities = self.feed_forward_out(X)\n",
-    "        return probabilities\n",
-    "\n",
-    "    def train(self):\n",
-    "        data_indices = np.arange(self.n_inputs)\n",
-    "\n",
-    "        for i in range(self.epochs):\n",
-    "            for j in range(self.iterations):\n",
-    "                # pick datapoints with replacement\n",
-    "                chosen_datapoints = np.random.choice(\n",
-    "                    data_indices, size=self.batch_size, replace=False\n",
-    "                )\n",
-    "\n",
-    "                # minibatch training data\n",
-    "                self.X_data = self.X_data_full[chosen_datapoints]\n",
-    "                self.Y_data = self.Y_data_full[chosen_datapoints]\n",
-    "\n",
-    "                self.feed_forward()\n",
-    "                self.backpropagation()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "a417307d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Evaluate model performance on test data\n",
-    "\n",
-    "To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data.  \n",
-    "We measure the performance of the network using the *accuracy* score.  \n",
-    "The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of $1$.  \n",
-    "\n",
-    "$$ \\text{Accuracy} = \\frac{\\sum_{i=1}^n I(\\tilde{y}_i = y_i)}{n} ,$$  \n",
-    "\n",
-    "where $I$ is the indicator function, $1$ if $\\tilde{y}_i = y_i$ and $0$ otherwise."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "id": "8ee4b306",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "epochs = 100\n",
-    "batch_size = 100\n",
-    "\n",
-    "dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n",
-    "                    n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n",
-    "dnn.train()\n",
-    "test_predict = dnn.predict(X_test)\n",
-    "\n",
-    "# accuracy score from scikit library\n",
-    "print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n",
-    "\n",
-    "# equivalent in numpy\n",
-    "def accuracy_score_numpy(Y_test, Y_pred):\n",
-    "    return np.sum(Y_test == Y_pred) / len(Y_test)\n",
-    "\n",
-    "#print(\"Accuracy score on test set: \", accuracy_score_numpy(Y_test, test_predict))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "efcbd954",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Adjust hyperparameters\n",
-    "\n",
-    "We now perform a grid search to find the optimal hyperparameters for the network.  \n",
-    "Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around $98\\%$ ($2\\%$ error rate)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "bb527e6e",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "eta_vals = np.logspace(-5, 1, 7)\n",
-    "lmbd_vals = np.logspace(-5, 1, 7)\n",
-    "# store the models for later use\n",
-    "DNN_numpy = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
-    "\n",
-    "# grid search\n",
-    "for i, eta in enumerate(eta_vals):\n",
-    "    for j, lmbd in enumerate(lmbd_vals):\n",
-    "        dnn = NeuralNetwork(X_train, Y_train_onehot, eta=eta, lmbd=lmbd, epochs=epochs, batch_size=batch_size,\n",
-    "                            n_hidden_neurons=n_hidden_neurons, n_categories=n_categories)\n",
-    "        dnn.train()\n",
-    "        \n",
-    "        DNN_numpy[i][j] = dnn\n",
-    "        \n",
-    "        test_predict = dnn.predict(X_test)\n",
-    "        \n",
-    "        print(\"Learning rate  = \", eta)\n",
-    "        print(\"Lambda = \", lmbd)\n",
-    "        print(\"Accuracy score on test set: \", accuracy_score(Y_test, test_predict))\n",
-    "        print()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d282951d",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Visualization"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "69d3d9c8",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# visual representation of grid search\n",
-    "# uses seaborn heatmap, you can also do this with matplotlib imshow\n",
-    "import seaborn as sns\n",
-    "\n",
-    "sns.set()\n",
-    "\n",
-    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "\n",
-    "for i in range(len(eta_vals)):\n",
-    "    for j in range(len(lmbd_vals)):\n",
-    "        dnn = DNN_numpy[i][j]\n",
-    "        \n",
-    "        train_pred = dnn.predict(X_train) \n",
-    "        test_pred = dnn.predict(X_test)\n",
-    "\n",
-    "        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n",
-    "        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n",
-    "\n",
-    "        \n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Training Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Test Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "99f5058c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## scikit-learn implementation\n",
-    "\n",
-    "**scikit-learn** focuses more\n",
-    "on traditional machine learning methods, such as regression,\n",
-    "clustering, decision trees, etc. As such, it has only two types of\n",
-    "neural networks: Multi Layer Perceptron outputting continuous values,\n",
-    "*MPLRegressor*, and Multi Layer Perceptron outputting labels,\n",
-    "*MLPClassifier*. We will see how simple it is to use these classes.\n",
-    "\n",
-    "**scikit-learn** implements a few improvements from our neural network,\n",
-    "such as early stopping, a varying learning rate, different\n",
-    "optimization methods, etc. We would therefore expect a better\n",
-    "performance overall."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "7898d99f",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "from sklearn.neural_network import MLPClassifier\n",
-    "# store models for later use\n",
-    "DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
-    "\n",
-    "for i, eta in enumerate(eta_vals):\n",
-    "    for j, lmbd in enumerate(lmbd_vals):\n",
-    "        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',\n",
-    "                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)\n",
-    "        dnn.fit(X_train, Y_train)\n",
-    "        \n",
-    "        DNN_scikit[i][j] = dnn\n",
-    "        \n",
-    "        print(\"Learning rate  = \", eta)\n",
-    "        print(\"Lambda = \", lmbd)\n",
-    "        print(\"Accuracy score on test set: \", dnn.score(X_test, Y_test))\n",
-    "        print()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7ceec918",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Visualization"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "id": "98abf229",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# optional\n",
-    "# visual representation of grid search\n",
-    "# uses seaborn heatmap, could probably do this in matplotlib\n",
-    "import seaborn as sns\n",
-    "\n",
-    "sns.set()\n",
-    "\n",
-    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "\n",
-    "for i in range(len(eta_vals)):\n",
-    "    for j in range(len(lmbd_vals)):\n",
-    "        dnn = DNN_scikit[i][j]\n",
-    "        \n",
-    "        train_pred = dnn.predict(X_train) \n",
-    "        test_pred = dnn.predict(X_test)\n",
-    "\n",
-    "        train_accuracy[i][j] = accuracy_score(Y_train, train_pred)\n",
-    "        test_accuracy[i][j] = accuracy_score(Y_test, test_pred)\n",
-    "\n",
-    "        \n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Training Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Test Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "ba07c374",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Building neural networks in Tensorflow and Keras\n",
-    "\n",
-    "Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn\n",
-    "and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy\n",
-    "and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.  \n",
-    "\n",
-    "In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite\n",
-    "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n",
-    "NumPy arrays."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1cf09819",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Tensorflow\n",
-    "\n",
-    "Tensorflow is an open source library machine learning library\n",
-    "developed by the Google Brain team for internal use. It was released\n",
-    "under the Apache 2.0 open source license in November 9, 2015.\n",
-    "\n",
-    "Tensorflow is a computational framework that allows you to construct\n",
-    "machine learning models at different levels of abstraction, from\n",
-    "high-level, object-oriented APIs like Keras, down to the C++ kernels\n",
-    "that Tensorflow is built upon. The higher levels of abstraction are\n",
-    "simpler to use, but less flexible, and our choice of implementation\n",
-    "should reflect the problems we are trying to solve.\n",
-    "\n",
-    "[Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation\n",
-    "in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*\n",
-    "to represent your model, and then create a Tensorflow *session* to run the graph.\n",
-    "\n",
-    "In this guide we will analyze the same data as we did in our NumPy and\n",
-    "scikit-learn tutorial, gathered from the MNIST database of images. We\n",
-    "will give an introduction to the lower level Python Application\n",
-    "Program Interfaces (APIs), and see how we use them to build our graph.\n",
-    "Then we will build (effectively) the same graph in Keras, to see just\n",
-    "how simple solving a machine learning problem can be.\n",
-    "\n",
-    "To install tensorflow on Unix/Linux systems, use pip as"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "id": "2c2c3ec5",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "pip3 install tensorflow"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "39d013b1",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n",
-    "(current release of CPU-only TensorFlow)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "id": "fbf36c26",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "conda create -n tf tensorflow\n",
-    "conda activate tf"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "94e66380",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "To install the current release of GPU TensorFlow"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "5e72b1d2",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "conda create -n tf-gpu tensorflow-gpu\n",
-    "conda activate tf-gpu"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "40470dbd",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Using Keras\n",
-    "\n",
-    "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n",
-    "that supports Tensorflow, CTNK and Theano as backends.  \n",
-    "If you have Anaconda installed you may run the following command"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "id": "f2cd4f41",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "conda install keras"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "636940c6",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "You can look up the [instructions here](https://keras.io/) for more information.\n",
-    "\n",
-    "We will to a large extent use **keras** in this course."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d9f47b57",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Collect and pre-process data\n",
-    "\n",
-    "Let us look again at the MINST data set."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "id": "1489b5d5",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# import necessary packages\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "import tensorflow as tf\n",
-    "from sklearn import datasets\n",
-    "\n",
-    "\n",
-    "# ensure the same random numbers appear every time\n",
-    "np.random.seed(0)\n",
-    "\n",
-    "# display images in notebook\n",
-    "%matplotlib inline\n",
-    "plt.rcParams['figure.figsize'] = (12,12)\n",
-    "\n",
-    "\n",
-    "# download MNIST dataset\n",
-    "digits = datasets.load_digits()\n",
-    "\n",
-    "# define inputs and labels\n",
-    "inputs = digits.images\n",
-    "labels = digits.target\n",
-    "\n",
-    "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
-    "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
-    "\n",
-    "\n",
-    "# flatten the image\n",
-    "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
-    "n_inputs = len(inputs)\n",
-    "inputs = inputs.reshape(n_inputs, -1)\n",
-    "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
-    "\n",
-    "\n",
-    "# choose some random images to display\n",
-    "indices = np.arange(n_inputs)\n",
-    "random_indices = np.random.choice(indices, size=5)\n",
-    "\n",
-    "for i, image in enumerate(digits.images[random_indices]):\n",
-    "    plt.subplot(1, 5, i+1)\n",
-    "    plt.axis('off')\n",
-    "    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
-    "    plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "id": "672dc5a2",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "from tensorflow.keras.layers import Input\n",
-    "from tensorflow.keras.models import Sequential      #This allows appending layers to existing models\n",
-    "from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer\n",
-    "from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n",
-    "from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)\n",
-    "from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function\n",
-    "\n",
-    "from sklearn.model_selection import train_test_split\n",
-    "\n",
-    "# one-hot representation of labels\n",
-    "labels = to_categorical(labels)\n",
-    "\n",
-    "# split into train and test data\n",
-    "train_size = 0.8\n",
-    "test_size = 1 - train_size\n",
-    "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
-    "                                                    test_size=test_size)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "id": "0513084f",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "\n",
-    "epochs = 100\n",
-    "batch_size = 100\n",
-    "n_neurons_layer1 = 100\n",
-    "n_neurons_layer2 = 50\n",
-    "n_categories = 10\n",
-    "eta_vals = np.logspace(-5, 1, 7)\n",
-    "lmbd_vals = np.logspace(-5, 1, 7)\n",
-    "def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):\n",
-    "    model = Sequential()\n",
-    "    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
-    "    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
-    "    model.add(Dense(n_categories, activation='softmax'))\n",
-    "    \n",
-    "    sgd = optimizers.SGD(lr=eta)\n",
-    "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
-    "    \n",
-    "    return model"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "id": "02a34777",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
-    "        \n",
-    "for i, eta in enumerate(eta_vals):\n",
-    "    for j, lmbd in enumerate(lmbd_vals):\n",
-    "        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,\n",
-    "                                         eta=eta, lmbd=lmbd)\n",
-    "        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n",
-    "        scores = DNN.evaluate(X_test, Y_test)\n",
-    "        \n",
-    "        DNN_keras[i][j] = DNN\n",
-    "        \n",
-    "        print(\"Learning rate = \", eta)\n",
-    "        print(\"Lambda = \", lmbd)\n",
-    "        print(\"Test accuracy: %.3f\" % scores[1])\n",
-    "        print()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "id": "52c1d6e2",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "# optional\n",
-    "# visual representation of grid search\n",
-    "# uses seaborn heatmap, could probably do this in matplotlib\n",
-    "import seaborn as sns\n",
-    "\n",
-    "sns.set()\n",
-    "\n",
-    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
-    "\n",
-    "for i in range(len(eta_vals)):\n",
-    "    for j in range(len(lmbd_vals)):\n",
-    "        DNN = DNN_keras[i][j]\n",
-    "\n",
-    "        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]\n",
-    "        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]\n",
-    "\n",
-    "        \n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Training Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize = (10, 10))\n",
-    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
-    "ax.set_title(\"Test Accuracy\")\n",
-    "ax.set_ylabel(\"$\\eta$\")\n",
-    "ax.set_xlabel(\"$\\lambda$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "53f9be79",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Building a neural network code\n",
-    "\n",
-    "Here we  present a flexible object oriented codebase\n",
-    "for a feed forward neural network, along with a demonstration of how\n",
-    "to use it. Before we get into the details of the neural network, we\n",
-    "will first present some implementations of various schedulers, cost\n",
-    "functions and activation functions that can be used together with the\n",
-    "neural network.\n",
-    "\n",
-    "The codes here were developed by Eric Reber and Gregor Kajda during spring 2023."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "39bd1718",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### Learning rate methods\n",
-    "\n",
-    "The code below shows object oriented implementations of the Constant,\n",
-    "Momentum, Adagrad, AdagradMomentum, RMS prop and Adam schedulers. All\n",
-    "of the classes belong to the shared abstract Scheduler class, and\n",
-    "share the update_change() and reset() methods allowing for any of the\n",
-    "schedulers to be seamlessly used during the training stage, as will\n",
-    "later be shown in the fit() method of the neural\n",
-    "network. Update_change() only has one parameter, the gradient\n",
-    "($δ^l_ja^{l−1}_k$), and returns the change which will be subtracted\n",
-    "from the weights. The reset() function takes no parameters, and resets\n",
-    "the desired variables. For Constant and Momentum, reset does nothing."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "id": "4c1f42f1",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import autograd.numpy as np\n",
-    "\n",
-    "class Scheduler:\n",
-    "    \"\"\"\n",
-    "    Abstract class for Schedulers\n",
-    "    \"\"\"\n",
-    "\n",
-    "    def __init__(self, eta):\n",
-    "        self.eta = eta\n",
-    "\n",
-    "    # should be overwritten\n",
-    "    def update_change(self, gradient):\n",
-    "        raise NotImplementedError\n",
-    "\n",
-    "    # overwritten if needed\n",
-    "    def reset(self):\n",
-    "        pass\n",
-    "\n",
-    "\n",
-    "class Constant(Scheduler):\n",
-    "    def __init__(self, eta):\n",
-    "        super().__init__(eta)\n",
-    "\n",
-    "    def update_change(self, gradient):\n",
-    "        return self.eta * gradient\n",
-    "    \n",
-    "    def reset(self):\n",
-    "        pass\n",
-    "\n",
-    "\n",
-    "class Momentum(Scheduler):\n",
-    "    def __init__(self, eta: float, momentum: float):\n",
-    "        super().__init__(eta)\n",
-    "        self.momentum = momentum\n",
-    "        self.change = 0\n",
-    "\n",
-    "    def update_change(self, gradient):\n",
-    "        self.change = self.momentum * self.change + self.eta * gradient\n",
-    "        return self.change\n",
-    "\n",
-    "    def reset(self):\n",
-    "        pass\n",
-    "\n",
-    "\n",
-    "class Adagrad(Scheduler):\n",
-    "    def __init__(self, eta):\n",
-    "        super().__init__(eta)\n",
-    "        self.G_t = None\n",
-    "\n",
-    "    def update_change(self, gradient):\n",
-    "        delta = 1e-8  # avoid division ny zero\n",
-    "\n",
-    "        if self.G_t is None:\n",
-    "            self.G_t = np.zeros((gradient.shape[0], gradient.shape[0]))\n",
-    "\n",
-    "        self.G_t += gradient @ gradient.T\n",
-    "\n",
-    "        G_t_inverse = 1 / (\n",
-    "            delta + np.sqrt(np.reshape(np.diagonal(self.G_t), (self.G_t.shape[0], 1)))\n",
-    "        )\n",
-    "        return self.eta * gradient * G_t_inverse\n",
-    "\n",
-    "    def reset(self):\n",
-    "        self.G_t = None\n",
-    "\n",
-    "\n",
-    "class AdagradMomentum(Scheduler):\n",
-    "    def __init__(self, eta, momentum):\n",
-    "        super().__init__(eta)\n",
-    "        self.G_t = None\n",
-    "        self.momentum = momentum\n",
-    "        self.change = 0\n",
-    "\n",
-    "    def update_change(self, gradient):\n",
-    "        delta = 1e-8  # avoid division ny zero\n",
-    "\n",
-    "        if self.G_t is None:\n",
-    "            self.G_t = np.zeros((gradient.shape[0], gradient.shape[0]))\n",
-    "\n",
-    "        self.G_t += gradient @ gradient.T\n",
-    "\n",
-    "        G_t_inverse = 1 / (\n",
-    "            delta + np.sqrt(np.reshape(np.diagonal(self.G_t), (self.G_t.shape[0], 1)))\n",
-    "        )\n",
-    "        self.change = self.change * self.momentum + self.eta * gradient * G_t_inverse\n",
-    "        return self.change\n",
-    "\n",
-    "    def reset(self):\n",
-    "        self.G_t = None\n",
-    "\n",
-    "\n",
-    "class RMS_prop(Scheduler):\n",
-    "    def __init__(self, eta, rho):\n",
-    "        super().__init__(eta)\n",
-    "        self.rho = rho\n",
-    "        self.second = 0.0\n",
-    "\n",
-    "    def update_change(self, gradient):\n",
-    "        delta = 1e-8  # avoid division ny zero\n",
-    "        self.second = self.rho * self.second + (1 - self.rho) * gradient * gradient\n",
-    "        return self.eta * gradient / (np.sqrt(self.second + delta))\n",
-    "\n",
-    "    def reset(self):\n",
-    "        self.second = 0.0\n",
-    "\n",
-    "\n",
-    "class Adam(Scheduler):\n",
-    "    def __init__(self, eta, rho, rho2):\n",
-    "        super().__init__(eta)\n",
-    "        self.rho = rho\n",
-    "        self.rho2 = rho2\n",
-    "        self.moment = 0\n",
-    "        self.second = 0\n",
-    "        self.n_epochs = 1\n",
-    "\n",
-    "    def update_change(self, gradient):\n",
-    "        delta = 1e-8  # avoid division ny zero\n",
-    "\n",
-    "        self.moment = self.rho * self.moment + (1 - self.rho) * gradient\n",
-    "        self.second = self.rho2 * self.second + (1 - self.rho2) * gradient * gradient\n",
-    "\n",
-    "        moment_corrected = self.moment / (1 - self.rho**self.n_epochs)\n",
-    "        second_corrected = self.second / (1 - self.rho2**self.n_epochs)\n",
-    "\n",
-    "        return self.eta * moment_corrected / (np.sqrt(second_corrected + delta))\n",
-    "\n",
-    "    def reset(self):\n",
-    "        self.n_epochs += 1\n",
-    "        self.moment = 0\n",
-    "        self.second = 0"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "532aecc2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### Usage of the above learning rate schedulers\n",
-    "\n",
-    "To initalize a scheduler, simply create the object and pass in the\n",
-    "necessary parameters such as the learning rate and the momentum as\n",
-    "shown below. As the Scheduler class is an abstract class it should not\n",
-    "called directly, and will raise an error upon usage."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "id": "b24b4414",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n",
-    "adam_scheduler = Adam(eta=1e-3, rho=0.9, rho2=0.999)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "32a25c0b",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Here is a small example for how a segment of code using schedulers\n",
-    "could look. Switching out the schedulers is simple."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "id": "7a7d273f",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "weights = np.ones((3,3))\n",
-    "print(f\"Before scheduler:\\n{weights=}\")\n",
-    "\n",
-    "epochs = 10\n",
-    "for e in range(epochs):\n",
-    "    gradient = np.random.rand(3, 3)\n",
-    "    change = adam_scheduler.update_change(gradient)\n",
-    "    weights = weights - change\n",
-    "    adam_scheduler.reset()\n",
-    "\n",
-    "print(f\"\\nAfter scheduler:\\n{weights=}\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d34cd45c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### Cost functions\n",
-    "\n",
-    "Here we discuss cost functions that can be used when creating the\n",
-    "neural network. Every cost function takes the target vector as its\n",
-    "parameter, and returns a function valued only at $x$ such that it may\n",
-    "easily be differentiated."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "id": "9ad6425d",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import autograd.numpy as np\n",
-    "\n",
-    "def CostOLS(target):\n",
-    "    \n",
-    "    def func(X):\n",
-    "        return (1.0 / target.shape[0]) * np.sum((target - X) ** 2)\n",
-    "\n",
-    "    return func\n",
-    "\n",
-    "\n",
-    "def CostLogReg(target):\n",
-    "\n",
-    "    def func(X):\n",
-    "        \n",
-    "        return -(1.0 / target.shape[0]) * np.sum(\n",
-    "            (target * np.log(X + 10e-10)) + ((1 - target) * np.log(1 - X + 10e-10))\n",
-    "        )\n",
-    "\n",
-    "    return func\n",
-    "\n",
-    "\n",
-    "def CostCrossEntropy(target):\n",
-    "    \n",
-    "    def func(X):\n",
-    "        return -(1.0 / target.size) * np.sum(target * np.log(X + 10e-10))\n",
-    "\n",
-    "    return func"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "baaaff79",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Below we give a short example of how these cost function may be used\n",
-    "to obtain results if you wish to test them out on your own using\n",
-    "AutoGrad's automatics differentiation."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "id": "78f11b83",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "from autograd import grad\n",
-    "\n",
-    "target = np.array([[1, 2, 3]]).T\n",
-    "a = np.array([[4, 5, 6]]).T\n",
-    "\n",
-    "cost_func = CostCrossEntropy\n",
-    "cost_func_derivative = grad(cost_func(target))\n",
-    "\n",
-    "valued_at_a = cost_func_derivative(a)\n",
-    "print(f\"Derivative of cost function {cost_func.__name__} valued at a:\\n{valued_at_a}\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "05285af5",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### Activation functions\n",
-    "\n",
-    "Finally, before we look at the neural network, we will look at the\n",
-    "activation functions which can be specified between the hidden layers\n",
-    "and as the output function. Each function can be valued for any given\n",
-    "vector or matrix X, and can be differentiated via derivate()."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "id": "7ac52c84",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import autograd.numpy as np\n",
-    "from autograd import elementwise_grad\n",
-    "\n",
-    "def identity(X):\n",
-    "    return X\n",
-    "\n",
-    "\n",
-    "def sigmoid(X):\n",
-    "    try:\n",
-    "        return 1.0 / (1 + np.exp(-X))\n",
-    "    except FloatingPointError:\n",
-    "        return np.where(X > np.zeros(X.shape), np.ones(X.shape), np.zeros(X.shape))\n",
-    "\n",
-    "\n",
-    "def softmax(X):\n",
-    "    X = X - np.max(X, axis=-1, keepdims=True)\n",
-    "    delta = 10e-10\n",
-    "    return np.exp(X) / (np.sum(np.exp(X), axis=-1, keepdims=True) + delta)\n",
-    "\n",
-    "\n",
-    "def RELU(X):\n",
-    "    return np.where(X > np.zeros(X.shape), X, np.zeros(X.shape))\n",
-    "\n",
-    "\n",
-    "def LRELU(X):\n",
-    "    delta = 10e-4\n",
-    "    return np.where(X > np.zeros(X.shape), X, delta * X)\n",
-    "\n",
-    "\n",
-    "def derivate(func):\n",
-    "    if func.__name__ == \"RELU\":\n",
-    "\n",
-    "        def func(X):\n",
-    "            return np.where(X > 0, 1, 0)\n",
-    "\n",
-    "        return func\n",
-    "\n",
-    "    elif func.__name__ == \"LRELU\":\n",
-    "\n",
-    "        def func(X):\n",
-    "            delta = 10e-4\n",
-    "            return np.where(X > 0, 1, delta)\n",
-    "\n",
-    "        return func\n",
-    "\n",
-    "    else:\n",
-    "        return elementwise_grad(func)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "873e7caa",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Below follows a short demonstration of how to use an activation\n",
-    "function. The derivative of the activation function will be important\n",
-    "when calculating the output delta term during backpropagation. Note\n",
-    "that derivate() can also be used for cost functions for a more\n",
-    "generalized approach."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "id": "bd43ac18",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "z = np.array([[4, 5, 6]]).T\n",
-    "print(f\"Input to activation function:\\n{z}\")\n",
-    "\n",
-    "act_func = sigmoid\n",
-    "a = act_func(z)\n",
-    "print(f\"\\nOutput from {act_func.__name__} activation function:\\n{a}\")\n",
-    "\n",
-    "act_func_derivative = derivate(act_func)\n",
-    "valued_at_z = act_func_derivative(a)\n",
-    "print(f\"\\nDerivative of {act_func.__name__} activation function valued at z:\\n{valued_at_z}\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3dc2175e",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### The Neural Network\n",
-    "\n",
-    "Now that we have gotten a good understanding of the implementation of\n",
-    "some important components, we can take a look at an object oriented\n",
-    "implementation of a feed forward neural network. The feed forward\n",
-    "neural network has been implemented as a class named FFNN, which can\n",
-    "be initiated as a regressor or classifier dependant on the choice of\n",
-    "cost function. The FFNN can have any number of input nodes, hidden\n",
-    "layers with any amount of hidden nodes, and any amount of output nodes\n",
-    "meaning it can perform multiclass classification as well as binary\n",
-    "classification and regression problems. Although there is a lot of\n",
-    "code present, it makes for an easy to use and generalizeable interface\n",
-    "for creating many types of neural networks as will be demonstrated\n",
-    "below."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "id": "5b4b161c",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import math\n",
-    "import autograd.numpy as np\n",
-    "import sys\n",
-    "import warnings\n",
-    "from autograd import grad, elementwise_grad\n",
-    "from random import random, seed\n",
-    "from copy import deepcopy, copy\n",
-    "from typing import Tuple, Callable\n",
-    "from sklearn.utils import resample\n",
-    "\n",
-    "warnings.simplefilter(\"error\")\n",
-    "\n",
-    "\n",
-    "class FFNN:\n",
-    "    \"\"\"\n",
-    "    Description:\n",
-    "    ------------\n",
-    "        Feed Forward Neural Network with interface enabling flexible design of a\n",
-    "        nerual networks architecture and the specification of activation function\n",
-    "        in the hidden layers and output layer respectively. This model can be used\n",
-    "        for both regression and classification problems, depending on the output function.\n",
-    "\n",
-    "    Attributes:\n",
-    "    ------------\n",
-    "        I   dimensions (tuple[int]): A list of positive integers, which specifies the\n",
-    "            number of nodes in each of the networks layers. The first integer in the array\n",
-    "            defines the number of nodes in the input layer, the second integer defines number\n",
-    "            of nodes in the first hidden layer and so on until the last number, which\n",
-    "            specifies the number of nodes in the output layer.\n",
-    "        II  hidden_func (Callable): The activation function for the hidden layers\n",
-    "        III output_func (Callable): The activation function for the output layer\n",
-    "        IV  cost_func (Callable): Our cost function\n",
-    "        V   seed (int): Sets random seed, makes results reproducible\n",
-    "    \"\"\"\n",
-    "\n",
-    "    def __init__(\n",
-    "        self,\n",
-    "        dimensions: tuple[int],\n",
-    "        hidden_func: Callable = sigmoid,\n",
-    "        output_func: Callable = lambda x: x,\n",
-    "        cost_func: Callable = CostOLS,\n",
-    "        seed: int = None,\n",
-    "    ):\n",
-    "        self.dimensions = dimensions\n",
-    "        self.hidden_func = hidden_func\n",
-    "        self.output_func = output_func\n",
-    "        self.cost_func = cost_func\n",
-    "        self.seed = seed\n",
-    "        self.weights = list()\n",
-    "        self.schedulers_weight = list()\n",
-    "        self.schedulers_bias = list()\n",
-    "        self.a_matrices = list()\n",
-    "        self.z_matrices = list()\n",
-    "        self.classification = None\n",
-    "\n",
-    "        self.reset_weights()\n",
-    "        self._set_classification()\n",
-    "\n",
-    "    def fit(\n",
-    "        self,\n",
-    "        X: np.ndarray,\n",
-    "        t: np.ndarray,\n",
-    "        scheduler: Scheduler,\n",
-    "        batches: int = 1,\n",
-    "        epochs: int = 100,\n",
-    "        lam: float = 0,\n",
-    "        X_val: np.ndarray = None,\n",
-    "        t_val: np.ndarray = None,\n",
-    "    ):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            This function performs the training the neural network by performing the feedforward and backpropagation\n",
-    "            algorithm to update the networks weights.\n",
-    "\n",
-    "        Parameters:\n",
-    "        ------------\n",
-    "            I    X (np.ndarray) : training data\n",
-    "            II   t (np.ndarray) : target data\n",
-    "            III  scheduler (Scheduler) : specified scheduler (algorithm for optimization of gradient descent)\n",
-    "            IV   scheduler_args (list[int]) : list of all arguments necessary for scheduler\n",
-    "\n",
-    "        Optional Parameters:\n",
-    "        ------------\n",
-    "            V    batches (int) : number of batches the datasets are split into, default equal to 1\n",
-    "            VI   epochs (int) : number of iterations used to train the network, default equal to 100\n",
-    "            VII  lam (float) : regularization hyperparameter lambda\n",
-    "            VIII X_val (np.ndarray) : validation set\n",
-    "            IX   t_val (np.ndarray) : validation target set\n",
-    "\n",
-    "        Returns:\n",
-    "        ------------\n",
-    "            I   scores (dict) : A dictionary containing the performance metrics of the model.\n",
-    "                The number of the metrics depends on the parameters passed to the fit-function.\n",
-    "\n",
-    "        \"\"\"\n",
-    "\n",
-    "        # setup \n",
-    "        if self.seed is not None:\n",
-    "            np.random.seed(self.seed)\n",
-    "\n",
-    "        val_set = False\n",
-    "        if X_val is not None and t_val is not None:\n",
-    "            val_set = True\n",
-    "\n",
-    "        # creating arrays for score metrics\n",
-    "        train_errors = np.empty(epochs)\n",
-    "        train_errors.fill(np.nan)\n",
-    "        val_errors = np.empty(epochs)\n",
-    "        val_errors.fill(np.nan)\n",
-    "\n",
-    "        train_accs = np.empty(epochs)\n",
-    "        train_accs.fill(np.nan)\n",
-    "        val_accs = np.empty(epochs)\n",
-    "        val_accs.fill(np.nan)\n",
-    "\n",
-    "        self.schedulers_weight = list()\n",
-    "        self.schedulers_bias = list()\n",
-    "\n",
-    "        batch_size = X.shape[0] // batches\n",
-    "\n",
-    "        X, t = resample(X, t)\n",
-    "\n",
-    "        # this function returns a function valued only at X\n",
-    "        cost_function_train = self.cost_func(t)\n",
-    "        if val_set:\n",
-    "            cost_function_val = self.cost_func(t_val)\n",
-    "\n",
-    "        # create schedulers for each weight matrix\n",
-    "        for i in range(len(self.weights)):\n",
-    "            self.schedulers_weight.append(copy(scheduler))\n",
-    "            self.schedulers_bias.append(copy(scheduler))\n",
-    "\n",
-    "        print(f\"{scheduler.__class__.__name__}: Eta={scheduler.eta}, Lambda={lam}\")\n",
-    "\n",
-    "        try:\n",
-    "            for e in range(epochs):\n",
-    "                for i in range(batches):\n",
-    "                    # allows for minibatch gradient descent\n",
-    "                    if i == batches - 1:\n",
-    "                        # If the for loop has reached the last batch, take all thats left\n",
-    "                        X_batch = X[i * batch_size :, :]\n",
-    "                        t_batch = t[i * batch_size :, :]\n",
-    "                    else:\n",
-    "                        X_batch = X[i * batch_size : (i + 1) * batch_size, :]\n",
-    "                        t_batch = t[i * batch_size : (i + 1) * batch_size, :]\n",
-    "\n",
-    "                    self._feedforward(X_batch)\n",
-    "                    self._backpropagate(X_batch, t_batch, lam)\n",
-    "\n",
-    "                # reset schedulers for each epoch (some schedulers pass in this call)\n",
-    "                for scheduler in self.schedulers_weight:\n",
-    "                    scheduler.reset()\n",
-    "\n",
-    "                for scheduler in self.schedulers_bias:\n",
-    "                    scheduler.reset()\n",
-    "\n",
-    "                # computing performance metrics\n",
-    "                pred_train = self.predict(X)\n",
-    "                train_error = cost_function_train(pred_train)\n",
-    "\n",
-    "                train_errors[e] = train_error\n",
-    "                if val_set:\n",
-    "                    \n",
-    "                    pred_val = self.predict(X_val)\n",
-    "                    val_error = cost_function_val(pred_val)\n",
-    "                    val_errors[e] = val_error\n",
-    "\n",
-    "                if self.classification:\n",
-    "                    train_acc = self._accuracy(self.predict(X), t)\n",
-    "                    train_accs[e] = train_acc\n",
-    "                    if val_set:\n",
-    "                        val_acc = self._accuracy(pred_val, t_val)\n",
-    "                        val_accs[e] = val_acc\n",
-    "\n",
-    "                # printing progress bar\n",
-    "                progression = e / epochs\n",
-    "                print_length = self._progress_bar(\n",
-    "                    progression,\n",
-    "                    train_error=train_errors[e],\n",
-    "                    train_acc=train_accs[e],\n",
-    "                    val_error=val_errors[e],\n",
-    "                    val_acc=val_accs[e],\n",
-    "                )\n",
-    "        except KeyboardInterrupt:\n",
-    "            # allows for stopping training at any point and seeing the result\n",
-    "            pass\n",
-    "\n",
-    "        # visualization of training progression (similiar to tensorflow progression bar)\n",
-    "        sys.stdout.write(\"\\r\" + \" \" * print_length)\n",
-    "        sys.stdout.flush()\n",
-    "        self._progress_bar(\n",
-    "            1,\n",
-    "            train_error=train_errors[e],\n",
-    "            train_acc=train_accs[e],\n",
-    "            val_error=val_errors[e],\n",
-    "            val_acc=val_accs[e],\n",
-    "        )\n",
-    "        sys.stdout.write(\"\")\n",
-    "\n",
-    "        # return performance metrics for the entire run\n",
-    "        scores = dict()\n",
-    "\n",
-    "        scores[\"train_errors\"] = train_errors\n",
-    "\n",
-    "        if val_set:\n",
-    "            scores[\"val_errors\"] = val_errors\n",
-    "\n",
-    "        if self.classification:\n",
-    "            scores[\"train_accs\"] = train_accs\n",
-    "\n",
-    "            if val_set:\n",
-    "                scores[\"val_accs\"] = val_accs\n",
-    "\n",
-    "        return scores\n",
-    "\n",
-    "    def predict(self, X: np.ndarray, *, threshold=0.5):\n",
-    "        \"\"\"\n",
-    "         Description:\n",
-    "         ------------\n",
-    "             Performs prediction after training of the network has been finished.\n",
-    "\n",
-    "         Parameters:\n",
-    "        ------------\n",
-    "             I   X (np.ndarray): The design matrix, with n rows of p features each\n",
-    "\n",
-    "         Optional Parameters:\n",
-    "         ------------\n",
-    "             II  threshold (float) : sets minimal value for a prediction to be predicted as the positive class\n",
-    "                 in classification problems\n",
-    "\n",
-    "         Returns:\n",
-    "         ------------\n",
-    "             I   z (np.ndarray): A prediction vector (row) for each row in our design matrix\n",
-    "                 This vector is thresholded if regression=False, meaning that classification results\n",
-    "                 in a vector of 1s and 0s, while regressions in an array of decimal numbers\n",
-    "\n",
-    "        \"\"\"\n",
-    "\n",
-    "        predict = self._feedforward(X)\n",
-    "\n",
-    "        if self.classification:\n",
-    "            return np.where(predict > threshold, 1, 0)\n",
-    "        else:\n",
-    "            return predict\n",
-    "\n",
-    "    def reset_weights(self):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Resets/Reinitializes the weights in order to train the network for a new problem.\n",
-    "\n",
-    "        \"\"\"\n",
-    "        if self.seed is not None:\n",
-    "            np.random.seed(self.seed)\n",
-    "\n",
-    "        self.weights = list()\n",
-    "        for i in range(len(self.dimensions) - 1):\n",
-    "            weight_array = np.random.randn(\n",
-    "                self.dimensions[i] + 1, self.dimensions[i + 1]\n",
-    "            )\n",
-    "            weight_array[0, :] = np.random.randn(self.dimensions[i + 1]) * 0.01\n",
-    "\n",
-    "            self.weights.append(weight_array)\n",
-    "\n",
-    "    def _feedforward(self, X: np.ndarray):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Calculates the activation of each layer starting at the input and ending at the output.\n",
-    "            Each following activation is calculated from a weighted sum of each of the preceeding\n",
-    "            activations (except in the case of the input layer).\n",
-    "\n",
-    "        Parameters:\n",
-    "        ------------\n",
-    "            I   X (np.ndarray): The design matrix, with n rows of p features each\n",
-    "\n",
-    "        Returns:\n",
-    "        ------------\n",
-    "            I   z (np.ndarray): A prediction vector (row) for each row in our design matrix\n",
-    "        \"\"\"\n",
-    "\n",
-    "        # reset matrices\n",
-    "        self.a_matrices = list()\n",
-    "        self.z_matrices = list()\n",
-    "\n",
-    "        # if X is just a vector, make it into a matrix\n",
-    "        if len(X.shape) == 1:\n",
-    "            X = X.reshape((1, X.shape[0]))\n",
-    "\n",
-    "        # Add a coloumn of zeros as the first coloumn of the design matrix, in order\n",
-    "        # to add bias to our data\n",
-    "        bias = np.ones((X.shape[0], 1)) * 0.01\n",
-    "        X = np.hstack([bias, X])\n",
-    "\n",
-    "        # a^0, the nodes in the input layer (one a^0 for each row in X - where the\n",
-    "        # exponent indicates layer number).\n",
-    "        a = X\n",
-    "        self.a_matrices.append(a)\n",
-    "        self.z_matrices.append(a)\n",
-    "\n",
-    "        # The feed forward algorithm\n",
-    "        for i in range(len(self.weights)):\n",
-    "            if i < len(self.weights) - 1:\n",
-    "                z = a @ self.weights[i]\n",
-    "                self.z_matrices.append(z)\n",
-    "                a = self.hidden_func(z)\n",
-    "                # bias column again added to the data here\n",
-    "                bias = np.ones((a.shape[0], 1)) * 0.01\n",
-    "                a = np.hstack([bias, a])\n",
-    "                self.a_matrices.append(a)\n",
-    "            else:\n",
-    "                try:\n",
-    "                    # a^L, the nodes in our output layers\n",
-    "                    z = a @ self.weights[i]\n",
-    "                    a = self.output_func(z)\n",
-    "                    self.a_matrices.append(a)\n",
-    "                    self.z_matrices.append(z)\n",
-    "                except Exception as OverflowError:\n",
-    "                    print(\n",
-    "                        \"OverflowError in fit() in FFNN\\nHOW TO DEBUG ERROR: Consider lowering your learning rate or scheduler specific parameters such as momentum, or check if your input values need scaling\"\n",
-    "                    )\n",
-    "\n",
-    "        # this will be a^L\n",
-    "        return a\n",
-    "\n",
-    "    def _backpropagate(self, X, t, lam):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Performs the backpropagation algorithm. In other words, this method\n",
-    "            calculates the gradient of all the layers starting at the\n",
-    "            output layer, and moving from right to left accumulates the gradient until\n",
-    "            the input layer is reached. Each layers respective weights are updated while\n",
-    "            the algorithm propagates backwards from the output layer (auto-differentation in reverse mode).\n",
-    "\n",
-    "        Parameters:\n",
-    "        ------------\n",
-    "            I   X (np.ndarray): The design matrix, with n rows of p features each.\n",
-    "            II  t (np.ndarray): The target vector, with n rows of p targets.\n",
-    "            III lam (float32): regularization parameter used to punish the weights in case of overfitting\n",
-    "\n",
-    "        Returns:\n",
-    "        ------------\n",
-    "            No return value.\n",
-    "\n",
-    "        \"\"\"\n",
-    "        out_derivative = derivate(self.output_func)\n",
-    "        hidden_derivative = derivate(self.hidden_func)\n",
-    "\n",
-    "        for i in range(len(self.weights) - 1, -1, -1):\n",
-    "            # delta terms for output\n",
-    "            if i == len(self.weights) - 1:\n",
-    "                # for multi-class classification\n",
-    "                if (\n",
-    "                    self.output_func.__name__ == \"softmax\"\n",
-    "                ):\n",
-    "                    delta_matrix = self.a_matrices[i + 1] - t\n",
-    "                # for single class classification\n",
-    "                else:\n",
-    "                    cost_func_derivative = grad(self.cost_func(t))\n",
-    "                    delta_matrix = out_derivative(\n",
-    "                        self.z_matrices[i + 1]\n",
-    "                    ) * cost_func_derivative(self.a_matrices[i + 1])\n",
-    "\n",
-    "            # delta terms for hidden layer\n",
-    "            else:\n",
-    "                delta_matrix = (\n",
-    "                    self.weights[i + 1][1:, :] @ delta_matrix.T\n",
-    "                ).T * hidden_derivative(self.z_matrices[i + 1])\n",
-    "\n",
-    "            # calculate gradient\n",
-    "            gradient_weights = self.a_matrices[i][:, 1:].T @ delta_matrix\n",
-    "            gradient_bias = np.sum(delta_matrix, axis=0).reshape(\n",
-    "                1, delta_matrix.shape[1]\n",
-    "            )\n",
-    "\n",
-    "            # regularization term\n",
-    "            gradient_weights += self.weights[i][1:, :] * lam\n",
-    "\n",
-    "            # use scheduler\n",
-    "            update_matrix = np.vstack(\n",
-    "                [\n",
-    "                    self.schedulers_bias[i].update_change(gradient_bias),\n",
-    "                    self.schedulers_weight[i].update_change(gradient_weights),\n",
-    "                ]\n",
-    "            )\n",
-    "\n",
-    "            # update weights and bias\n",
-    "            self.weights[i] -= update_matrix\n",
-    "\n",
-    "    def _accuracy(self, prediction: np.ndarray, target: np.ndarray):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Calculates accuracy of given prediction to target\n",
-    "\n",
-    "        Parameters:\n",
-    "        ------------\n",
-    "            I   prediction (np.ndarray): vector of predicitons output network\n",
-    "                (1s and 0s in case of classification, and real numbers in case of regression)\n",
-    "            II  target (np.ndarray): vector of true values (What the network ideally should predict)\n",
-    "\n",
-    "        Returns:\n",
-    "        ------------\n",
-    "            A floating point number representing the percentage of correctly classified instances.\n",
-    "        \"\"\"\n",
-    "        assert prediction.size == target.size\n",
-    "        return np.average((target == prediction))\n",
-    "    def _set_classification(self):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Decides if FFNN acts as classifier (True) og regressor (False),\n",
-    "            sets self.classification during init()\n",
-    "        \"\"\"\n",
-    "        self.classification = False\n",
-    "        if (\n",
-    "            self.cost_func.__name__ == \"CostLogReg\"\n",
-    "            or self.cost_func.__name__ == \"CostCrossEntropy\"\n",
-    "        ):\n",
-    "            self.classification = True\n",
-    "\n",
-    "    def _progress_bar(self, progression, **kwargs):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Displays progress of training\n",
-    "        \"\"\"\n",
-    "        print_length = 40\n",
-    "        num_equals = int(progression * print_length)\n",
-    "        num_not = print_length - num_equals\n",
-    "        arrow = \">\" if num_equals > 0 else \"\"\n",
-    "        bar = \"[\" + \"=\" * (num_equals - 1) + arrow + \"-\" * num_not + \"]\"\n",
-    "        perc_print = self._format(progression * 100, decimals=5)\n",
-    "        line = f\"  {bar} {perc_print}% \"\n",
-    "\n",
-    "        for key in kwargs:\n",
-    "            if not np.isnan(kwargs[key]):\n",
-    "                value = self._format(kwargs[key], decimals=4)\n",
-    "                line += f\"| {key}: {value} \"\n",
-    "        sys.stdout.write(\"\\r\" + line)\n",
-    "        sys.stdout.flush()\n",
-    "        return len(line)\n",
-    "\n",
-    "    def _format(self, value, decimals=4):\n",
-    "        \"\"\"\n",
-    "        Description:\n",
-    "        ------------\n",
-    "            Formats decimal numbers for progress bar\n",
-    "        \"\"\"\n",
-    "        if value > 0:\n",
-    "            v = value\n",
-    "        elif value < 0:\n",
-    "            v = -10 * value\n",
-    "        else:\n",
-    "            v = 1\n",
-    "        n = 1 + math.floor(math.log10(v))\n",
-    "        if n >= decimals - 1:\n",
-    "            return str(round(value))\n",
-    "        return f\"{value:.{decimals-n-1}f}\""
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9596ae53",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Before we make a model, we will quickly generate a dataset we can use\n",
-    "for our linear regression problem as shown below"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "id": "a11f680f",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import autograd.numpy as np\n",
-    "from sklearn.model_selection import train_test_split\n",
-    "\n",
-    "def SkrankeFunction(x, y):\n",
-    "    return np.ravel(0 + 1*x + 2*y + 3*x**2 + 4*x*y + 5*y**2)\n",
-    "\n",
-    "def create_X(x, y, n):\n",
-    "    if len(x.shape) > 1:\n",
-    "        x = np.ravel(x)\n",
-    "        y = np.ravel(y)\n",
-    "\n",
-    "    N = len(x)\n",
-    "    l = int((n + 1) * (n + 2) / 2)  # Number of elements in beta\n",
-    "    X = np.ones((N, l))\n",
-    "\n",
-    "    for i in range(1, n + 1):\n",
-    "        q = int((i) * (i + 1) / 2)\n",
-    "        for k in range(i + 1):\n",
-    "            X[:, q + k] = (x ** (i - k)) * (y**k)\n",
-    "\n",
-    "    return X\n",
-    "\n",
-    "step=0.5\n",
-    "x = np.arange(0, 1, step)\n",
-    "y = np.arange(0, 1, step)\n",
-    "x, y = np.meshgrid(x, y)\n",
-    "target = SkrankeFunction(x, y)\n",
-    "target = target.reshape(target.shape[0], 1)\n",
-    "\n",
-    "poly_degree=3\n",
-    "X = create_X(x, y, poly_degree)\n",
-    "\n",
-    "X_train, X_test, t_train, t_test = train_test_split(X, target)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0fc39e40",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Now that we have our dataset ready for the regression, we can create\n",
-    "our regressor. Note that with the seed parameter, we can make sure our\n",
-    "results stay the same every time we run the neural network. For\n",
-    "inititialization, we simply specify the dimensions (we wish the amount\n",
-    "of input nodes to be equal to the datapoints, and the output to\n",
-    "predict one value)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "id": "a67ab3a0",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "input_nodes = X_train.shape[1]\n",
-    "output_nodes = 1\n",
-    "\n",
-    "linear_regression = FFNN((input_nodes, output_nodes), output_func=identity, cost_func=CostOLS, seed=2023)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3add8665",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "We then fit our model with our training data using the scheduler of our choice."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "id": "4a4fbc7a",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
-    "\n",
-    "scheduler = Constant(eta=1e-3)\n",
-    "scores = linear_regression.fit(X_train, t_train, scheduler)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4dff1871",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Due to the progress bar we can see the MSE (train_error) throughout\n",
-    "the FFNN's training. Note that the fit() function has some optional\n",
-    "parameters with defualt arguments. For example, the regularization\n",
-    "hyperparameter can be left ignored if not needed, and equally the FFNN\n",
-    "will by default run for 100 epochs. These can easily be changed, such\n",
-    "as for example:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "id": "ad40e38c",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
-    "\n",
-    "scores = linear_regression.fit(X_train, t_train, scheduler, lam=1e-4, epochs=1000)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "43cd1e22",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "We see that given more epochs to train on, the regressor reaches a lower MSE.\n",
-    "\n",
-    "Let us then switch to a binary classification. We use a binary\n",
-    "classification dataset, and follow a similar setup to the regression\n",
-    "case."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "id": "cde36b38",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "from sklearn.datasets import load_breast_cancer\n",
-    "from sklearn.preprocessing import MinMaxScaler\n",
-    "\n",
-    "wisconsin = load_breast_cancer()\n",
-    "X = wisconsin.data\n",
-    "target = wisconsin.target\n",
-    "target = target.reshape(target.shape[0], 1)\n",
-    "\n",
-    "X_train, X_val, t_train, t_val = train_test_split(X, target)\n",
-    "\n",
-    "scaler = MinMaxScaler()\n",
-    "scaler.fit(X_train)\n",
-    "X_train = scaler.transform(X_train)\n",
-    "X_val = scaler.transform(X_val)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "id": "2bc572a4",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "input_nodes = X_train.shape[1]\n",
-    "output_nodes = 1\n",
-    "\n",
-    "logistic_regression = FFNN((input_nodes, output_nodes), output_func=sigmoid, cost_func=CostLogReg, seed=2023)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e3e6fa31",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "We will now make use of our validation data by passing it into our fit function as a keyword argument"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "id": "575ceb29",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
-    "\n",
-    "scheduler = Adam(eta=1e-3, rho=0.9, rho2=0.999)\n",
-    "scores = logistic_regression.fit(X_train, t_train, scheduler, epochs=1000, X_val=X_val, t_val=t_val)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "622015f0",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Finally, we will create a neural network with 2 hidden layers with activation functions."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "id": "9c075b36",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "input_nodes = X_train.shape[1]\n",
-    "hidden_nodes1 = 100\n",
-    "hidden_nodes2 = 30\n",
-    "output_nodes = 1\n",
-    "\n",
-    "dims = (input_nodes, hidden_nodes1, hidden_nodes2, output_nodes)\n",
-    "\n",
-    "neural_network = FFNN(dims, hidden_func=RELU, output_func=sigmoid, cost_func=CostLogReg, seed=2023)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "id": "44ded771",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "neural_network.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
-    "\n",
-    "scheduler = Adam(eta=1e-4, rho=0.9, rho2=0.999)\n",
-    "scores = neural_network.fit(X_train, t_train, scheduler, epochs=1000, X_val=X_val, t_val=t_val)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "317e6e5c",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "### Multiclass classification\n",
-    "\n",
-    "Finally, we will demonstrate the use case of multiclass classification\n",
-    "using our FFNN with the famous MNIST dataset, which contain images of\n",
-    "digits between the range of 0 to 9."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "id": "8911de9d",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "from sklearn.datasets import load_digits\n",
-    "\n",
-    "def onehot(target: np.ndarray):\n",
-    "    onehot = np.zeros((target.size, target.max() + 1))\n",
-    "    onehot[np.arange(target.size), target] = 1\n",
-    "    return onehot\n",
-    "\n",
-    "digits = load_digits()\n",
-    "\n",
-    "X = digits.data\n",
-    "target = digits.target\n",
-    "target = onehot(target)\n",
-    "\n",
-    "input_nodes = 64\n",
-    "hidden_nodes1 = 100\n",
-    "hidden_nodes2 = 30\n",
-    "output_nodes = 10\n",
-    "\n",
-    "dims = (input_nodes, hidden_nodes1, hidden_nodes2, output_nodes)\n",
-    "\n",
-    "multiclass = FFNN(dims, hidden_func=LRELU, output_func=softmax, cost_func=CostCrossEntropy)\n",
-    "\n",
-    "multiclass.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
-    "\n",
-    "scheduler = Adam(eta=1e-4, rho=0.9, rho2=0.999)\n",
-    "scores = multiclass.fit(X, target, scheduler, epochs=1000)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "82d61377",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "## Testing the XOR gate and other gates\n",
-    "\n",
-    "Let us now use our code to test the XOR gate."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "id": "2a72a374",
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
-    "\n",
-    "# The XOR gate\n",
-    "yXOR = np.array( [[ 0], [1] ,[1], [0]])\n",
-    "\n",
-    "input_nodes = X.shape[1]\n",
-    "output_nodes = 1\n",
-    "\n",
-    "logistic_regression = FFNN((input_nodes, output_nodes), output_func=sigmoid, cost_func=CostLogReg, seed=2023)\n",
-    "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
-    "scheduler = Adam(eta=1e-1, rho=0.9, rho2=0.999)\n",
-    "scores = logistic_regression.fit(X, yXOR, scheduler, epochs=1000)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2d892009",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "Not bad, but the results depend strongly on the learning reate. Try different learning rates."
-   ]
-  }
- ],
- "metadata": {},
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/doc/pub/week43/html/week43-bs.html b/doc/pub/week43/html/week43-bs.html
index 52b4cc052..1c5be76a7 100644
--- a/doc/pub/week43/html/week43-bs.html
+++ b/doc/pub/week43/html/week43-bs.html
@@ -400,9 +400,9 @@ MathJax.Hub.Config({
 <li> Reminder from last week, see also lecture notes from week 42 at <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html" target="_self"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html</tt></a> as well as those from week 41, see see <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html" target="_self"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html</tt></a>.</li> 
 <li> Building our own Feed-forward Neural Network.</li>
 <li> Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13..</li> 
-<li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.
-<!-- * Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_self"><tt>https://youtu.be/vkBNTn-MLqs</tt></a> -->
-<!-- * Whiteboard notes on solving differential equations at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_self"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a> --></li>
+<li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.</li>
+<li> Video of lecture at <a href="https://youtu.be/Gi6mzxAT0Ew" target="_self"><tt>https://youtu.be/Gi6mzxAT0Ew</tt></a></li>
+<li> Whiteboard notes at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_self"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a></li>  
 </ol>
 </div>
 </div>
diff --git a/doc/pub/week43/html/week43-reveal.html b/doc/pub/week43/html/week43-reveal.html
index 04d2f9675..3678cbd4c 100644
--- a/doc/pub/week43/html/week43-reveal.html
+++ b/doc/pub/week43/html/week43-reveal.html
@@ -201,9 +201,9 @@ MathJax.Hub.Config({
 <p><li> Reminder from last week, see also lecture notes from week 42 at <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html" target="_blank"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html</tt></a> as well as those from week 41, see see <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html" target="_blank"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html</tt></a>.</li> 
 <p><li> Building our own Feed-forward Neural Network.</li>
 <p><li> Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13..</li> 
-<p><li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.
-<!-- * Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_blank"><tt>https://youtu.be/vkBNTn-MLqs</tt></a> -->
-<!-- * Whiteboard notes on solving differential equations at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_blank"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a> --></li>
+<p><li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.</li>
+<p><li> Video of lecture at <a href="https://youtu.be/Gi6mzxAT0Ew" target="_blank"><tt>https://youtu.be/Gi6mzxAT0Ew</tt></a></li>
+<p><li> Whiteboard notes at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_blank"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a></li>  
 </ol>
 </div>
 </section>
diff --git a/doc/pub/week43/html/week43-solarized.html b/doc/pub/week43/html/week43-solarized.html
index 7efee0800..37267c7df 100644
--- a/doc/pub/week43/html/week43-solarized.html
+++ b/doc/pub/week43/html/week43-solarized.html
@@ -321,9 +321,9 @@ MathJax.Hub.Config({
 <li> Reminder from last week, see also lecture notes from week 42 at <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html" target="_blank"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html</tt></a> as well as those from week 41, see see <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html" target="_blank"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html</tt></a>.</li> 
 <li> Building our own Feed-forward Neural Network.</li>
 <li> Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13..</li> 
-<li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.
-<!-- * Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_blank"><tt>https://youtu.be/vkBNTn-MLqs</tt></a> -->
-<!-- * Whiteboard notes on solving differential equations at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_blank"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a> --></li>
+<li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.</li>
+<li> Video of lecture at <a href="https://youtu.be/Gi6mzxAT0Ew" target="_blank"><tt>https://youtu.be/Gi6mzxAT0Ew</tt></a></li>
+<li> Whiteboard notes at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_blank"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a></li>  
 </ol>
 </div>
 
diff --git a/doc/pub/week43/html/week43.html b/doc/pub/week43/html/week43.html
index 901ed5b9b..ac8c08010 100644
--- a/doc/pub/week43/html/week43.html
+++ b/doc/pub/week43/html/week43.html
@@ -398,9 +398,9 @@ MathJax.Hub.Config({
 <li> Reminder from last week, see also lecture notes from week 42 at <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html" target="_blank"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html</tt></a> as well as those from week 41, see see <a href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html" target="_blank"><tt>https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html</tt></a>.</li> 
 <li> Building our own Feed-forward Neural Network.</li>
 <li> Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13..</li> 
-<li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.
-<!-- * Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_blank"><tt>https://youtu.be/vkBNTn-MLqs</tt></a> -->
-<!-- * Whiteboard notes on solving differential equations at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_blank"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a> --></li>
+<li> Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.</li>
+<li> Video of lecture at <a href="https://youtu.be/Gi6mzxAT0Ew" target="_blank"><tt>https://youtu.be/Gi6mzxAT0Ew</tt></a></li>
+<li> Whiteboard notes at <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf" target="_blank"><tt>https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf</tt></a></li>  
 </ol>
 </div>
 
diff --git a/doc/pub/week43/ipynb/.ipynb_checkpoints/week43-checkpoint.ipynb b/doc/pub/week43/ipynb/.ipynb_checkpoints/week43-checkpoint.ipynb
index d9260ad4f..713df5efc 100644
--- a/doc/pub/week43/ipynb/.ipynb_checkpoints/week43-checkpoint.ipynb
+++ b/doc/pub/week43/ipynb/.ipynb_checkpoints/week43-checkpoint.ipynb
@@ -2,54 +2,3663 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "b10156d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "<!-- dom:TITLE: Week 43: Solving Differential Equations with Deep Learning and Dimensionality Reduction methods -->\n",
-    "# Week 43: Solving Differential Equations with Deep Learning and Dimensionality Reduction methods\n",
-    "<!-- dom:AUTHOR: Morten Hjorth-Jensen at Department of Physics, University of Oslo & Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University -->\n",
-    "<!-- Author: -->  \n",
-    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html week43.do.txt --no_mako -->\n",
+    "<!-- dom:TITLE: Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f85baa2f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations\n",
+    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway\n",
     "\n",
-<<<<<<< HEAD
-    "Date: **Oct 22, 2020**\n",
-=======
-    "Date: **Oct 23, 2020**\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
+    "Date: **October 20, 2025**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "543fad4a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Plans for week 43\n",
     "\n",
-    "Copyright 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
+    "**Material for the lecture on Monday October 20, 2025.**\n",
+    "\n",
+    "1. Reminder from last week, see also lecture notes from week 42 at <https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week42.html> as well as those from week 41, see see <https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html>. \n",
+    "\n",
+    "2. Building our own Feed-forward Neural Network.\n",
+    "\n",
+    "3. Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13.. \n",
+    "\n",
+    "4. Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.\n",
+    "<!-- * Video of lecture at <https://youtu.be/vkBNTn-MLqs> -->\n",
+    "<!-- * Whiteboard notes on solving differential equations at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf> -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "72acb4e9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Exercises and lab session week 43\n",
+    "**Lab sessions on Tuesday and Wednesday.**\n",
+    "\n",
+    "1. Work  on writing your own neural network code and discussions of project 2. If you didn't get time to do the exercises from the two last weeks, we recommend doing so as these exercises give you the basic elements of a neural network code.\n",
+    "\n",
+    "2. The exercises this week are tailored to the optional part of project 2, and deal with studying ways to display results from classification problems"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "361768dc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Automatic differentiation\n",
+    "\n",
+    "In our discussions of ordinary differential equations and neural network codes\n",
+    "we will also study the usage of Autograd, see for example <https://www.youtube.com/watch?v=fRf4l5qaX1M&ab_channel=AlexSmola> in computing gradients for deep learning. For the documentation of Autograd and examples see the Autograd documentation at <https://github.com/HIPS/autograd> and the lecture slides from week 41, see <https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/week41.html>."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3e058671",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Back propagation and automatic differentiation\n",
+    "\n",
+    "For more details on the back propagation algorithm and automatic differentiation see\n",
+    "1. <https://www.jmlr.org/papers/volume18/17-468/17-468.pdf>\n",
+    "\n",
+    "2. <https://deepimaging.github.io/lectures/lecture_11_Backpropagation.pdf>\n",
+    "\n",
+    "3. Slides 12-44 at <http://cs231n.stanford.edu/slides/2017/cs231n_2017_lecture4.pdf>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cbbf2bf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Lecture Monday  October 20"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78e2de21",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations\n",
+    "This is a reminder from last week.\n",
+    "\n",
+    "**The architecture (our model).**\n",
+    "\n",
+    "1. Set up your inputs and outputs (scalars, vectors, matrices or higher-order arrays)\n",
+    "\n",
+    "2. Define the number of hidden layers and hidden nodes\n",
+    "\n",
+    "3. Define activation functions for hidden layers and output layers\n",
+    "\n",
+    "4. Define optimizer (plan learning rate, momentum, ADAgrad, RMSprop, ADAM etc) and array of initial learning rates\n",
+    "\n",
+    "5. Define cost function and possible regularization terms with hyperparameters\n",
+    "\n",
+    "6. Initialize weights and biases\n",
+    "\n",
+    "7. Fix number of iterations for the feed forward part and back propagation part"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "41a3dc23",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up the back propagation algorithm, part 1\n",
+    "\n",
+    "Let us write this out in the form of an algorithm.\n",
+    "\n",
+    "**First**, we set up the input data $\\boldsymbol{x}$ and the activations\n",
+    "$\\boldsymbol{z}_1$ of the input layer and compute the activation function and\n",
+    "the pertinent outputs $\\boldsymbol{a}^1$.\n",
+    "\n",
+    "**Secondly**, we perform then the feed forward till we reach the output\n",
+    "layer and compute all $\\boldsymbol{z}_l$ of the input layer and compute the\n",
+    "activation function and the pertinent outputs $\\boldsymbol{a}^l$ for\n",
+    "$l=1,2,3,\\dots,L$.\n",
+    "\n",
+    "**Notation**: The first hidden layer has $l=1$ as label and the final output layer has $l=L$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0e4ac2c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up the back propagation algorithm, part 2\n",
+    "\n",
+    "Thereafter we compute the ouput error $\\boldsymbol{\\delta}^L$ by computing all"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9fd2f83",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\delta_j^L = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "16e2b900",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f9f4b9d8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "01be6441",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Setting up the Back propagation algorithm, part 3\n",
+    "\n",
+    "Finally, we update the weights and the biases using gradient descent\n",
+    "for each $l=L-1,L-2,\\dots,1$ (the first hidden layer) and update the weights and biases\n",
+    "according to the rules"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce898b85",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e2e7314",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b7114295",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $\\eta$ being the learning rate."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "69dfa048",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Updating the gradients\n",
+    "\n",
+    "With the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6efa469c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "076e4937",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,1$ and update the weights and biases according to the rules"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1072f5a1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f77a7074",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f12effab",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Activation functions\n",
+    "\n",
+    "A property that characterizes a neural network, other than its\n",
+    "connectivity, is the choice of activation function(s).  The following\n",
+    "restrictions are imposed on an activation function for an FFNN to\n",
+    "fulfill the universal approximation theorem\n",
+    "\n",
+    "  * Non-constant\n",
+    "\n",
+    "  * Bounded\n",
+    "\n",
+    "  * Monotonically-increasing\n",
+    "\n",
+    "  * Continuous"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31eb54b1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Activation functions, examples\n",
+    "\n",
+    "Typical examples are the logistic *Sigmoid*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7a549168",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\sigma(x) = \\frac{1}{1 + e^{-x}},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce35ae73",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and the *hyperbolic tangent* function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d6cdfc89",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\sigma(x) = \\tanh(x)\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ddd59bb0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The RELU function family\n",
+    "\n",
+    "The ReLU activation function suffers from a problem known as the dying\n",
+    "ReLUs: during training, some neurons effectively die, meaning they\n",
+    "stop outputting anything other than 0.\n",
+    "\n",
+    "In some cases, you may find that half of your network’s neurons are\n",
+    "dead, especially if you used a large learning rate. During training,\n",
+    "if a neuron’s weights get updated such that the weighted sum of the\n",
+    "neuron’s inputs is negative, it will start outputting 0. When this\n",
+    "happen, the neuron is unlikely to come back to life since the gradient\n",
+    "of the ReLU function is 0 when its input is negative."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f2a78e55",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## ELU function\n",
+    "\n",
+    "To solve this problem, nowadays practitioners use a variant of the\n",
+    "ReLU function, such as the leaky ReLU discussed above or the so-called\n",
+    "exponential linear unit (ELU) function"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cde73faf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\  z & z \\ge 0.\\end{array}\\right.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "08048672",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Which activation function should we use?\n",
+    "\n",
+    "In general it seems that the ELU activation function is better than\n",
+    "the leaky ReLU function (and its variants), which is better than\n",
+    "ReLU. ReLU performs better than $\\tanh$ which in turn performs better\n",
+    "than the logistic function.\n",
+    "\n",
+    "If runtime performance is an issue, then you may opt for the leaky\n",
+    "ReLU function over the ELU function If you don’t want to tweak yet\n",
+    "another hyperparameter, you may just use the default $\\alpha$ of\n",
+    "$0.01$ for the leaky ReLU, and $1$ for ELU. If you have spare time and\n",
+    "computing power, you can use cross-validation or bootstrap to evaluate\n",
+    "other activation functions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a7085280",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on activation functions, output layers\n",
+    "\n",
+    "In most cases you can use the ReLU activation function in the hidden\n",
+    "layers (or one of its variants).\n",
+    "\n",
+    "It is a bit faster to compute than other activation functions, and the\n",
+    "gradient descent optimization does in general not get stuck.\n",
+    "\n",
+    "**For the output layer:**\n",
+    "\n",
+    "* For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).\n",
+    "\n",
+    "* For regression tasks, you can simply use no activation function at all."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "291e4fb2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Building neural networks in Tensorflow and Keras\n",
+    "\n",
+    "Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn\n",
+    "and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy\n",
+    "and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.  \n",
+    "\n",
+    "In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite\n",
+    "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n",
+    "NumPy arrays."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a8c5f4c2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Tensorflow\n",
+    "\n",
+    "Tensorflow is an open source library machine learning library\n",
+    "developed by the Google Brain team for internal use. It was released\n",
+    "under the Apache 2.0 open source license in November 9, 2015.\n",
+    "\n",
+    "Tensorflow is a computational framework that allows you to construct\n",
+    "machine learning models at different levels of abstraction, from\n",
+    "high-level, object-oriented APIs like Keras, down to the C++ kernels\n",
+    "that Tensorflow is built upon. The higher levels of abstraction are\n",
+    "simpler to use, but less flexible, and our choice of implementation\n",
+    "should reflect the problems we are trying to solve.\n",
+    "\n",
+    "[Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation\n",
+    "in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*\n",
+    "to represent your model, and then create a Tensorflow *session* to run the graph.\n",
+    "\n",
+    "In this guide we will analyze the same data as we did in our NumPy and\n",
+    "scikit-learn tutorial, gathered from the MNIST database of images. We\n",
+    "will give an introduction to the lower level Python Application\n",
+    "Program Interfaces (APIs), and see how we use them to build our graph.\n",
+    "Then we will build (effectively) the same graph in Keras, to see just\n",
+    "how simple solving a machine learning problem can be.\n",
+    "\n",
+    "To install tensorflow on Unix/Linux systems, use pip as"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9a0aac03",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "pip3 install tensorflow"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca0c7865",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n",
+    "(current release of CPU-only TensorFlow)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "d0c581f7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "conda create -n tf tensorflow\n",
+    "conda activate tf"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe086bc9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "To install the current release of GPU TensorFlow"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "f551fad9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "conda create -n tf-gpu tensorflow-gpu\n",
+    "conda activate tf-gpu"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "58152cef",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Keras\n",
+    "\n",
+    "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n",
+    "that supports Tensorflow, CTNK and Theano as backends.  \n",
+    "If you have Anaconda installed you may run the following command"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "579b6a4a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "conda install keras"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5da15206",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "You can look up the [instructions here](https://keras.io/) for more information.\n",
+    "\n",
+    "We will to a large extent use **keras** in this course."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cc970d32",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Collect and pre-process data\n",
+    "\n",
+    "Let us look again at the MINST data set."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "a4f2c8a8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)\n",
+      "labels = (n_inputs) = (1797,)\n",
+      "X = (n_inputs, n_features) = (1797, 64)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 1200x1200 with 5 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "# import necessary packages\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import tensorflow as tf\n",
+    "from sklearn import datasets\n",
+    "\n",
+    "\n",
+    "# ensure the same random numbers appear every time\n",
+    "np.random.seed(0)\n",
+    "\n",
+    "# display images in notebook\n",
+    "%matplotlib inline\n",
+    "plt.rcParams['figure.figsize'] = (12,12)\n",
+    "\n",
+    "\n",
+    "# download MNIST dataset\n",
+    "digits = datasets.load_digits()\n",
+    "\n",
+    "# define inputs and labels\n",
+    "inputs = digits.images\n",
+    "labels = digits.target\n",
+    "\n",
+    "print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
+    "print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
+    "\n",
+    "\n",
+    "# flatten the image\n",
+    "# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
+    "n_inputs = len(inputs)\n",
+    "inputs = inputs.reshape(n_inputs, -1)\n",
+    "print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
+    "\n",
+    "\n",
+    "# choose some random images to display\n",
+    "indices = np.arange(n_inputs)\n",
+    "random_indices = np.random.choice(indices, size=5)\n",
+    "\n",
+    "for i, image in enumerate(digits.images[random_indices]):\n",
+    "    plt.subplot(1, 5, i+1)\n",
+    "    plt.axis('off')\n",
+    "    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
+    "    plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "d0c06f34",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from tensorflow.keras.layers import Input\n",
+    "from tensorflow.keras.models import Sequential      #This allows appending layers to existing models\n",
+    "from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer\n",
+    "from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n",
+    "from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)\n",
+    "from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function\n",
+    "\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "\n",
+    "# one-hot representation of labels\n",
+    "labels = to_categorical(labels)\n",
+    "\n",
+    "# split into train and test data\n",
+    "train_size = 0.8\n",
+    "test_size = 1 - train_size\n",
+    "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
+    "                                                    test_size=test_size)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "8272ca95",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "epochs = 100\n",
+    "batch_size = 100\n",
+    "n_neurons_layer1 = 100\n",
+    "n_neurons_layer2 = 50\n",
+    "n_categories = 10\n",
+    "eta_vals = np.logspace(-5, 1, 7)\n",
+    "lmbd_vals = np.logspace(-5, 1, 7)\n",
+    "def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):\n",
+    "    model = Sequential()\n",
+    "    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
+    "    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
+    "    model.add(Dense(n_categories, activation='softmax'))\n",
+    "    \n",
+    "    sgd = optimizers.SGD(learning_rate=eta)\n",
+    "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
+    "    \n",
+    "    return model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "616613a7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n",
+      "2025-10-20 13:19:24.847167: W tensorflow/tsl/platform/profile_utils/cpu_utils.cc:128] Failed to get CPU frequency: 0 Hz\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "12/12 [==============================] - 1s 77ms/step - loss: 2.3648 - accuracy: 0.0833\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.083\n",
+      "\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 2.5249 - accuracy: 0.1278\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.128\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 2.6284 - accuracy: 0.1250\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.125\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 3.8276 - accuracy: 0.0889\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.089\n",
+      "\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 17.2502 - accuracy: 0.1056\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.106\n",
+      "\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 137.7438 - accuracy: 0.1167\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.117\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 791.1546 - accuracy: 0.1028\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1e-05\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.103\n",
+      "\n",
+      "12/12 [==============================] - 0s 18ms/step - loss: 2.4095 - accuracy: 0.0917\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.092\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "12/12 [==============================] - 0s 13ms/step - loss: 2.4702 - accuracy: 0.1167\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.117\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.4999 - accuracy: 0.0917\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.092\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 3.8617 - accuracy: 0.0889\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.089\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 15.9813 - accuracy: 0.1139\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.114\n",
+      "\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 81.3855 - accuracy: 0.0889\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.089\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 6.0620 - accuracy: 0.1139\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.0001\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.114\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 2.2036 - accuracy: 0.3917\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.392\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.1645 - accuracy: 0.3694\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.369\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 2.3489 - accuracy: 0.3333\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.333\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 3.5798 - accuracy: 0.2611\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.261\n",
+      "\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 10.2003 - accuracy: 0.4333\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.433\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 2.6594 - accuracy: 0.0889\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.089\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.3030 - accuracy: 0.1167\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.001\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.117\n",
+      "\n",
+      "12/12 [==============================] - 0s 12ms/step - loss: 1.0555 - accuracy: 0.8694\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.869\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 1.1238 - accuracy: 0.8583\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.858\n",
+      "\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 1.2342 - accuracy: 0.8806\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.881\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 2.1114 - accuracy: 0.8833\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.883\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.2776 - accuracy: 0.5139\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.514\n",
+      "\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 2.3079 - accuracy: 0.0778\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.078\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 2.3081 - accuracy: 0.0778\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.01\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.078\n",
+      "\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 0.1069 - accuracy: 0.9722\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.972\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 0.1282 - accuracy: 0.9667\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.967\n",
+      "\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 0.2611 - accuracy: 0.9694\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.969\n",
+      "\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 0.4928 - accuracy: 0.9639\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.964\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 1.6045 - accuracy: 0.6222\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.622\n",
+      "\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 2.3218 - accuracy: 0.0861\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.086\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 1597.5353 - accuracy: 0.0444\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  0.1\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.044\n",
+      "\n",
+      "12/12 [==============================] - 0s 12ms/step - loss: 0.0781 - accuracy: 0.9806\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.981\n",
+      "\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 0.0868 - accuracy: 0.9861\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.986\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 0.4859 - accuracy: 0.9222\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.922\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 2.9575 - accuracy: 0.1583\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.158\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 2.5299 - accuracy: 0.0889\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.089\n",
+      "\n",
+      "12/12 [==============================] - 0s 12ms/step - loss: 371.5039 - accuracy: 0.1139\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.114\n",
+      "\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: nan - accuracy: 0.0778\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  1.0\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.078\n",
+      "\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 4.4885 - accuracy: 0.1056\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  10.0\n",
+      "Lambda =  1e-05\n",
+      "Test accuracy: 0.106\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.4071 - accuracy: 0.1250\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  10.0\n",
+      "Lambda =  0.0001\n",
+      "Test accuracy: 0.125\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.4936 - accuracy: 0.1167\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  10.0\n",
+      "Lambda =  0.001\n",
+      "Test accuracy: 0.117\n",
+      "\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 2.4569 - accuracy: 0.0861\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  10.0\n",
+      "Lambda =  0.01\n",
+      "Test accuracy: 0.086\n",
+      "\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 959.3554 - accuracy: 0.1167\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  10.0\n",
+      "Lambda =  0.1\n",
+      "Test accuracy: 0.117\n",
+      "\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: nan - accuracy: 0.0778\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Learning rate =  10.0\n",
+      "Lambda =  1.0\n",
+      "Test accuracy: 0.078\n",
+      "\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: nan - accuracy: 0.0778\n",
+      "Learning rate =  10.0\n",
+      "Lambda =  10.0\n",
+      "Test accuracy: 0.078\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
+    "        \n",
+    "for i, eta in enumerate(eta_vals):\n",
+    "    for j, lmbd in enumerate(lmbd_vals):\n",
+    "        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,\n",
+    "                                         eta=eta, lmbd=lmbd)\n",
+    "        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n",
+    "        scores = DNN.evaluate(X_test, Y_test)\n",
+    "        \n",
+    "        DNN_keras[i][j] = DNN\n",
+    "        \n",
+    "        print(\"Learning rate = \", eta)\n",
+    "        print(\"Lambda = \", lmbd)\n",
+    "        print(\"Test accuracy: %.3f\" % scores[1])\n",
+    "        print()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "f57a7b70",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "45/45 [==============================] - 1s 15ms/step - loss: 2.3829 - accuracy: 0.0995\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.3648 - accuracy: 0.0833\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 2.5299 - accuracy: 0.0946\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 2.5249 - accuracy: 0.1278\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 2.5953 - accuracy: 0.1427\n",
+      "12/12 [==============================] - 0s 12ms/step - loss: 2.6284 - accuracy: 0.1250\n",
+      "45/45 [==============================] - 1s 17ms/step - loss: 3.8118 - accuracy: 0.0995\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 3.8276 - accuracy: 0.0889\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 17.2903 - accuracy: 0.0905\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 17.2502 - accuracy: 0.1056\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 137.7373 - accuracy: 0.0932\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 137.7438 - accuracy: 0.1167\n",
+      "45/45 [==============================] - 1s 16ms/step - loss: 791.1535 - accuracy: 0.0960\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 791.1546 - accuracy: 0.1028\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 2.3828 - accuracy: 0.1016\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.4095 - accuracy: 0.0917\n",
+      "45/45 [==============================] - 1s 13ms/step - loss: 2.5109 - accuracy: 0.0939\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 2.4702 - accuracy: 0.1167\n",
+      "45/45 [==============================] - 1s 13ms/step - loss: 2.5195 - accuracy: 0.0647\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 2.4999 - accuracy: 0.0917\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 3.8371 - accuracy: 0.1044\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 3.8617 - accuracy: 0.0889\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 15.9897 - accuracy: 0.0953\n",
+      "12/12 [==============================] - 0s 17ms/step - loss: 15.9813 - accuracy: 0.1139\n",
+      "45/45 [==============================] - 1s 17ms/step - loss: 81.3778 - accuracy: 0.1037\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 81.3855 - accuracy: 0.0889\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 6.0581 - accuracy: 0.0967\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 6.0620 - accuracy: 0.1139\n",
+      "45/45 [==============================] - 1s 16ms/step - loss: 2.1808 - accuracy: 0.4509\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 2.2036 - accuracy: 0.3917\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 2.1643 - accuracy: 0.3800\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.1645 - accuracy: 0.3694\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 2.3447 - accuracy: 0.3834\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.3489 - accuracy: 0.3333\n",
+      "45/45 [==============================] - 1s 13ms/step - loss: 3.5658 - accuracy: 0.2902\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 3.5798 - accuracy: 0.2611\n",
+      "45/45 [==============================] - 1s 13ms/step - loss: 10.1893 - accuracy: 0.4621\n",
+      "12/12 [==============================] - 0s 12ms/step - loss: 10.2003 - accuracy: 0.4333\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 2.6642 - accuracy: 0.1044\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 2.6594 - accuracy: 0.0889\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 2.3056 - accuracy: 0.0939\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 2.3030 - accuracy: 0.1167\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 1.0158 - accuracy: 0.8970\n",
+      "12/12 [==============================] - 0s 15ms/step - loss: 1.0555 - accuracy: 0.8694\n",
+      "45/45 [==============================] - 1s 16ms/step - loss: 1.0723 - accuracy: 0.8824\n",
+      "12/12 [==============================] - 0s 16ms/step - loss: 1.1238 - accuracy: 0.8583\n",
+      "45/45 [==============================] - 1s 16ms/step - loss: 1.1955 - accuracy: 0.8866\n",
+      "12/12 [==============================] - 0s 18ms/step - loss: 1.2342 - accuracy: 0.8806\n",
+      "45/45 [==============================] - 1s 17ms/step - loss: 2.0627 - accuracy: 0.9088\n",
+      "12/12 [==============================] - 0s 12ms/step - loss: 2.1114 - accuracy: 0.8833\n",
+      "45/45 [==============================] - 1s 13ms/step - loss: 2.2699 - accuracy: 0.5560\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 2.2776 - accuracy: 0.5139\n",
+      "45/45 [==============================] - 1s 11ms/step - loss: 2.3020 - accuracy: 0.1044\n",
+      "12/12 [==============================] - 0s 11ms/step - loss: 2.3079 - accuracy: 0.0778\n",
+      "45/45 [==============================] - 1s 12ms/step - loss: 2.3020 - accuracy: 0.1044\n",
+      "12/12 [==============================] - 0s 13ms/step - loss: 2.3081 - accuracy: 0.0778\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 0.0471 - accuracy: 0.9986\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 0.1069 - accuracy: 0.9722\n",
+      "45/45 [==============================] - 1s 15ms/step - loss: 0.0652 - accuracy: 0.9986\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 0.1282 - accuracy: 0.9667\n",
+      "45/45 [==============================] - 1s 25ms/step - loss: 0.2069 - accuracy: 0.9979\n",
+      "12/12 [==============================] - 0s 14ms/step - loss: 0.2611 - accuracy: 0.9694\n",
+      "45/45 [==============================] - 1s 14ms/step - loss: 0.4478 - accuracy: 0.9812\n",
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",
+      "text/plain": [
+       "<Figure size 1000x1000 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1000x1000 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# optional\n",
+    "# visual representation of grid search\n",
+    "# uses seaborn heatmap, could probably do this in matplotlib\n",
+    "import seaborn as sns\n",
+    "\n",
+    "sns.set()\n",
+    "\n",
+    "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
+    "\n",
+    "for i in range(len(eta_vals)):\n",
+    "    for j in range(len(lmbd_vals)):\n",
+    "        DNN = DNN_keras[i][j]\n",
+    "\n",
+    "        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]\n",
+    "        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]\n",
+    "\n",
+    "        \n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Training Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize = (10, 10))\n",
+    "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
+    "ax.set_title(\"Test Accuracy\")\n",
+    "ax.set_ylabel(\"$\\eta$\")\n",
+    "ax.set_xlabel(\"$\\lambda$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a61b50a8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Pytorch with the full MNIST data set"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "d220a7ad",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import torch\n",
+    "import torch.nn as nn\n",
+    "import torch.optim as optim\n",
+    "import torchvision\n",
+    "import torchvision.transforms as transforms\n",
+    "\n",
+    "# Device configuration: use GPU if available\n",
+    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
+    "\n",
+    "# MNIST dataset (downloads if not already present)\n",
+    "transform = transforms.Compose([\n",
+    "    transforms.ToTensor(),\n",
+    "    transforms.Normalize((0.5,), (0.5,))  # normalize to mean=0.5, std=0.5 (approx. [-1,1] pixel range)\n",
+    "])\n",
+    "train_dataset = torchvision.datasets.MNIST(root='./data', train=True, download=True, transform=transform)\n",
+    "test_dataset  = torchvision.datasets.MNIST(root='./data', train=False, download=True, transform=transform)\n",
+    "\n",
+    "train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=64, shuffle=True)\n",
+    "test_loader  = torch.utils.data.DataLoader(test_dataset, batch_size=64, shuffle=False)\n",
+    "\n",
+    "\n",
+    "class NeuralNet(nn.Module):\n",
+    "    def __init__(self):\n",
+    "        super(NeuralNet, self).__init__()\n",
+    "        self.fc1 = nn.Linear(28*28, 100)   # first hidden layer (784 -> 100)\n",
+    "        self.fc2 = nn.Linear(100, 100)    # second hidden layer (100 -> 100)\n",
+    "        self.fc3 = nn.Linear(100, 10)     # output layer (100 -> 10 classes)\n",
+    "    def forward(self, x):\n",
+    "        x = x.view(x.size(0), -1)         # flatten images into vectors of size 784\n",
+    "        x = torch.relu(self.fc1(x))       # hidden layer 1 + ReLU activation\n",
+    "        x = torch.relu(self.fc2(x))       # hidden layer 2 + ReLU activation\n",
+    "        x = self.fc3(x)                   # output layer (logits for 10 classes)\n",
+    "        return x\n",
+    "\n",
+    "model = NeuralNet().to(device)\n",
+    "\n",
+    "\n",
+    "criterion = nn.CrossEntropyLoss()\n",
+    "optimizer = optim.SGD(model.parameters(), lr=0.01, weight_decay=1e-4)\n",
+    "\n",
+    "num_epochs = 10\n",
+    "for epoch in range(num_epochs):\n",
+    "    model.train()  # set model to training mode\n",
+    "    running_loss = 0.0\n",
+    "    for images, labels in train_loader:\n",
+    "        # Move data to device (GPU if available, else CPU)\n",
+    "        images, labels = images.to(device), labels.to(device)\n",
+    "\n",
+    "        optimizer.zero_grad()            # reset gradients to zero\n",
+    "        outputs = model(images)          # forward pass: compute predictions\n",
+    "        loss = criterion(outputs, labels)  # compute cross-entropy loss\n",
+    "        loss.backward()                 # backpropagate to compute gradients\n",
+    "        optimizer.step()                # update weights using SGD step \n",
+    "\n",
+    "        running_loss += loss.item()\n",
+    "    # Compute average loss over all batches in this epoch\n",
+    "    avg_loss = running_loss / len(train_loader)\n",
+    "    print(f\"Epoch {epoch+1}/{num_epochs}, Loss: {avg_loss:.4f}\")\n",
+    "\n",
+    "#Evaluation on the Test Set\n",
     "\n",
     "\n",
     "\n",
+    "model.eval()  # set model to evaluation mode \n",
+    "correct = 0\n",
+    "total = 0\n",
+    "with torch.no_grad():  # disable gradient calculation for evaluation \n",
+    "    for images, labels in test_loader:\n",
+    "        images, labels = images.to(device), labels.to(device)\n",
+    "        outputs = model(images)\n",
+    "        _, predicted = torch.max(outputs, dim=1)  # class with highest score\n",
+    "        total += labels.size(0)\n",
+    "        correct += (predicted == labels).sum().item()\n",
     "\n",
-<<<<<<< HEAD
-    "* Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. \n",
+    "accuracy = 100 * correct / total\n",
+    "print(f\"Test Accuracy: {accuracy:.2f}%\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d87d7514",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And a similar example using Tensorflow with Keras"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "c6df6115",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "GPUs available: [PhysicalDevice(name='/physical_device:GPU:0', device_type='GPU')]\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:At this time, the v2.11+ optimizer `tf.keras.optimizers.SGD` runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at `tf.keras.optimizers.legacy.SGD`.\n",
+      "WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., `tf.keras.optimizers.legacy.SGD`.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Model: \"sequential_49\"\n",
+      "_________________________________________________________________\n",
+      " Layer (type)                Output Shape              Param #   \n",
+      "=================================================================\n",
+      " flatten (Flatten)           (None, 784)               0         \n",
+      "                                                                 \n",
+      " dense_147 (Dense)           (None, 100)               78500     \n",
+      "                                                                 \n",
+      " dense_148 (Dense)           (None, 100)               10100     \n",
+      "                                                                 \n",
+      " dense_149 (Dense)           (None, 10)                1010      \n",
+      "                                                                 \n",
+      "=================================================================\n",
+      "Total params: 89,610\n",
+      "Trainable params: 89,610\n",
+      "Non-trainable params: 0\n",
+      "_________________________________________________________________\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'\\n# 4) Train\\nhistory = model.fit(\\n    x_train, y_train,\\n    epochs=10,\\n    batch_size=64,\\n    validation_split=0.1,  # optional: monitor validation during training\\n    verbose=1\\n)\\n\\n# 5) Evaluate on test set\\ntest_loss, test_acc = model.evaluate(x_test, y_test, verbose=0)\\nprint(f\"Test accuracy: {test_acc:.4f}, Test loss: {test_loss:.4f}\")\\n'"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
     "\n",
-    "* Friday: Principal Component Analysis and Dimensionality Reduction\n",
-=======
-    "* Thursday: Wrapping up Recurrent Neural Networks and solving differential equations. [Video of Lecture October 22](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober22.mp4?vrtx=view-as-webpage)\n",
+    "import tensorflow as tf\n",
+    "from tensorflow import keras\n",
+    "from tensorflow.keras import layers, regularizers\n",
     "\n",
-    "* Friday: Principal Component Analysis and Dimensionality Reduction. [Video of Lecture October 23](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureOctober23.mp4?vrtx=view-as-webpage)\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
+    "# Check for GPU (TensorFlow will use it automatically if available)\n",
+    "gpus = tf.config.list_physical_devices('GPU')\n",
+    "print(f\"GPUs available: {gpus}\")\n",
     "\n",
-    "We will also study the usage of [Autograd](https://www.youtube.com/watch?v=fRf4l5qaX1M&ab_channel=AlexSmola) in computing gradients for deep learning. For the documentation of Autograd and examples see the lectures slides from [week 40](https://compphysics.github.io/MachineLearning/doc/pub/week40/html/week40.html) and the [Autograd doucmentation](https://github.com/HIPS/autograd).\n",
+    "# 1) Load and preprocess MNIST\n",
+    "(x_train, y_train), (x_test, y_test) = keras.datasets.mnist.load_data()\n",
+    "# Normalize to [0, 1]\n",
+    "x_train = (x_train.astype(\"float32\") / 255.0)\n",
+    "x_test  = (x_test.astype(\"float32\") / 255.0)\n",
     "\n",
-    "## Recurrent Neural Networks\n",
+    "# 2) Build the model: 784 -> 100 -> 100 -> 10\n",
+    "l2_reg = 1e-4  # L2 regularization strength\n",
     "\n",
-    "[Overview video](https://www.youtube.com/watch?v=SEnXr6v2ifU&ab_channel=AlexanderAmini).\n",
-    "See also lecture on Thursday October 22 and examples from [week 42](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html).\n",
+    "model = keras.Sequential([\n",
+    "    layers.Input(shape=(28, 28)),\n",
+    "    layers.Flatten(),\n",
+    "    layers.Dense(100, activation=\"relu\",\n",
+    "                 kernel_regularizer=regularizers.l2(l2_reg)),\n",
+    "    layers.Dense(100, activation=\"relu\",\n",
+    "                 kernel_regularizer=regularizers.l2(l2_reg)),\n",
+    "    layers.Dense(10, activation=\"softmax\")  # output probabilities for 10 classes\n",
+    "])\n",
     "\n",
-    "[IN5400 at UiO Lecture](https://www.uio.no/studier/emner/matnat/ifi/IN5400/v20/material/week10/in5400_2020_week10_recurrent_neural_network.pdf)\n",
+    "# 3) Compile with SGD + weight decay via L2 regularizers\n",
+    "model.compile(\n",
+    "    optimizer=keras.optimizers.SGD(learning_rate=0.01),\n",
+    "    loss=\"sparse_categorical_crossentropy\",\n",
+    "    metrics=[\"accuracy\"],\n",
+    ")\n",
     "\n",
-    "[CS231 at Stanford Lecture](https://www.youtube.com/watch?v=6niqTuYFZLQ&list=PLzUTmXVwsnXod6WNdg57Yc3zFx_f-RYsq&index=10&ab_channel=StanfordUniversitySchoolofEngineering)\n",
+    "model.summary()\n",
+    "\"\"\"\n",
+    "# 4) Train\n",
+    "history = model.fit(\n",
+    "    x_train, y_train,\n",
+    "    epochs=10,\n",
+    "    batch_size=64,\n",
+    "    validation_split=0.1,  # optional: monitor validation during training\n",
+    "    verbose=1\n",
+    ")\n",
     "\n",
-    "## Solving ODEs with Deep Learning\n",
+    "# 5) Evaluate on test set\n",
+    "test_loss, test_acc = model.evaluate(x_test, y_test, verbose=0)\n",
+    "print(f\"Test accuracy: {test_acc:.4f}, Test loss: {test_loss:.4f}\")\n",
+    "\"\"\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5fd4d319",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Building our own  neural network code\n",
+    "\n",
+    "Here we  present a flexible object oriented codebase\n",
+    "for a feed forward neural network, along with a demonstration of how\n",
+    "to use it. Before we get into the details of the neural network, we\n",
+    "will first present some implementations of various schedulers, cost\n",
+    "functions and activation functions that can be used together with the\n",
+    "neural network.\n",
+    "\n",
+    "The codes here were developed by Eric Reber and Gregor Kajda during spring 2023."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "64134feb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Learning rate methods\n",
+    "\n",
+    "The code below shows object oriented implementations of the Constant,\n",
+    "Momentum, Adagrad, AdagradMomentum, RMS prop and Adam schedulers. All\n",
+    "of the classes belong to the shared abstract Scheduler class, and\n",
+    "share the update_change() and reset() methods allowing for any of the\n",
+    "schedulers to be seamlessly used during the training stage, as will\n",
+    "later be shown in the fit() method of the neural\n",
+    "network. Update_change() only has one parameter, the gradient\n",
+    "($δ^l_ja^{l−1}_k$), and returns the change which will be subtracted\n",
+    "from the weights. The reset() function takes no parameters, and resets\n",
+    "the desired variables. For Constant and Momentum, reset does nothing."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "643f7a82",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "\n",
+    "class Scheduler:\n",
+    "    \"\"\"\n",
+    "    Abstract class for Schedulers\n",
+    "    \"\"\"\n",
+    "\n",
+    "    def __init__(self, eta):\n",
+    "        self.eta = eta\n",
+    "\n",
+    "    # should be overwritten\n",
+    "    def update_change(self, gradient):\n",
+    "        raise NotImplementedError\n",
+    "\n",
+    "    # overwritten if needed\n",
+    "    def reset(self):\n",
+    "        pass\n",
+    "\n",
+    "\n",
+    "class Constant(Scheduler):\n",
+    "    def __init__(self, eta):\n",
+    "        super().__init__(eta)\n",
+    "\n",
+    "    def update_change(self, gradient):\n",
+    "        return self.eta * gradient\n",
+    "    \n",
+    "    def reset(self):\n",
+    "        pass\n",
+    "\n",
+    "\n",
+    "class Momentum(Scheduler):\n",
+    "    def __init__(self, eta: float, momentum: float):\n",
+    "        super().__init__(eta)\n",
+    "        self.momentum = momentum\n",
+    "        self.change = 0\n",
+    "\n",
+    "    def update_change(self, gradient):\n",
+    "        self.change = self.momentum * self.change + self.eta * gradient\n",
+    "        return self.change\n",
+    "\n",
+    "    def reset(self):\n",
+    "        pass\n",
+    "\n",
+    "\n",
+    "class Adagrad(Scheduler):\n",
+    "    def __init__(self, eta):\n",
+    "        super().__init__(eta)\n",
+    "        self.G_t = None\n",
+    "\n",
+    "    def update_change(self, gradient):\n",
+    "        delta = 1e-8  # avoid division ny zero\n",
+    "\n",
+    "        if self.G_t is None:\n",
+    "            self.G_t = np.zeros((gradient.shape[0], gradient.shape[0]))\n",
+    "\n",
+    "        self.G_t += gradient @ gradient.T\n",
+    "\n",
+    "        G_t_inverse = 1 / (\n",
+    "            delta + np.sqrt(np.reshape(np.diagonal(self.G_t), (self.G_t.shape[0], 1)))\n",
+    "        )\n",
+    "        return self.eta * gradient * G_t_inverse\n",
+    "\n",
+    "    def reset(self):\n",
+    "        self.G_t = None\n",
+    "\n",
+    "\n",
+    "class AdagradMomentum(Scheduler):\n",
+    "    def __init__(self, eta, momentum):\n",
+    "        super().__init__(eta)\n",
+    "        self.G_t = None\n",
+    "        self.momentum = momentum\n",
+    "        self.change = 0\n",
+    "\n",
+    "    def update_change(self, gradient):\n",
+    "        delta = 1e-8  # avoid division ny zero\n",
+    "\n",
+    "        if self.G_t is None:\n",
+    "            self.G_t = np.zeros((gradient.shape[0], gradient.shape[0]))\n",
+    "\n",
+    "        self.G_t += gradient @ gradient.T\n",
+    "\n",
+    "        G_t_inverse = 1 / (\n",
+    "            delta + np.sqrt(np.reshape(np.diagonal(self.G_t), (self.G_t.shape[0], 1)))\n",
+    "        )\n",
+    "        self.change = self.change * self.momentum + self.eta * gradient * G_t_inverse\n",
+    "        return self.change\n",
+    "\n",
+    "    def reset(self):\n",
+    "        self.G_t = None\n",
+    "\n",
+    "\n",
+    "class RMS_prop(Scheduler):\n",
+    "    def __init__(self, eta, rho):\n",
+    "        super().__init__(eta)\n",
+    "        self.rho = rho\n",
+    "        self.second = 0.0\n",
+    "\n",
+    "    def update_change(self, gradient):\n",
+    "        delta = 1e-8  # avoid division ny zero\n",
+    "        self.second = self.rho * self.second + (1 - self.rho) * gradient * gradient\n",
+    "        return self.eta * gradient / (np.sqrt(self.second + delta))\n",
+    "\n",
+    "    def reset(self):\n",
+    "        self.second = 0.0\n",
+    "\n",
+    "\n",
+    "class Adam(Scheduler):\n",
+    "    def __init__(self, eta, rho, rho2):\n",
+    "        super().__init__(eta)\n",
+    "        self.rho = rho\n",
+    "        self.rho2 = rho2\n",
+    "        self.moment = 0\n",
+    "        self.second = 0\n",
+    "        self.n_epochs = 1\n",
+    "\n",
+    "    def update_change(self, gradient):\n",
+    "        delta = 1e-8  # avoid division ny zero\n",
+    "\n",
+    "        self.moment = self.rho * self.moment + (1 - self.rho) * gradient\n",
+    "        self.second = self.rho2 * self.second + (1 - self.rho2) * gradient * gradient\n",
+    "\n",
+    "        moment_corrected = self.moment / (1 - self.rho**self.n_epochs)\n",
+    "        second_corrected = self.second / (1 - self.rho2**self.n_epochs)\n",
+    "\n",
+    "        return self.eta * moment_corrected / (np.sqrt(second_corrected + delta))\n",
+    "\n",
+    "    def reset(self):\n",
+    "        self.n_epochs += 1\n",
+    "        self.moment = 0\n",
+    "        self.second = 0"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dfa32b7e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Usage of the above learning rate schedulers\n",
+    "\n",
+    "To initalize a scheduler, simply create the object and pass in the\n",
+    "necessary parameters such as the learning rate and the momentum as\n",
+    "shown below. As the Scheduler class is an abstract class it should not\n",
+    "called directly, and will raise an error upon usage."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "4b88b24e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n",
+    "adam_scheduler = Adam(eta=1e-3, rho=0.9, rho2=0.999)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2eea0e52",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Here is a small example for how a segment of code using schedulers\n",
+    "could look. Switching out the schedulers is simple."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "090bee3c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Before scheduler:\n",
+      "weights=array([[1., 1., 1.],\n",
+      "       [1., 1., 1.],\n",
+      "       [1., 1., 1.]])\n",
+      "\n",
+      "After scheduler:\n",
+      "weights=array([[0.993993  , 0.99403075, 0.99399314],\n",
+      "       [0.99399303, 0.99399301, 0.993993  ],\n",
+      "       [0.993993  , 0.99399301, 0.993993  ]])\n"
+     ]
+    }
+   ],
+   "source": [
+    "weights = np.ones((3,3))\n",
+    "print(f\"Before scheduler:\\n{weights=}\")\n",
+    "\n",
+    "epochs = 10\n",
+    "for e in range(epochs):\n",
+    "    gradient = np.random.rand(3, 3)\n",
+    "    change = adam_scheduler.update_change(gradient)\n",
+    "    weights = weights - change\n",
+    "    adam_scheduler.reset()\n",
+    "\n",
+    "print(f\"\\nAfter scheduler:\\n{weights=}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e0eee286",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Cost functions\n",
+    "\n",
+    "Here we discuss cost functions that can be used when creating the\n",
+    "neural network. Every cost function takes the target vector as its\n",
+    "parameter, and returns a function valued only at $x$ such that it may\n",
+    "easily be differentiated."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "191224bb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "\n",
+    "def CostOLS(target):\n",
+    "    \n",
+    "    def func(X):\n",
+    "        return (1.0 / target.shape[0]) * np.sum((target - X) ** 2)\n",
+    "\n",
+    "    return func\n",
+    "\n",
+    "\n",
+    "def CostLogReg(target):\n",
+    "\n",
+    "    def func(X):\n",
+    "        \n",
+    "        return -(1.0 / target.shape[0]) * np.sum(\n",
+    "            (target * np.log(X + 10e-10)) + ((1 - target) * np.log(1 - X + 10e-10))\n",
+    "        )\n",
+    "\n",
+    "    return func\n",
+    "\n",
+    "\n",
+    "def CostCrossEntropy(target):\n",
+    "    \n",
+    "    def func(X):\n",
+    "        return -(1.0 / target.size) * np.sum(target * np.log(X + 10e-10))\n",
+    "\n",
+    "    return func"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7f4a0238",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Below we give a short example of how these cost function may be used\n",
+    "to obtain results if you wish to test them out on your own using\n",
+    "AutoGrad's automatics differentiation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "d822b656",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Derivative of cost function CostCrossEntropy valued at a:\n",
+      "[[-0.08333333]\n",
+      " [-0.13333333]\n",
+      " [-0.16666667]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "from autograd import grad\n",
+    "\n",
+    "target = np.array([[1, 2, 3]]).T\n",
+    "a = np.array([[4, 5, 6]]).T\n",
+    "\n",
+    "cost_func = CostCrossEntropy\n",
+    "cost_func_derivative = grad(cost_func(target))\n",
+    "\n",
+    "valued_at_a = cost_func_derivative(a)\n",
+    "print(f\"Derivative of cost function {cost_func.__name__} valued at a:\\n{valued_at_a}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ff32a3b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Activation functions\n",
+    "\n",
+    "Finally, before we look at the neural network, we will look at the\n",
+    "activation functions which can be specified between the hidden layers\n",
+    "and as the output function. Each function can be valued for any given\n",
+    "vector or matrix X, and can be differentiated via derivate()."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "90045474",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import elementwise_grad\n",
+    "\n",
+    "def identity(X):\n",
+    "    return X\n",
+    "\n",
+    "\n",
+    "def sigmoid(X):\n",
+    "    try:\n",
+    "        return 1.0 / (1 + np.exp(-X))\n",
+    "    except FloatingPointError:\n",
+    "        return np.where(X > np.zeros(X.shape), np.ones(X.shape), np.zeros(X.shape))\n",
+    "\n",
+    "\n",
+    "def softmax(X):\n",
+    "    X = X - np.max(X, axis=-1, keepdims=True)\n",
+    "    delta = 10e-10\n",
+    "    return np.exp(X) / (np.sum(np.exp(X), axis=-1, keepdims=True) + delta)\n",
+    "\n",
+    "\n",
+    "def RELU(X):\n",
+    "    return np.where(X > np.zeros(X.shape), X, np.zeros(X.shape))\n",
+    "\n",
+    "\n",
+    "def LRELU(X):\n",
+    "    delta = 10e-4\n",
+    "    return np.where(X > np.zeros(X.shape), X, delta * X)\n",
+    "\n",
+    "\n",
+    "def derivate(func):\n",
+    "    if func.__name__ == \"RELU\":\n",
+    "\n",
+    "        def func(X):\n",
+    "            return np.where(X > 0, 1, 0)\n",
+    "\n",
+    "        return func\n",
+    "\n",
+    "    elif func.__name__ == \"LRELU\":\n",
+    "\n",
+    "        def func(X):\n",
+    "            delta = 10e-4\n",
+    "            return np.where(X > 0, 1, delta)\n",
+    "\n",
+    "        return func\n",
+    "\n",
+    "    else:\n",
+    "        return elementwise_grad(func)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eec681dc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Below follows a short demonstration of how to use an activation\n",
+    "function. The derivative of the activation function will be important\n",
+    "when calculating the output delta term during backpropagation. Note\n",
+    "that derivate() can also be used for cost functions for a more\n",
+    "generalized approach."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "a36d4506",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Input to activation function:\n",
+      "[[4]\n",
+      " [5]\n",
+      " [6]]\n",
+      "\n",
+      "Output from sigmoid activation function:\n",
+      "[[0.98201379]\n",
+      " [0.99330715]\n",
+      " [0.99752738]]\n",
+      "\n",
+      "Derivative of sigmoid activation function valued at z:\n",
+      "[[0.19824029]\n",
+      " [0.19721923]\n",
+      " [0.19683648]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "z = np.array([[4, 5, 6]]).T\n",
+    "print(f\"Input to activation function:\\n{z}\")\n",
+    "\n",
+    "act_func = sigmoid\n",
+    "a = act_func(z)\n",
+    "print(f\"\\nOutput from {act_func.__name__} activation function:\\n{a}\")\n",
+    "\n",
+    "act_func_derivative = derivate(act_func)\n",
+    "valued_at_z = act_func_derivative(a)\n",
+    "print(f\"\\nDerivative of {act_func.__name__} activation function valued at z:\\n{valued_at_z}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d2358581",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### The Neural Network\n",
+    "\n",
+    "Now that we have gotten a good understanding of the implementation of\n",
+    "some important components, we can take a look at an object oriented\n",
+    "implementation of a feed forward neural network. The feed forward\n",
+    "neural network has been implemented as a class named FFNN, which can\n",
+    "be initiated as a regressor or classifier dependant on the choice of\n",
+    "cost function. The FFNN can have any number of input nodes, hidden\n",
+    "layers with any amount of hidden nodes, and any amount of output nodes\n",
+    "meaning it can perform multiclass classification as well as binary\n",
+    "classification and regression problems. Although there is a lot of\n",
+    "code present, it makes for an easy to use and generalizeable interface\n",
+    "for creating many types of neural networks as will be demonstrated\n",
+    "below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "9dd0b112",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "import autograd.numpy as np\n",
+    "import sys\n",
+    "import warnings\n",
+    "from autograd import grad, elementwise_grad\n",
+    "from random import random, seed\n",
+    "from copy import deepcopy, copy\n",
+    "from typing import Tuple, Callable\n",
+    "from sklearn.utils import resample\n",
+    "\n",
+    "warnings.simplefilter(\"error\")\n",
+    "\n",
+    "\n",
+    "class FFNN:\n",
+    "    \"\"\"\n",
+    "    Description:\n",
+    "    ------------\n",
+    "        Feed Forward Neural Network with interface enabling flexible design of a\n",
+    "        nerual networks architecture and the specification of activation function\n",
+    "        in the hidden layers and output layer respectively. This model can be used\n",
+    "        for both regression and classification problems, depending on the output function.\n",
+    "\n",
+    "    Attributes:\n",
+    "    ------------\n",
+    "        I   dimensions (tuple[int]): A list of positive integers, which specifies the\n",
+    "            number of nodes in each of the networks layers. The first integer in the array\n",
+    "            defines the number of nodes in the input layer, the second integer defines number\n",
+    "            of nodes in the first hidden layer and so on until the last number, which\n",
+    "            specifies the number of nodes in the output layer.\n",
+    "        II  hidden_func (Callable): The activation function for the hidden layers\n",
+    "        III output_func (Callable): The activation function for the output layer\n",
+    "        IV  cost_func (Callable): Our cost function\n",
+    "        V   seed (int): Sets random seed, makes results reproducible\n",
+    "    \"\"\"\n",
+    "\n",
+    "    def __init__(\n",
+    "        self,\n",
+    "        dimensions: tuple[int],\n",
+    "        hidden_func: Callable = sigmoid,\n",
+    "        output_func: Callable = lambda x: x,\n",
+    "        cost_func: Callable = CostOLS,\n",
+    "        seed: int = None,\n",
+    "    ):\n",
+    "        self.dimensions = dimensions\n",
+    "        self.hidden_func = hidden_func\n",
+    "        self.output_func = output_func\n",
+    "        self.cost_func = cost_func\n",
+    "        self.seed = seed\n",
+    "        self.weights = list()\n",
+    "        self.schedulers_weight = list()\n",
+    "        self.schedulers_bias = list()\n",
+    "        self.a_matrices = list()\n",
+    "        self.z_matrices = list()\n",
+    "        self.classification = None\n",
+    "\n",
+    "        self.reset_weights()\n",
+    "        self._set_classification()\n",
+    "\n",
+    "    def fit(\n",
+    "        self,\n",
+    "        X: np.ndarray,\n",
+    "        t: np.ndarray,\n",
+    "        scheduler: Scheduler,\n",
+    "        batches: int = 1,\n",
+    "        epochs: int = 100,\n",
+    "        lam: float = 0,\n",
+    "        X_val: np.ndarray = None,\n",
+    "        t_val: np.ndarray = None,\n",
+    "    ):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            This function performs the training the neural network by performing the feedforward and backpropagation\n",
+    "            algorithm to update the networks weights.\n",
+    "\n",
+    "        Parameters:\n",
+    "        ------------\n",
+    "            I    X (np.ndarray) : training data\n",
+    "            II   t (np.ndarray) : target data\n",
+    "            III  scheduler (Scheduler) : specified scheduler (algorithm for optimization of gradient descent)\n",
+    "            IV   scheduler_args (list[int]) : list of all arguments necessary for scheduler\n",
+    "\n",
+    "        Optional Parameters:\n",
+    "        ------------\n",
+    "            V    batches (int) : number of batches the datasets are split into, default equal to 1\n",
+    "            VI   epochs (int) : number of iterations used to train the network, default equal to 100\n",
+    "            VII  lam (float) : regularization hyperparameter lambda\n",
+    "            VIII X_val (np.ndarray) : validation set\n",
+    "            IX   t_val (np.ndarray) : validation target set\n",
+    "\n",
+    "        Returns:\n",
+    "        ------------\n",
+    "            I   scores (dict) : A dictionary containing the performance metrics of the model.\n",
+    "                The number of the metrics depends on the parameters passed to the fit-function.\n",
+    "\n",
+    "        \"\"\"\n",
+    "\n",
+    "        # setup \n",
+    "        if self.seed is not None:\n",
+    "            np.random.seed(self.seed)\n",
+    "\n",
+    "        val_set = False\n",
+    "        if X_val is not None and t_val is not None:\n",
+    "            val_set = True\n",
+    "\n",
+    "        # creating arrays for score metrics\n",
+    "        train_errors = np.empty(epochs)\n",
+    "        train_errors.fill(np.nan)\n",
+    "        val_errors = np.empty(epochs)\n",
+    "        val_errors.fill(np.nan)\n",
+    "\n",
+    "        train_accs = np.empty(epochs)\n",
+    "        train_accs.fill(np.nan)\n",
+    "        val_accs = np.empty(epochs)\n",
+    "        val_accs.fill(np.nan)\n",
+    "\n",
+    "        self.schedulers_weight = list()\n",
+    "        self.schedulers_bias = list()\n",
+    "\n",
+    "        batch_size = X.shape[0] // batches\n",
+    "\n",
+    "        X, t = resample(X, t)\n",
+    "\n",
+    "        # this function returns a function valued only at X\n",
+    "        cost_function_train = self.cost_func(t)\n",
+    "        if val_set:\n",
+    "            cost_function_val = self.cost_func(t_val)\n",
+    "\n",
+    "        # create schedulers for each weight matrix\n",
+    "        for i in range(len(self.weights)):\n",
+    "            self.schedulers_weight.append(copy(scheduler))\n",
+    "            self.schedulers_bias.append(copy(scheduler))\n",
+    "\n",
+    "        print(f\"{scheduler.__class__.__name__}: Eta={scheduler.eta}, Lambda={lam}\")\n",
+    "\n",
+    "        try:\n",
+    "            for e in range(epochs):\n",
+    "                for i in range(batches):\n",
+    "                    # allows for minibatch gradient descent\n",
+    "                    if i == batches - 1:\n",
+    "                        # If the for loop has reached the last batch, take all thats left\n",
+    "                        X_batch = X[i * batch_size :, :]\n",
+    "                        t_batch = t[i * batch_size :, :]\n",
+    "                    else:\n",
+    "                        X_batch = X[i * batch_size : (i + 1) * batch_size, :]\n",
+    "                        t_batch = t[i * batch_size : (i + 1) * batch_size, :]\n",
+    "\n",
+    "                    self._feedforward(X_batch)\n",
+    "                    self._backpropagate(X_batch, t_batch, lam)\n",
+    "\n",
+    "                # reset schedulers for each epoch (some schedulers pass in this call)\n",
+    "                for scheduler in self.schedulers_weight:\n",
+    "                    scheduler.reset()\n",
+    "\n",
+    "                for scheduler in self.schedulers_bias:\n",
+    "                    scheduler.reset()\n",
+    "\n",
+    "                # computing performance metrics\n",
+    "                pred_train = self.predict(X)\n",
+    "                train_error = cost_function_train(pred_train)\n",
+    "\n",
+    "                train_errors[e] = train_error\n",
+    "                if val_set:\n",
+    "                    \n",
+    "                    pred_val = self.predict(X_val)\n",
+    "                    val_error = cost_function_val(pred_val)\n",
+    "                    val_errors[e] = val_error\n",
+    "\n",
+    "                if self.classification:\n",
+    "                    train_acc = self._accuracy(self.predict(X), t)\n",
+    "                    train_accs[e] = train_acc\n",
+    "                    if val_set:\n",
+    "                        val_acc = self._accuracy(pred_val, t_val)\n",
+    "                        val_accs[e] = val_acc\n",
+    "\n",
+    "                # printing progress bar\n",
+    "                progression = e / epochs\n",
+    "                print_length = self._progress_bar(\n",
+    "                    progression,\n",
+    "                    train_error=train_errors[e],\n",
+    "                    train_acc=train_accs[e],\n",
+    "                    val_error=val_errors[e],\n",
+    "                    val_acc=val_accs[e],\n",
+    "                )\n",
+    "        except KeyboardInterrupt:\n",
+    "            # allows for stopping training at any point and seeing the result\n",
+    "            pass\n",
+    "\n",
+    "        # visualization of training progression (similiar to tensorflow progression bar)\n",
+    "        sys.stdout.write(\"\\r\" + \" \" * print_length)\n",
+    "        sys.stdout.flush()\n",
+    "        self._progress_bar(\n",
+    "            1,\n",
+    "            train_error=train_errors[e],\n",
+    "            train_acc=train_accs[e],\n",
+    "            val_error=val_errors[e],\n",
+    "            val_acc=val_accs[e],\n",
+    "        )\n",
+    "        sys.stdout.write(\"\")\n",
+    "\n",
+    "        # return performance metrics for the entire run\n",
+    "        scores = dict()\n",
+    "\n",
+    "        scores[\"train_errors\"] = train_errors\n",
+    "\n",
+    "        if val_set:\n",
+    "            scores[\"val_errors\"] = val_errors\n",
+    "\n",
+    "        if self.classification:\n",
+    "            scores[\"train_accs\"] = train_accs\n",
+    "\n",
+    "            if val_set:\n",
+    "                scores[\"val_accs\"] = val_accs\n",
+    "\n",
+    "        return scores\n",
+    "\n",
+    "    def predict(self, X: np.ndarray, *, threshold=0.5):\n",
+    "        \"\"\"\n",
+    "         Description:\n",
+    "         ------------\n",
+    "             Performs prediction after training of the network has been finished.\n",
+    "\n",
+    "         Parameters:\n",
+    "        ------------\n",
+    "             I   X (np.ndarray): The design matrix, with n rows of p features each\n",
+    "\n",
+    "         Optional Parameters:\n",
+    "         ------------\n",
+    "             II  threshold (float) : sets minimal value for a prediction to be predicted as the positive class\n",
+    "                 in classification problems\n",
+    "\n",
+    "         Returns:\n",
+    "         ------------\n",
+    "             I   z (np.ndarray): A prediction vector (row) for each row in our design matrix\n",
+    "                 This vector is thresholded if regression=False, meaning that classification results\n",
+    "                 in a vector of 1s and 0s, while regressions in an array of decimal numbers\n",
+    "\n",
+    "        \"\"\"\n",
+    "\n",
+    "        predict = self._feedforward(X)\n",
+    "\n",
+    "        if self.classification:\n",
+    "            return np.where(predict > threshold, 1, 0)\n",
+    "        else:\n",
+    "            return predict\n",
+    "\n",
+    "    def reset_weights(self):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Resets/Reinitializes the weights in order to train the network for a new problem.\n",
+    "\n",
+    "        \"\"\"\n",
+    "        if self.seed is not None:\n",
+    "            np.random.seed(self.seed)\n",
+    "\n",
+    "        self.weights = list()\n",
+    "        for i in range(len(self.dimensions) - 1):\n",
+    "            weight_array = np.random.randn(\n",
+    "                self.dimensions[i] + 1, self.dimensions[i + 1]\n",
+    "            )\n",
+    "            weight_array[0, :] = np.random.randn(self.dimensions[i + 1]) * 0.01\n",
+    "\n",
+    "            self.weights.append(weight_array)\n",
+    "\n",
+    "    def _feedforward(self, X: np.ndarray):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Calculates the activation of each layer starting at the input and ending at the output.\n",
+    "            Each following activation is calculated from a weighted sum of each of the preceeding\n",
+    "            activations (except in the case of the input layer).\n",
+    "\n",
+    "        Parameters:\n",
+    "        ------------\n",
+    "            I   X (np.ndarray): The design matrix, with n rows of p features each\n",
+    "\n",
+    "        Returns:\n",
+    "        ------------\n",
+    "            I   z (np.ndarray): A prediction vector (row) for each row in our design matrix\n",
+    "        \"\"\"\n",
+    "\n",
+    "        # reset matrices\n",
+    "        self.a_matrices = list()\n",
+    "        self.z_matrices = list()\n",
+    "\n",
+    "        # if X is just a vector, make it into a matrix\n",
+    "        if len(X.shape) == 1:\n",
+    "            X = X.reshape((1, X.shape[0]))\n",
+    "\n",
+    "        # Add a coloumn of zeros as the first coloumn of the design matrix, in order\n",
+    "        # to add bias to our data\n",
+    "        bias = np.ones((X.shape[0], 1)) * 0.01\n",
+    "        X = np.hstack([bias, X])\n",
+    "\n",
+    "        # a^0, the nodes in the input layer (one a^0 for each row in X - where the\n",
+    "        # exponent indicates layer number).\n",
+    "        a = X\n",
+    "        self.a_matrices.append(a)\n",
+    "        self.z_matrices.append(a)\n",
+    "\n",
+    "        # The feed forward algorithm\n",
+    "        for i in range(len(self.weights)):\n",
+    "            if i < len(self.weights) - 1:\n",
+    "                z = a @ self.weights[i]\n",
+    "                self.z_matrices.append(z)\n",
+    "                a = self.hidden_func(z)\n",
+    "                # bias column again added to the data here\n",
+    "                bias = np.ones((a.shape[0], 1)) * 0.01\n",
+    "                a = np.hstack([bias, a])\n",
+    "                self.a_matrices.append(a)\n",
+    "            else:\n",
+    "                try:\n",
+    "                    # a^L, the nodes in our output layers\n",
+    "                    z = a @ self.weights[i]\n",
+    "                    a = self.output_func(z)\n",
+    "                    self.a_matrices.append(a)\n",
+    "                    self.z_matrices.append(z)\n",
+    "                except Exception as OverflowError:\n",
+    "                    print(\n",
+    "                        \"OverflowError in fit() in FFNN\\nHOW TO DEBUG ERROR: Consider lowering your learning rate or scheduler specific parameters such as momentum, or check if your input values need scaling\"\n",
+    "                    )\n",
+    "\n",
+    "        # this will be a^L\n",
+    "        return a\n",
+    "\n",
+    "    def _backpropagate(self, X, t, lam):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Performs the backpropagation algorithm. In other words, this method\n",
+    "            calculates the gradient of all the layers starting at the\n",
+    "            output layer, and moving from right to left accumulates the gradient until\n",
+    "            the input layer is reached. Each layers respective weights are updated while\n",
+    "            the algorithm propagates backwards from the output layer (auto-differentation in reverse mode).\n",
+    "\n",
+    "        Parameters:\n",
+    "        ------------\n",
+    "            I   X (np.ndarray): The design matrix, with n rows of p features each.\n",
+    "            II  t (np.ndarray): The target vector, with n rows of p targets.\n",
+    "            III lam (float32): regularization parameter used to punish the weights in case of overfitting\n",
+    "\n",
+    "        Returns:\n",
+    "        ------------\n",
+    "            No return value.\n",
+    "\n",
+    "        \"\"\"\n",
+    "        out_derivative = derivate(self.output_func)\n",
+    "        hidden_derivative = derivate(self.hidden_func)\n",
+    "\n",
+    "        for i in range(len(self.weights) - 1, -1, -1):\n",
+    "            # delta terms for output\n",
+    "            if i == len(self.weights) - 1:\n",
+    "                # for multi-class classification\n",
+    "                if (\n",
+    "                    self.output_func.__name__ == \"softmax\"\n",
+    "                ):\n",
+    "                    delta_matrix = self.a_matrices[i + 1] - t\n",
+    "                # for single class classification\n",
+    "                else:\n",
+    "                    cost_func_derivative = grad(self.cost_func(t))\n",
+    "                    delta_matrix = out_derivative(\n",
+    "                        self.z_matrices[i + 1]\n",
+    "                    ) * cost_func_derivative(self.a_matrices[i + 1])\n",
+    "\n",
+    "            # delta terms for hidden layer\n",
+    "            else:\n",
+    "                delta_matrix = (\n",
+    "                    self.weights[i + 1][1:, :] @ delta_matrix.T\n",
+    "                ).T * hidden_derivative(self.z_matrices[i + 1])\n",
+    "\n",
+    "            # calculate gradient\n",
+    "            gradient_weights = self.a_matrices[i][:, 1:].T @ delta_matrix\n",
+    "            gradient_bias = np.sum(delta_matrix, axis=0).reshape(\n",
+    "                1, delta_matrix.shape[1]\n",
+    "            )\n",
+    "\n",
+    "            # regularization term\n",
+    "            gradient_weights += self.weights[i][1:, :] * lam\n",
+    "\n",
+    "            # use scheduler\n",
+    "            update_matrix = np.vstack(\n",
+    "                [\n",
+    "                    self.schedulers_bias[i].update_change(gradient_bias),\n",
+    "                    self.schedulers_weight[i].update_change(gradient_weights),\n",
+    "                ]\n",
+    "            )\n",
+    "\n",
+    "            # update weights and bias\n",
+    "            self.weights[i] -= update_matrix\n",
+    "\n",
+    "    def _accuracy(self, prediction: np.ndarray, target: np.ndarray):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Calculates accuracy of given prediction to target\n",
+    "\n",
+    "        Parameters:\n",
+    "        ------------\n",
+    "            I   prediction (np.ndarray): vector of predicitons output network\n",
+    "                (1s and 0s in case of classification, and real numbers in case of regression)\n",
+    "            II  target (np.ndarray): vector of true values (What the network ideally should predict)\n",
+    "\n",
+    "        Returns:\n",
+    "        ------------\n",
+    "            A floating point number representing the percentage of correctly classified instances.\n",
+    "        \"\"\"\n",
+    "        assert prediction.size == target.size\n",
+    "        return np.average((target == prediction))\n",
+    "    def _set_classification(self):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Decides if FFNN acts as classifier (True) og regressor (False),\n",
+    "            sets self.classification during init()\n",
+    "        \"\"\"\n",
+    "        self.classification = False\n",
+    "        if (\n",
+    "            self.cost_func.__name__ == \"CostLogReg\"\n",
+    "            or self.cost_func.__name__ == \"CostCrossEntropy\"\n",
+    "        ):\n",
+    "            self.classification = True\n",
+    "\n",
+    "    def _progress_bar(self, progression, **kwargs):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Displays progress of training\n",
+    "        \"\"\"\n",
+    "        print_length = 40\n",
+    "        num_equals = int(progression * print_length)\n",
+    "        num_not = print_length - num_equals\n",
+    "        arrow = \">\" if num_equals > 0 else \"\"\n",
+    "        bar = \"[\" + \"=\" * (num_equals - 1) + arrow + \"-\" * num_not + \"]\"\n",
+    "        perc_print = self._format(progression * 100, decimals=5)\n",
+    "        line = f\"  {bar} {perc_print}% \"\n",
+    "\n",
+    "        for key in kwargs:\n",
+    "            if not np.isnan(kwargs[key]):\n",
+    "                value = self._format(kwargs[key], decimals=4)\n",
+    "                line += f\"| {key}: {value} \"\n",
+    "        sys.stdout.write(\"\\r\" + line)\n",
+    "        sys.stdout.flush()\n",
+    "        return len(line)\n",
+    "\n",
+    "    def _format(self, value, decimals=4):\n",
+    "        \"\"\"\n",
+    "        Description:\n",
+    "        ------------\n",
+    "            Formats decimal numbers for progress bar\n",
+    "        \"\"\"\n",
+    "        if value > 0:\n",
+    "            v = value\n",
+    "        elif value < 0:\n",
+    "            v = -10 * value\n",
+    "        else:\n",
+    "            v = 1\n",
+    "        n = 1 + math.floor(math.log10(v))\n",
+    "        if n >= decimals - 1:\n",
+    "            return str(round(value))\n",
+    "        return f\"{value:.{decimals-n-1}f}\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b5aaa66b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Before we make a model, we will quickly generate a dataset we can use\n",
+    "for our linear regression problem as shown below"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "35f13536",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from sklearn.model_selection import train_test_split\n",
+    "\n",
+    "def SkrankeFunction(x, y):\n",
+    "    return np.ravel(0 + 1*x + 2*y + 3*x**2 + 4*x*y + 5*y**2)\n",
+    "\n",
+    "def create_X(x, y, n):\n",
+    "    if len(x.shape) > 1:\n",
+    "        x = np.ravel(x)\n",
+    "        y = np.ravel(y)\n",
+    "\n",
+    "    N = len(x)\n",
+    "    l = int((n + 1) * (n + 2) / 2)  # Number of elements in beta\n",
+    "    X = np.ones((N, l))\n",
+    "\n",
+    "    for i in range(1, n + 1):\n",
+    "        q = int((i) * (i + 1) / 2)\n",
+    "        for k in range(i + 1):\n",
+    "            X[:, q + k] = (x ** (i - k)) * (y**k)\n",
+    "\n",
+    "    return X\n",
+    "\n",
+    "step=0.5\n",
+    "x = np.arange(0, 1, step)\n",
+    "y = np.arange(0, 1, step)\n",
+    "x, y = np.meshgrid(x, y)\n",
+    "target = SkrankeFunction(x, y)\n",
+    "target = target.reshape(target.shape[0], 1)\n",
+    "\n",
+    "poly_degree=3\n",
+    "X = create_X(x, y, poly_degree)\n",
+    "\n",
+    "X_train, X_test, t_train, t_test = train_test_split(X, target)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "12780998",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Now that we have our dataset ready for the regression, we can create\n",
+    "our regressor. Note that with the seed parameter, we can make sure our\n",
+    "results stay the same every time we run the neural network. For\n",
+    "inititialization, we simply specify the dimensions (we wish the amount\n",
+    "of input nodes to be equal to the datapoints, and the output to\n",
+    "predict one value)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "3de4263c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "input_nodes = X_train.shape[1]\n",
+    "output_nodes = 1\n",
+    "\n",
+    "linear_regression = FFNN((input_nodes, output_nodes), output_func=identity, cost_func=CostOLS, seed=2023)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3ca1fb5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We then fit our model with our training data using the scheduler of our choice."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "714229a9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Constant: Eta=0.001, Lambda=0\n",
+      "  [=======================================>] 100.0% | train_error: 10.9 "
+     ]
+    }
+   ],
+   "source": [
+    "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
+    "\n",
+    "scheduler = Constant(eta=1e-3)\n",
+    "scores = linear_regression.fit(X_train, t_train, scheduler)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2240c6b8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Due to the progress bar we can see the MSE (train_error) throughout\n",
+    "the FFNN's training. Note that the fit() function has some optional\n",
+    "parameters with defualt arguments. For example, the regularization\n",
+    "hyperparameter can be left ignored if not needed, and equally the FFNN\n",
+    "will by default run for 100 epochs. These can easily be changed, such\n",
+    "as for example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "96f9f1ab",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Constant: Eta=0.001, Lambda=0.0001\n",
+      "  [=======================================>] 100.0% | train_error: 1.00  "
+     ]
+    }
+   ],
+   "source": [
+    "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
+    "\n",
+    "scores = linear_regression.fit(X_train, t_train, scheduler, lam=1e-4, epochs=1000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21af3f64",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We see that given more epochs to train on, the regressor reaches a lower MSE.\n",
+    "\n",
+    "Let us then switch to a binary classification. We use a binary\n",
+    "classification dataset, and follow a similar setup to the regression\n",
+    "case."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "98f0055d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from sklearn.datasets import load_breast_cancer\n",
+    "from sklearn.preprocessing import MinMaxScaler\n",
+    "\n",
+    "wisconsin = load_breast_cancer()\n",
+    "X = wisconsin.data\n",
+    "target = wisconsin.target\n",
+    "target = target.reshape(target.shape[0], 1)\n",
+    "\n",
+    "X_train, X_val, t_train, t_val = train_test_split(X, target)\n",
+    "\n",
+    "scaler = MinMaxScaler()\n",
+    "scaler.fit(X_train)\n",
+    "X_train = scaler.transform(X_train)\n",
+    "X_val = scaler.transform(X_val)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "fbd2675f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "input_nodes = X_train.shape[1]\n",
+    "output_nodes = 1\n",
+    "\n",
+    "logistic_regression = FFNN((input_nodes, output_nodes), output_func=sigmoid, cost_func=CostLogReg, seed=2023)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "64ed3461",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We will now make use of our validation data by passing it into our fit function as a keyword argument"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "1cdc9d23",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Adam: Eta=0.001, Lambda=0\n",
+      "  [=======================================>] 100.0% | train_error: 3.21 | train_acc: 0.845 | val_error: 3.77 | val_acc: 0.818  "
+     ]
+    }
+   ],
+   "source": [
+    "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
+    "\n",
+    "scheduler = Adam(eta=1e-3, rho=0.9, rho2=0.999)\n",
+    "scores = logistic_regression.fit(X_train, t_train, scheduler, epochs=1000, X_val=X_val, t_val=t_val)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13e2f881",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Finally, we will create a neural network with 2 hidden layers with activation functions."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "c28f2181",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "input_nodes = X_train.shape[1]\n",
+    "hidden_nodes1 = 100\n",
+    "hidden_nodes2 = 30\n",
+    "output_nodes = 1\n",
+    "\n",
+    "dims = (input_nodes, hidden_nodes1, hidden_nodes2, output_nodes)\n",
+    "\n",
+    "neural_network = FFNN(dims, hidden_func=RELU, output_func=sigmoid, cost_func=CostLogReg, seed=2023)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "3150b724",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Adam: Eta=0.0001, Lambda=0\n",
+      "  [=======================================>] 100.0% | train_error: 0.0973 | train_acc: 0.995 | val_error: 1.74 | val_acc: 0.916 "
+     ]
+    }
+   ],
+   "source": [
+    "neural_network.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
+    "\n",
+    "scheduler = Adam(eta=1e-4, rho=0.9, rho2=0.999)\n",
+    "scores = neural_network.fit(X_train, t_train, scheduler, epochs=1000, X_val=X_val, t_val=t_val)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "17aebab2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "### Multiclass classification\n",
+    "\n",
+    "Finally, we will demonstrate the use case of multiclass classification\n",
+    "using our FFNN with the famous MNIST dataset, which contain images of\n",
+    "digits between the range of 0 to 9."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "997c5001",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Adam: Eta=0.0001, Lambda=0\n",
+      "  [=======================================>] 100.0% | train_error: 0.175 | train_acc: 0.983 "
+     ]
+    }
+   ],
+   "source": [
+    "from sklearn.datasets import load_digits\n",
+    "\n",
+    "def onehot(target: np.ndarray):\n",
+    "    onehot = np.zeros((target.size, target.max() + 1))\n",
+    "    onehot[np.arange(target.size), target] = 1\n",
+    "    return onehot\n",
+    "\n",
+    "digits = load_digits()\n",
+    "\n",
+    "X = digits.data\n",
+    "target = digits.target\n",
+    "target = onehot(target)\n",
+    "\n",
+    "input_nodes = 64\n",
+    "hidden_nodes1 = 100\n",
+    "hidden_nodes2 = 30\n",
+    "output_nodes = 10\n",
+    "\n",
+    "dims = (input_nodes, hidden_nodes1, hidden_nodes2, output_nodes)\n",
+    "\n",
+    "multiclass = FFNN(dims, hidden_func=LRELU, output_func=softmax, cost_func=CostCrossEntropy)\n",
+    "\n",
+    "multiclass.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
+    "\n",
+    "scheduler = Adam(eta=1e-4, rho=0.9, rho2=0.999)\n",
+    "scores = multiclass.fit(X, target, scheduler, epochs=1000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "43d805bc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Testing the XOR gate and other gates\n",
+    "\n",
+    "Let us now use our code to test the XOR gate."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "4bbaf697",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Adam: Eta=0.001, Lambda=0\n",
+      "  [=======================================>] 100.0% | train_error: 10.4 | train_acc: 0.500  "
+     ]
+    }
+   ],
+   "source": [
+    "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
+    "\n",
+    "# The XOR gate\n",
+    "yXOR = np.array( [[ 0], [1] ,[1], [0]])\n",
+    "\n",
+    "input_nodes = X.shape[1]\n",
+    "output_nodes = 1\n",
+    "\n",
+    "logistic_regression = FFNN((input_nodes, output_nodes), output_func=sigmoid, cost_func=CostLogReg, seed=2023)\n",
+    "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
+    "scheduler = Adam(eta=1e-3, rho=0.9, rho2=0.999)\n",
+    "scores = logistic_regression.fit(X, yXOR, scheduler, epochs=1000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31e852a7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Not bad, but the results depend strongly on the learning reate. Try different learning rates."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9792c0c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Solving differential equations  with Deep Learning\n",
     "\n",
     "The Universal Approximation Theorem states that a neural network can\n",
     "approximate any function at a single hidden layer along with one input\n",
-    "and output layer to any given precision.  \n",
+    "and output layer to any given precision.\n",
     "\n",
+    "**Book on solving differential equations with ML methods.**\n",
     "\n",
-    "## Ordinary Differential Equations\n",
+    "[An Introduction to Neural Network Methods for Differential Equations](https://www.springer.com/gp/book/9789401798150), by Yadav and Kumar.\n",
+    "\n",
+    "**Physics informed neural networks.**\n",
+    "\n",
+    "[Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next](https://link.springer.com/article/10.1007/s10915-022-01939-z), by Cuomo et al\n",
+    "\n",
+    "**Thanks to Kristine Baluka Hein.**\n",
+    "\n",
+    "The lectures on differential equations were developed by Kristine Baluka Hein, now PhD student at IFI.\n",
+    "A great thanks to Kristine."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9214a407",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Ordinary Differential Equations first\n",
     "\n",
     "An ordinary differential equation (ODE) is an equation involving functions having one variable.\n",
     "\n",
@@ -58,7 +3667,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "40a78c33",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"ode\"></div>\n",
@@ -72,7 +3684,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "42dae561",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n",
     "\n",
@@ -80,8 +3695,16 @@
     "The highest order of derivative, that is the value of $n$, determines to the order of the equation.\n",
     "The equation is referred to as a $n$-th order ODE.\n",
     "Along with ([1](#ode)), some additional conditions of the function $g(x)$ are typically given\n",
-    "for the solution to be unique.\n",
-    "\n",
+    "for the solution to be unique."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b4bf5f2e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## The trial solution\n",
     "\n",
     "Let the trial solution $g_t(x)$ be"
@@ -89,7 +3712,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "1f4f3eba",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -104,7 +3730,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d799a47c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n",
     "of conditions, $N(x,P)$ a neural network with weights and biases\n",
@@ -117,10 +3746,16 @@
     "\n",
     "But what about the network $N(x,P)$?\n",
     "\n",
-    "\n",
-    "As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation.\n",
-    "\n",
-    "\n",
+    "As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "abb02959",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Minimization process\n",
     "\n",
     "For the minimization to be defined, we need to have a cost function at hand to minimize.\n",
@@ -133,7 +3768,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "6468ecf8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n",
@@ -142,7 +3780,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "e7441b12",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n",
     "the cost function becomes"
@@ -150,7 +3791,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "0ffd1c29",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cost\"></div>\n",
@@ -164,20 +3808,38 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "e55c8d3e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The neural net should then find the parameters $P$ that minimizes the cost function in\n",
-    "([3](#cost)) for a set of $N$ training samples $x_i$.\n",
-    "\n",
+    "([3](#cost)) for a set of $N$ training samples $x_i$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8a940e88",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Minimizing the cost function using gradient descent and automatic differentiation\n",
     "\n",
     "To perform the minimization using gradient descent, the gradient of $C\\left(\\boldsymbol{x}, P\\right)$ is needed.\n",
     "It might happen so that finding an analytical expression of the gradient of $C(\\boldsymbol{x}, P)$ from ([3](#cost)) gets too messy, depending on which cost function one desires to use.\n",
     "\n",
     "Luckily, there exists libraries that makes the job for us through automatic differentiation.\n",
-    "Automatic differentiation is a method of finding the derivatives numerically with very high precision.\n",
-    "\n",
-    "\n",
+    "Automatic differentiation is a method of finding the derivatives numerically with very high precision."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "547613c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Example: Exponential decay\n",
     "\n",
     "An exponential decay of a quantity $g(x)$ is described by the equation"
@@ -185,7 +3847,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "826651d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solve_expdec\"></div>\n",
@@ -199,7 +3864,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "870b960b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $g(0) = g_0$ for some chosen initial value $g_0$.\n",
     "\n",
@@ -208,7 +3876,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "5a8fd1e3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -223,11 +3894,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "55b4f286",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec))."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e4f689b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec)).\n",
-    "\n",
-    "\n",
     "## The function to solve for\n",
     "\n",
     "The program will use a neural network to solve"
@@ -235,7 +3916,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "01e8e999",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode\"></div>\n",
@@ -249,19 +3933,33 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "7ccea9f1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n",
     "\n",
-    "In this example, $\\gamma = 2$ and $g_0 = 10$.\n",
-    "\n",
+    "In this example, $\\gamma = 2$ and $g_0 = 10$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "47fde776",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## The trial solution\n",
     "To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "f7a8f626",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n",
@@ -270,10 +3968,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "66551df0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c354ef4e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer.\n",
-    "\n",
     "## Setup of Network\n",
     "\n",
     "In this network, there are no weights and bias at the input layer, so $P = \\{ P_{\\text{hidden}},  P_{\\text{output}} \\}$.\n",
@@ -289,7 +3998,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "a574c0b7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"trial\"></div>\n",
@@ -303,7 +4015,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "22f440c8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reformulating the problem\n",
     "\n",
@@ -319,7 +4034,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "0ff80a83",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = g_0 + x \\cdot N(x, P)\n",
@@ -328,14 +4046,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "6829edab",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "381c61e2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"nnmin\"></div>\n",
@@ -349,10 +4073,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "ac36a03d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "is fulfilled as *best as possible*."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2899becc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "is fulfilled as *best as possible*.\n",
-    "\n",
     "## More technicalities\n",
     "\n",
     "The left hand side and right hand side of ([8](#nnmin)) must be computed separately, and then the neural network must choose weights and biases, contained in $P$, such that the sides are equal as best as possible.\n",
@@ -364,7 +4099,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d52c8124",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n",
@@ -373,7 +4111,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "3f8f684e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n",
     "\n",
@@ -382,7 +4123,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "92cc16c9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n",
@@ -391,10 +4135,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "628e0dfc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "for an input value $x$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e54b4c6e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "for an input value $x$.\n",
-    "\n",
     "## More details\n",
     "\n",
     "If the neural network evaluates $g_t(x, P)$ at more values for $x$, say $N$ values $x_i$ for $i = 1, \\dots, N$, then the *total* error to minimize becomes"
@@ -402,7 +4157,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "80dc48dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"min\"></div>\n",
@@ -416,14 +4174,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "e57a1d70",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "8ad67e57",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P} C(\\boldsymbol{x}, P)\n",
@@ -432,22 +4196,41 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "4eed66ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n",
     "\n",
     "$$\n",
     "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }} C(\\boldsymbol{x}, \\{P_{\\text{hidden} }, P_{\\text{output} }\\})\n",
-    "$$\n",
-    "\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9d652c56",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## A possible implementation of a neural network\n",
     "\n",
     "For simplicity, it is assumed that the input is an array $\\boldsymbol{x} = (x_1, \\dots, x_N)$ with $N$ elements. It is at these points the neural network should find $P$ such that it fulfills ([9](#min)).\n",
     "\n",
     "First, the neural network must feed forward the inputs.\n",
     "This means that $\\boldsymbol{x}s$ must be passed through an input layer, a hidden layer and a output layer. The input layer in this case, does not need to process the data any further.\n",
-    "The input layer will consist of $N_{\\text{input} }$ neurons, passing its element to each neuron in the hidden layer.  The number of neurons in the hidden layer will be $N_{\\text{hidden} }$.\n",
-    "\n",
+    "The input layer will consist of $N_{\\text{input} }$ neurons, passing its element to each neuron in the hidden layer.  The number of neurons in the hidden layer will be $N_{\\text{hidden} }$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a5a1ad7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Technicalities\n",
     "\n",
     "For the $i$-th in the hidden layer with weight $w_i^{\\text{hidden} }$ and bias $b_i^{\\text{hidden} }$, the weighting from the $j$-th neuron at the input layer is:"
@@ -455,7 +4238,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "ed15e067",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -474,7 +4260,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "827ac223",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities I\n",
     "\n",
@@ -483,7 +4272,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "a0a7b13f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -503,7 +4295,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "0879010a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities II\n",
     "\n",
@@ -516,7 +4311,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "66ac91b3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z) = \\frac{1}{1 + \\exp{(-z)}}\n",
@@ -525,7 +4323,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "470c74b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "It is possible to use other activations functions for the hidden layer also.\n",
     "\n",
@@ -541,17 +4342,27 @@
     "output from each of the neurons in the hidden layers. The output layer\n",
     "combines the results from the hidden layer using some weights $w_i^{\\text{output}}$\n",
     "and biases $b_i^{\\text{output}}$. In this case,\n",
-    "it is assumes that the number of neurons in the output layer is one.\n",
-    "\n",
+    "it is assumes that the number of neurons in the output layer is one."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bf5e6967",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Final technicalities III\n",
     "\n",
-    "\n",
     "The procedure of weighting the output neuron $j$ in the hidden layer to the $i$-th neuron in the output layer is similar as for the hidden layer described previously."
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "766b88f8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -569,7 +4380,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "5c114139",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities IV\n",
     "\n",
@@ -578,7 +4392,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "45596281",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{z}_{1}^{\\text{output}} =\n",
@@ -594,10 +4411,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "2c1378fb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "66a732e1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network.\n",
-    "\n",
     "## Back propagation\n",
     "\n",
     "The next step is to decide how the parameters should be changed such that they minimize the cost function.\n",
@@ -607,7 +4435,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "fdf81225",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n",
@@ -616,12 +4447,23 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "9bb52111",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In order to minimize the cost function, an optimization method must be chosen.\n",
     "\n",
-    "Here, gradient descent with a constant step size has been chosen.\n",
-    "\n",
+    "Here, gradient descent with a constant step size has been chosen."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f3e495b4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Gradient descent\n",
     "\n",
     "The idea of the gradient descent algorithm is to update parameters in\n",
@@ -634,7 +4476,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "adc904df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n",
@@ -643,7 +4488,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "2d01b1b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n",
     "\n",
@@ -662,7 +4510,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "5077f4f7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -674,45 +4525,27 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "fb01e943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The code for solving the ODE"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-<<<<<<< HEAD
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 367.01\n",
-      "Final cost: 0.0666807\n",
-      "Max absolute difference: 0.0437499\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 720x720 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
+   "execution_count": 31,
+   "id": "6347e101",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
     }
-   ],
-=======
+   },
    "outputs": [],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
    "source": [
-    "%matplotlib inline\n",
-    "\n",
     "import autograd.numpy as np\n",
     "from autograd import grad, elementwise_grad\n",
     "import autograd.numpy.random as npr\n",
@@ -861,7 +4694,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "59e5acda",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The network with one input layer, specified number of hidden layers, and one output layer\n",
     "\n",
@@ -872,34 +4708,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-<<<<<<< HEAD
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 324.246\n",
-      "Final cost: 0.119936\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 720x720 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
+   "execution_count": 32,
+   "id": "f1a60516",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
     }
-   ],
-=======
+   },
    "outputs": [],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad, elementwise_grad\n",
@@ -913,8 +4731,8 @@
     "# but with number of hidden layers specified by the user.\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consists of\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
     "                                        # parameters to all the hidden\n",
     "                                        # layers AND the output layer.\n",
     "\n",
@@ -1063,7 +4881,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "807a375c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Population growth\n",
     "\n",
@@ -1073,7 +4894,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d35839bb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"log\"></div>\n",
@@ -1087,7 +4911,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "2991d1fe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n",
     "Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n",
@@ -1095,8 +4922,16 @@
     "In this example, similar network as for the exponential decay using Autograd has been used to solve the equation. However, as the implementation might suffer from e.g numerical instability\n",
     "and high execution time (this might be more apparent in the examples solving PDEs),\n",
     "using a library like  TensorFlow is recommended.\n",
-    "Here, we stay with a more simple approach and implement for comparison, the simple forward Euler method.\n",
-    "\n",
+    "Here, we stay with a more simple approach and implement for comparison, the simple forward Euler method."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ee668a71",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Setting up the problem\n",
     "\n",
     "Here, we will model a population $g(t)$ in an environment having carrying capacity $A$.\n",
@@ -1105,7 +4940,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "febf10cc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode_population\"></div>\n",
@@ -1119,12 +4957,23 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "494194e3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$.\n",
     "\n",
-    "In this example, we let $\\alpha = 2$, $A = 1$, and $g_0 = 1.2$.\n",
-    "\n",
+    "In this example, we let $\\alpha = 2$, $A = 1$, and $g_0 = 1.2$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5efa7b11",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## The trial solution\n",
     "\n",
     "We will get a slightly different trial solution, as the boundary conditions are different\n",
@@ -1142,8 +4991,16 @@
     "\n",
     "$$\n",
     "g(t) = \\frac{Ag_0}{g_0 + (A - g_0)\\exp(-\\alpha A t)}\n",
-    "$$\n",
-    "\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "568131dc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## The program using Autograd\n",
     "\n",
     "The network will be the similar as for the exponential decay example, but with some small modifications for our problem."
@@ -1151,8 +5008,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
+   "execution_count": 33,
+   "id": "8737e028",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1171,9 +5035,12 @@
     "    g0 = 1.2\n",
     "    return alpha, A, g0\n",
     "\n",
-    "def deep_neural_network(P, x):\n",
+    "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(P) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -1190,7 +5057,7 @@
     "\n",
     "    for l in range(N_hidden):\n",
     "        # From the list of parameters P; find the correct weigths and bias for this layer\n",
-    "        w_hidden = P[l]\n",
+    "        w_hidden = deep_params[l]\n",
     "\n",
     "        # Add a row of ones to include bias\n",
     "        x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
@@ -1204,7 +5071,7 @@
     "    ## Output layer:\n",
     "\n",
     "    # Get the weights and bias for this layer\n",
-    "    w_output = P[-1]\n",
+    "    w_output = deep_params[-1]\n",
     "\n",
     "    # Include bias:\n",
     "    x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
@@ -1215,6 +5082,8 @@
     "    return x_output\n",
     "\n",
     "\n",
+    "\n",
+    "\n",
     "def cost_function_deep(P, x):\n",
     "\n",
     "    # Evaluate the trial function with the current parameters P\n",
@@ -1322,7 +5191,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "0904f64d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using forward Euler to solve the ODE\n",
     "\n",
@@ -1339,7 +5211,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "6f3577a8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -1351,7 +5226,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "56d4410b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the condition that $g(0) = g_0$.\n",
     "\n",
@@ -1362,7 +5240,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "48d2707e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -1375,14 +5256,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "66d99f85",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now, if $g_i = g(t_i)$ then"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "3c9447d9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odenum\"></div>\n",
@@ -1401,7 +5288,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "724b97f1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n",
     "\n",
@@ -1411,8 +5301,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
+   "execution_count": 34,
+   "id": "58b0da70",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "# Assume that all function definitions from the example program using Autograd\n",
@@ -1484,7 +5381,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "f1230dee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the one dimensional Poisson equation\n",
     "\n",
@@ -1493,7 +5393,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "ba2c6d0a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"poisson\"></div>\n",
@@ -1507,7 +5410,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "bab1c7d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function for $x \\in (0,1)$.\n",
     "\n",
@@ -1516,7 +5422,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "42bfde23",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -1528,12 +5437,23 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "7b3a2504",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n",
     "The results from the networks can then be compared to the analytical solution.\n",
-    "In addition, it could be interesting to see how a typical method for numerically solving second order ODEs compares to the neural networks.\n",
-    "\n",
+    "In addition, it could be interesting to see how a typical method for numerically solving second order ODEs compares to the neural networks."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a419909c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## The specific equation to solve for\n",
     "\n",
     "Here, the function $g(x)$ to solve for follows the equation"
@@ -1541,7 +5461,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "125f8197",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "-g''(x) = f(x),\\qquad x \\in (0,1)\n",
@@ -1550,14 +5473,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "16376b60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function, along with the chosen conditions"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "044c76ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cond\"></div>\n",
@@ -1571,7 +5500,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "0ec4860b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n",
     "\n",
@@ -1580,7 +5512,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "03e27ec0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n",
@@ -1589,14 +5524,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "82fdb51f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The analytical solution for this problem is"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "82e39d0e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g(x) = x(1 - x)\\exp(x)\n",
@@ -1605,15 +5546,25 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "bf029e6c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the equation using Autograd"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
+   "execution_count": 35,
+   "id": "e10d7641",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1626,7 +5577,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -1667,6 +5621,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -1770,7 +5725,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "82891392",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Comparing with a numerical scheme\n",
     "\n",
@@ -1789,7 +5747,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "ad4ef510",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"approx\"></div>\n",
@@ -1803,14 +5764,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "eb8ab804",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "f9b7b2a0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -1822,14 +5789,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "6a71c7bb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Since we know from our problem that"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d19780a8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -1841,7 +5814,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "00fedc6e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the conditions $g(0) = g(1) = 0$,\n",
     "the following scheme can be used to find an approximate solution for $g(x)$ numerically:"
@@ -1849,7 +5825,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "28005c86",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odesys\"></div>\n",
@@ -1866,7 +5845,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d562bb0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n",
     "\n",
@@ -1875,7 +5857,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "bdee81e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -1909,10 +5894,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "ddf436f5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which makes it possible to solve for the vector $\\boldsymbol{g}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "66ae2d44",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "which makes it possible to solve for the vector $\\boldsymbol{g}$.\n",
-    "\n",
     "## Setting up the code\n",
     "\n",
     "We can then compare the result from this numerical scheme with the output from our network using Autograd:"
@@ -1920,8 +5916,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
+   "execution_count": 36,
+   "id": "17f02a24",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1934,7 +5937,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -1975,6 +5981,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -2118,7 +6125,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "51ee4433",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Partial Differential Equations\n",
     "\n",
@@ -2132,7 +6142,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "1ec16aab",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"PDE\"></div>\n",
@@ -2146,10 +6159,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "64fd215d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3efab799",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given.\n",
-    "\n",
     "## Type of problem\n",
     "\n",
     "The problem our network must solve for, is similar to the ODE case.\n",
@@ -2160,7 +6184,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "80e6d77c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -2171,14 +6198,24 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "f08a42bd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n",
     "The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n",
     "\n",
-    "The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions.\n",
-    "\n",
-    "\n",
+    "The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "af035b50",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Network requirements\n",
     "\n",
     "The network tries then the minimize the cost function following the\n",
@@ -2194,7 +6231,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "ee147dfb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x_1, \\dots, x_N, P\\right) = \\left(  f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -2203,7 +6243,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "850e95ed",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -2212,7 +6255,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "96f9cca4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -2221,14 +6267,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "70394cae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d06e6c30",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n",
@@ -2237,7 +6289,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "b4972f88",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: The diffusion equation\n",
     "\n",
@@ -2246,7 +6301,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "3d35cbd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -2255,14 +6313,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "984bf645",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where a possible choice of conditions are"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "9d58d0ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -2275,10 +6339,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "99cf8f47",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $u(x)$ being some given function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "777ad3a8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "with $u(x)$ being some given function.\n",
-    "\n",
     "## Defining the problem\n",
     "\n",
     "For this case, we want to find $g(x,t)$ such that"
@@ -2286,7 +6361,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "7182b747",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"diffonedim\"></div>\n",
@@ -2300,14 +6378,20 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "3c40d528",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "7cb1e15a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -2320,16 +6404,25 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "5c4bcdb5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x) = \\sin(\\pi x)$.\n",
     "\n",
     "First, let us set up the deep neural network.\n",
     "The deep neural network will follow the same structure as discussed in the examples solving the ODEs.\n",
-    "First, we will look into how Autograd could be used in a network tailored to solve for bivariate functions.\n",
-    "\n",
-    "\n",
-    "\n",
+    "First, we will look into how Autograd could be used in a network tailored to solve for bivariate functions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c84ff432",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Setting up the network using Autograd\n",
     "\n",
     "The only change to do here, is to extend our network such that\n",
@@ -2343,8 +6436,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
+   "execution_count": 37,
+   "id": "ba62ab4c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "def sigmoid(z):\n",
@@ -2358,7 +6458,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -2395,7 +6495,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "7fd9e6dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The trial solution\n",
     "\n",
@@ -2417,8 +6520,16 @@
     "$$\n",
     "h_1(x,t) = (1-t)\\Big(u(x) - \\big((1-x)u(0) + x u(1)\\big)\\Big) = (1-t)u(x) = (1-t)\\sin(\\pi x)\n",
     "$$\n",
-    "since $(0) = u(1) = 0$ and $u(x) = \\sin(\\pi x)$.\n",
-    "\n",
+    "since $(0) = u(1) = 0$ and $u(x) = \\sin(\\pi x)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6c63c928",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Why the jacobian?\n",
     "\n",
     "The Jacobian is used because the program must find the derivative of\n",
@@ -2442,8 +6553,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
+   "execution_count": 38,
+   "id": "4192bf3d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "# Set up the trial function:\n",
@@ -2486,7 +6604,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "87f8417d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The full program\n",
     "\n",
@@ -2502,15 +6623,21 @@
     "Be aware, though, that it is fairly slow for the parameters used.\n",
     "A better result is possible, but requires more iterations, and thus longer time to complete.\n",
     "\n",
-    "\n",
     "Indeed, the program below is not optimal in its implementation, but rather serves as an example on how to implement and use a neural network to solve a PDE.\n",
     "Using TensorFlow results in a much better execution time. Try it!"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
+   "execution_count": 39,
+   "id": "1572e93b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2533,7 +6660,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -2676,7 +6803,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,g_dnn_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -2684,14 +6811,14 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,G_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
     "    ax.set_ylabel('Position $x$');\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -2740,7 +6867,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "bf7afd74",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the wave equation with Neural Networks\n",
     "\n",
@@ -2749,7 +6879,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "fdef78b2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -2758,7 +6891,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "be570613",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $c$ being the specified wave speed.\n",
     "\n",
@@ -2767,7 +6903,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "9f81e04f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -2781,10 +6920,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "91171d8b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dbbbb8a5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions.\n",
-    "\n",
     "## The problem to solve for\n",
     "\n",
     "The wave equation to solve for, is"
@@ -2792,7 +6942,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "3f1be58e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"wave\"></div>\n",
@@ -2806,7 +6959,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "d54c4188",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $c$ is the given wave speed.\n",
     "The chosen conditions for this equation are"
@@ -2814,7 +6970,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "952c58e8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"condwave\"></div>\n",
@@ -2831,11 +6990,21 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "a650bae2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9e0b8996",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$.\n",
-    "\n",
-    "\n",
     "## The trial solution\n",
     "Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n",
     "The only things we have to change, is the trial solution such that it satisfies the conditions from ([20](#condwave)) and the cost function.\n",
@@ -2852,23 +7021,46 @@
     "h_1(x,t) = (1-t^2)u(x) + tv(x)\n",
     "$$\n",
     "\n",
-    "Note that this trial solution satisfies the conditions only if $u(0) = v(0) = u(1) = v(1) = 0$, which is the case in this example.\n",
-    "\n",
+    "Note that this trial solution satisfies the conditions only if $u(0) = v(0) = u(1) = v(1) = 0$, which is the case in this example."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0f3f1985",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## The analytical solution\n",
     "\n",
     "The analytical solution for our specific problem, is\n",
     "\n",
     "$$\n",
     "g(x,t) = \\sin(\\pi x)\\cos(\\pi t) - \\sin(\\pi x)\\sin(\\pi t)\n",
-    "$$\n",
-    "\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fbd35329",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
     "## Solving the wave equation - the full program using Autograd"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
+   "execution_count": 40,
+   "id": "6ccf9344",
+   "metadata": {
+    "collapsed": false,
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2925,7 +7117,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -3030,7 +7222,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,res,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -3038,7 +7230,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,res_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -3046,7 +7238,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -3095,7 +7287,10 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "id": "988e09cf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resources on differential equations and deep learning\n",
     "\n",
@@ -3105,1635 +7300,13 @@
     "\n",
     "3. [Solving differential equations using neural networks by M.M Chiaramonte and M. Kiener](http://cs229.stanford.edu/proj2013/ChiaramonteKiener-SolvingDifferentialEquationsUsingNeuralNetworks.pdf)\n",
     "\n",
-    "4. [Introduction to Partial Differential Equations by A. Tveito, R. Winther](https://www.springer.com/us/book/9783540225515)\n",
-    "\n",
-    "## Friday, Principal Component Analysis\n",
-    "\n",
-    "[Overview video](https://www.youtube.com/watch?v=fkf4IBRSeEc&ab_channel=SteveBrunton)\n",
-    "\n",
-    "## Basic ideas of the Principal Component Analysis (PCA)\n",
-    "\n",
-    "The principal component analysis deals with the problem of fitting a\n",
-    "low-dimensional affine subspace $S$ of dimension $d$ much smaller than\n",
-<<<<<<< HEAD
-    "the totaldimension $D$ of the problem at hand (our data\n",
-    "set). Mathematically it can be formulated as a statistical problem or\n",
-    "a geometric problem.  In our discussion of the theorem for the\n",
-    "classical PCA, we will stay with a statistical approach. This is also\n",
-    "what set the scene historically which for the PCA.\n",
-=======
-    "the total dimension $D$ of the problem at hand (our data\n",
-    "set). Mathematically it can be formulated as a statistical problem or\n",
-    "a geometric problem.  In our discussion of the theorem for the\n",
-    "classical PCA, we will stay with a statistical approach. \n",
-    "Historically, the PCA was first formulated in a statistical setting in order to estimate the principal component of a multivariate random variable.\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "We have a data set defined by a design/feature matrix $\\boldsymbol{X}$ (see below for its definition) \n",
-    "* Each data point is determined by $p$ extrinsic (measurement) variables\n",
-    "\n",
-    "* We may want to ask the following question: Are there fewer intrinsic variables (say $d << p$) that still approximately describe the data?\n",
-    "\n",
-    "* If so, these intrinsic variables may tell us something important and finding these intrinsic variables is what dimension reduction methods do. \n",
-    "\n",
-<<<<<<< HEAD
-=======
-    "A good read is for example [Vidal, Ma and Sastry](https://www.springer.com/gp/book/9780387878102).\n",
-    "\n",
-    "\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "## Introducing the Covariance and Correlation functions\n",
-    "\n",
-    "Before we discuss the PCA theorem, we need to remind ourselves about\n",
-    "the definition of the covariance and the correlation function. These are quantities \n",
-    "\n",
-    "Suppose we have defined two vectors\n",
-    "$\\hat{x}$ and $\\hat{y}$ with $n$ elements each. The covariance matrix $\\boldsymbol{C}$ is defined as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n",
-    "                              \\mathrm{cov}[\\boldsymbol{y},\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{y},\\boldsymbol{y}] \\\\\n",
-    "             \\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where for example"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] =\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})(y_i- \\overline{y}).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "With this definition and recalling that the variance is defined as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{var}[\\boldsymbol{x}]=\\frac{1}{n} \\sum_{i=0}^{n-1}(x_i- \\overline{x})^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "we can rewrite the covariance matrix as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}] & \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n",
-    "                              \\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}] & \\mathrm{var}[\\boldsymbol{y}] \\\\\n",
-    "             \\end{bmatrix}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The covariance takes values between zero and infinity and may thus\n",
-    "lead to problems with loss of numerical precision for particularly\n",
-    "large values. It is common to scale the covariance matrix by\n",
-    "introducing instead the correlation matrix defined via the so-called\n",
-    "correlation function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]=\\frac{\\mathrm{cov}[\\boldsymbol{x},\\boldsymbol{y}]}{\\sqrt{\\mathrm{var}[\\boldsymbol{x}] \\mathrm{var}[\\boldsymbol{y}]}}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The correlation function is then given by values $\\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}]\n",
-    "\\in [-1,1]$. This avoids eventual problems with too large values. We\n",
-    "can then define the correlation matrix for the two vectors $\\boldsymbol{x}$\n",
-    "and $\\boldsymbol{y}$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{K}[\\boldsymbol{x},\\boldsymbol{y}] = \\begin{bmatrix} 1 & \\mathrm{corr}[\\boldsymbol{x},\\boldsymbol{y}] \\\\\n",
-    "                              \\mathrm{corr}[\\boldsymbol{y},\\boldsymbol{x}] & 1 \\\\\n",
-    "             \\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the above example this is the function we constructed using **pandas**.\n",
-    "\n",
-    "## Correlation Function and Design/Feature Matrix\n",
-    "\n",
-    "In our derivation of the various regression algorithms like **Ordinary Least Squares** or **Ridge regression**\n",
-    "we defined the design/feature matrix $\\boldsymbol{X}$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{X}=\\begin{bmatrix}\n",
-    "x_{0,0} & x_{0,1} & x_{0,2}& \\dots & \\dots x_{0,p-1}\\\\\n",
-    "x_{1,0} & x_{1,1} & x_{1,2}& \\dots & \\dots x_{1,p-1}\\\\\n",
-    "x_{2,0} & x_{2,1} & x_{2,2}& \\dots & \\dots x_{2,p-1}\\\\\n",
-    "\\dots & \\dots & \\dots & \\dots \\dots & \\dots \\\\\n",
-    "x_{n-2,0} & x_{n-2,1} & x_{n-2,2}& \\dots & \\dots x_{n-2,p-1}\\\\\n",
-    "x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \\dots & \\dots x_{n-1,p-1}\\\\\n",
-    "\\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "with $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors/features $p$  refering to the column numbers and the\n",
-    "entries $n$ being the row elements.\n",
-    "We can rewrite the design/feature matrix in terms of its column vectors as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{X}=\\begin{bmatrix} \\boldsymbol{x}_0 & \\boldsymbol{x}_1 & \\boldsymbol{x}_2 & \\dots & \\dots & \\boldsymbol{x}_{p-1}\\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "with a given vector"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{x}_i^T = \\begin{bmatrix}x_{0,i} & x_{1,i} & x_{2,i}& \\dots & \\dots x_{n-1,i}\\end{bmatrix}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "With these definitions, we can now rewrite our $2\\times 2$\n",
-    "correaltion/covariance matrix in terms of a moe general design/feature\n",
-    "matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$. This leads to a $p\\times p$\n",
-    "covariance matrix for the vectors $\\boldsymbol{x}_i$ with $i=0,1,\\dots,p-1$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}] = \\begin{bmatrix}\n",
-    "\\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1]  & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & \\mathrm{var}[\\boldsymbol{x}_1]  & \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_0]   & \\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_1] & \\mathrm{var}[\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{cov}[\\boldsymbol{x}_2,\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
-    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
-    "\\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_0]   & \\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_1] & \\mathrm{cov}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_{2}]  & \\dots & \\dots  & \\mathrm{var}[\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and the correlation matrix"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{K}[\\boldsymbol{x}] = \\begin{bmatrix}\n",
-    "1 & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_1]  & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_0,\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & 1  & \\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_2] & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_1,\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_0]   & \\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_1] & 1 & \\dots & \\dots & \\mathrm{corr}[\\boldsymbol{x}_2,\\boldsymbol{x}_{p-1}]\\\\\n",
-    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
-    "\\dots & \\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
-    "\\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_0]   & \\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_1] & \\mathrm{corr}[\\boldsymbol{x}_{p-1},\\boldsymbol{x}_{2}]  & \\dots & \\dots  & 1\\\\\n",
-    "\\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Covariance Matrix Examples\n",
-    "\n",
-    "\n",
-    "The Numpy function **np.cov** calculates the covariance elements using\n",
-    "the factor $1/(n-1)$ instead of $1/n$ since it assumes we do not have\n",
-    "the exact mean values.  The following simple function uses the\n",
-    "**np.vstack** function which takes each vector of dimension $1\\times n$\n",
-    "and produces a $2\\times n$ matrix $\\boldsymbol{W}$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{W} = \\begin{bmatrix} x_0 & y_0 \\\\\n",
-    "                          x_1 & y_1 \\\\\n",
-    "                          x_2 & y_2\\\\\n",
-    "                          \\dots & \\dots \\\\\n",
-    "                          x_{n-2} & y_{n-2}\\\\\n",
-    "                          x_{n-1} & y_{n-1} & \n",
-    "             \\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which in turn is converted into into the $2\\times 2$ covariance matrix\n",
-    "$\\boldsymbol{C}$ via the Numpy function **np.cov()**. We note that we can also calculate\n",
-    "the mean value of each set of samples $\\boldsymbol{x}$ etc using the Numpy\n",
-    "function **np.mean(x)**. We can also extract the eigenvalues of the\n",
-    "covariance matrix through the **np.linalg.eig()** function."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-0.0295549375800962\n",
-      "3.790157415516731\n",
-      "[[ 1.14945017  3.28385419]\n",
-      " [ 3.28385419 10.22579788]]\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "# Importing various packages\n",
-    "import numpy as np\n",
-    "n = 100\n",
-    "x = np.random.normal(size=n)\n",
-    "print(np.mean(x))\n",
-    "y = 4+3*x+np.random.normal(size=n)\n",
-    "print(np.mean(y))\n",
-    "W = np.vstack((x, y))\n",
-    "C = np.cov(W)\n",
-    "print(C)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Correlation Matrix\n",
-    "\n",
-    "The previous example can be converted into the correlation matrix by\n",
-    "simply scaling the matrix elements with the variances.  We should also\n",
-    "subtract the mean values for each column. This leads to the following\n",
-    "code which sets up the correlations matrix for the previous example in\n",
-    "a more brute force way. Here we scale the mean values for each column of the design matrix, calculate the relevant mean values and variances and then finally set up the $2\\times 2$ correlation matrix (since we have only two vectors)."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.08073726712724406\n",
-      "1.6145539590295142\n",
-      "[[1.         0.63404481]\n",
-      " [0.63404481 1.        ]]\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "import numpy as np\n",
-    "n = 100\n",
-    "# define two vectors                                                                                           \n",
-    "x = np.random.random(size=n)\n",
-    "y = 4+3*x+np.random.normal(size=n)\n",
-    "#scaling the x and y vectors                                                                                   \n",
-    "x = x - np.mean(x)\n",
-    "y = y - np.mean(y)\n",
-    "variance_x = np.sum(x@x)/n\n",
-    "variance_y = np.sum(y@y)/n\n",
-    "print(variance_x)\n",
-    "print(variance_y)\n",
-    "cov_xy = np.sum(x@y)/n\n",
-    "cov_xx = np.sum(x@x)/n\n",
-    "cov_yy = np.sum(y@y)/n\n",
-    "C = np.zeros((2,2))\n",
-    "C[0,0]= cov_xx/variance_x\n",
-    "C[1,1]= cov_yy/variance_y\n",
-    "C[0,1]= cov_xy/np.sqrt(variance_y*variance_x)\n",
-    "C[1,0]= C[0,1]\n",
-    "print(C)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see that the matrix elements along the diagonal are one as they\n",
-    "should be and that the matrix is symmetric. Furthermore, diagonalizing\n",
-    "this matrix we easily see that it is a positive definite matrix.\n",
-    "\n",
-    "The above procedure with **numpy** can be made more compact if we use **pandas**.\n",
-    "\n",
-    "## Correlation Matrix with Pandas\n",
-    "\n",
-    "We whow here how we can set up the correlation matrix using **pandas**, as done in this simple code"
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 0.01396941  0.49068974]\n",
-      " [ 0.54918099  2.04838299]\n",
-      " [-0.35991553 -1.16529785]\n",
-      " [ 0.74909071  1.11467729]\n",
-      " [ 1.10998316  4.0040917 ]\n",
-      " [-0.98934642 -2.16772616]\n",
-      " [ 0.25009971  0.75283979]\n",
-      " [-0.57918262 -1.70870953]\n",
-      " [-0.98545332 -3.90181134]\n",
-      " [ 0.24157391  0.53286336]]\n",
-      "          0         1\n",
-      "0  0.013969  0.490690\n",
-      "1  0.549181  2.048383\n",
-      "2 -0.359916 -1.165298\n",
-      "3  0.749091  1.114677\n",
-      "4  1.109983  4.004092\n",
-      "5 -0.989346 -2.167726\n",
-      "6  0.250100  0.752840\n",
-      "7 -0.579183 -1.708710\n",
-      "8 -0.985453 -3.901811\n",
-      "9  0.241574  0.532863\n",
-      "          0         1\n",
-      "0  1.000000  0.959994\n",
-      "1  0.959994  1.000000\n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "import numpy as np\n",
-    "import pandas as pd\n",
-    "n = 10\n",
-    "x = np.random.normal(size=n)\n",
-    "x = x - np.mean(x)\n",
-    "y = 4+3*x+np.random.normal(size=n)\n",
-    "y = y - np.mean(y)\n",
-    "X = (np.vstack((x, y))).T\n",
-    "print(X)\n",
-    "Xpd = pd.DataFrame(X)\n",
-    "print(Xpd)\n",
-    "correlation_matrix = Xpd.corr()\n",
-    "print(correlation_matrix)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We expand this model to the Franke function discussed above.\n",
-    "\n",
-    "## Correlation Matrix with Pandas and the Franke function"
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [],
-=======
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     0         1         2         3         4         5         6         7   \\\n",
-      "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1   0.0  0.072184  0.069825  0.069428  0.071162  0.072822  0.060421  0.061903   \n",
-      "2   0.0  0.069825  0.069297  0.065490  0.068155  0.070919  0.055665  0.057749   \n",
-      "3   0.0  0.069428  0.065490  0.071945  0.072269  0.072413  0.065947  0.066493   \n",
-      "4   0.0  0.071162  0.068155  0.072269  0.073368  0.074365  0.065102  0.066207   \n",
-      "5   0.0  0.072822  0.070919  0.072413  0.074365  0.076313  0.064012  0.065724   \n",
-      "6   0.0  0.060421  0.055665  0.065947  0.065102  0.064012  0.062745  0.062435   \n",
-      "7   0.0  0.061903  0.057749  0.066493  0.066207  0.065724  0.062435  0.062545   \n",
-      "8   0.0  0.063660  0.060176  0.067220  0.067552  0.067741  0.062209  0.062780   \n",
-      "9   0.0  0.065675  0.062949  0.068101  0.069119  0.070057  0.062036  0.063114   \n",
-      "10  0.0  0.052443  0.047291  0.059402  0.057799  0.055912  0.058081  0.057183   \n",
-      "11  0.0  0.053341  0.048621  0.059668  0.058469  0.057019  0.057756  0.057169   \n",
-      "12  0.0  0.054483  0.050229  0.060122  0.059366  0.058394  0.057550  0.057302   \n",
-      "13  0.0  0.055889  0.052145  0.060775  0.060506  0.060062  0.057464  0.057588   \n",
-      "14  0.0  0.057577  0.054396  0.061634  0.061905  0.062047  0.057497  0.058031   \n",
-      "\n",
-      "          8         9         10        11        12        13        14  \n",
-      "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
-      "1   0.063660  0.065675  0.052443  0.053341  0.054483  0.055889  0.057577  \n",
-      "2   0.060176  0.062949  0.047291  0.048621  0.050229  0.052145  0.054396  \n",
-      "3   0.067220  0.068101  0.059402  0.059668  0.060122  0.060775  0.061634  \n",
-      "4   0.067552  0.069119  0.057799  0.058469  0.059366  0.060506  0.061905  \n",
-      "5   0.067741  0.070057  0.055912  0.057019  0.058394  0.060062  0.062047  \n",
-      "6   0.062209  0.062036  0.058081  0.057756  0.057550  0.057464  0.057497  \n",
-      "7   0.062780  0.063114  0.057183  0.057169  0.057302  0.057588  0.058031  \n",
-      "8   0.063524  0.064419  0.056301  0.056626  0.057130  0.057825  0.058718  \n",
-      "9   0.064419  0.065935  0.055400  0.056095  0.057007  0.058150  0.059542  \n",
-      "10  0.056301  0.055400  0.054868  0.054129  0.053455  0.052843  0.052283  \n",
-      "11  0.056626  0.056095  0.054129  0.053624  0.053205  0.052870  0.052614  \n",
-      "12  0.057130  0.057007  0.053455  0.053205  0.053063  0.053031  0.053108  \n",
-      "13  0.057825  0.058150  0.052843  0.052870  0.053031  0.053332  0.053775  \n",
-      "14  0.058718  0.059542  0.052283  0.052614  0.053108  0.053775  0.054625  \n"
-     ]
-    }
-   ],
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "source": [
-    "# Common imports\n",
-    "import numpy as np\n",
-    "import pandas as pd\n",
-    "\n",
-    "\n",
-    "def FrankeFunction(x,y):\n",
-    "\tterm1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
-    "\tterm2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
-    "\tterm3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
-    "\tterm4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
-    "\treturn term1 + term2 + term3 + term4\n",
-    "\n",
-    "\n",
-    "def create_X(x, y, n ):\n",
-    "\tif len(x.shape) > 1:\n",
-    "\t\tx = np.ravel(x)\n",
-    "\t\ty = np.ravel(y)\n",
-    "\n",
-    "\tN = len(x)\n",
-    "\tl = int((n+1)*(n+2)/2)\t\t# Number of elements in beta\n",
-    "\tX = np.ones((N,l))\n",
-    "\n",
-    "\tfor i in range(1,n+1):\n",
-    "\t\tq = int((i)*(i+1)/2)\n",
-    "\t\tfor k in range(i+1):\n",
-    "\t\t\tX[:,q+k] = (x**(i-k))*(y**k)\n",
-    "\n",
-    "\treturn X\n",
-    "\n",
-    "\n",
-    "# Making meshgrid of datapoints and compute Franke's function\n",
-    "n = 4\n",
-    "N = 100\n",
-    "x = np.sort(np.random.uniform(0, 1, N))\n",
-    "y = np.sort(np.random.uniform(0, 1, N))\n",
-    "z = FrankeFunction(x, y)\n",
-    "X = create_X(x, y, n=n)    \n",
-    "\n",
-    "Xpd = pd.DataFrame(X)\n",
-    "# subtract the mean values and set up the covariance matrix\n",
-    "Xpd = Xpd - Xpd.mean()\n",
-    "covariance_matrix = Xpd.cov()\n",
-    "print(covariance_matrix)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We note here that the covariance is zero for the first rows and\n",
-    "columns since all matrix elements in the design matrix were set to one\n",
-<<<<<<< HEAD
-    "(we are fitting the function in terms of a polynomial of degree $n$).\n",
-    "\n",
-    "This means that the variance for these elements will be zero and will\n",
-    "cause problems when we set up the correlation matrix.  We can simply\n",
-    "drop these elements and construct a correlation\n",
-    "matrix without these elements. \n",
-=======
-    "(we are fitting the function in terms of a polynomial of degree $n$). We would however not include the intercept\n",
-    "and wee can simply\n",
-    "drop these elements and construct a correlation\n",
-    "matrix without them. \n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "\n",
-    "## Rewriting the Covariance and/or Correlation Matrix\n",
-    "\n",
-    "We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix $\\boldsymbol{X}$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T= \\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T].\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To see this let us simply look at a design matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{2\\times 2}$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{X}=\\begin{bmatrix}\n",
-    "x_{00} & x_{01}\\\\\n",
-    "x_{10} & x_{11}\\\\\n",
-    "\\end{bmatrix}=\\begin{bmatrix}\n",
-    "\\boldsymbol{x}_{0} & \\boldsymbol{x}_{1}\\\\\n",
-    "\\end{bmatrix}.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If we then compute the expectation value"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T=\\begin{bmatrix}\n",
-    "x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\\\\n",
-    "x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\\\\n",
-    "\\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which is just"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]=\\begin{bmatrix} \\mathrm{var}[\\boldsymbol{x}_0] & \\mathrm{cov}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] \\\\\n",
-    "                              \\mathrm{cov}[\\boldsymbol{x}_1,\\boldsymbol{x}_0] & \\mathrm{var}[\\boldsymbol{x}_1] \\\\\n",
-    "             \\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where we wrote $$\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]$$ to indicate that this the covariance of the vectors $\\boldsymbol{x}$ of the design/feature matrix $\\boldsymbol{X}$.\n",
-    "\n",
-    "It is easy to generalize this to a matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$.\n",
-    "\n",
-    "\n",
-    "## Towards the PCA theorem\n",
-    "\n",
-    "We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T= \\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T].\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us now assume that we can perform a series of orthogonal transformations where we employ some orthogonal matrices $\\boldsymbol{S}$.\n",
-    "These matrices are defined as $\\boldsymbol{S}\\in {\\mathbb{R}}^{p\\times p}$ and obey the orthogonality requirements $\\boldsymbol{S}\\boldsymbol{S}^T=\\boldsymbol{S}^T\\boldsymbol{S}=\\boldsymbol{I}$. The matrix can be written out in terms of the column vectors $\\boldsymbol{s}_i$ as $\\boldsymbol{S}=[\\boldsymbol{s}_0,\\boldsymbol{s}_1,\\dots,\\boldsymbol{s}_{p-1}]$ and $\\boldsymbol{s}_i \\in {\\mathbb{R}}^{p}$.\n",
-    "\n",
-    "Assume also that there is a transformation $\\boldsymbol{S}\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T=\\boldsymbol{C}[\\boldsymbol{y}]$ such that the new matrix $\\boldsymbol{C}[\\boldsymbol{y}]$ is diagonal with elements $[\\lambda_0,\\lambda_1,\\lambda_2,\\dots,\\lambda_{p-1}]$.  \n",
-    "\n",
-    "That is we have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{y}] = \\mathbb{E}[\\boldsymbol{S}\\boldsymbol{X}\\boldsymbol{X}^T\\boldsymbol{S}^T]=\\boldsymbol{S}\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "since the matrix $\\boldsymbol{S}$ is not a data dependent matrix.   Multiplying with $\\boldsymbol{S}^T$ from the left we have"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{S}^T\\boldsymbol{C}[\\boldsymbol{y}] = \\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and since $\\boldsymbol{C}[\\boldsymbol{y}]$ is diagonal we have for a given eigenvalue $i$ of the covariance matrix that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{S}^T_i\\lambda_i = \\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{S}^T_i.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In the derivation of the PCA theorem we will assume that the eigenvalues are ordered in descending order, that is\n",
-    "$\\lambda_0 > \\lambda_1 > \\dots > \\lambda_{p-1}$. \n",
-    "\n",
-    "\n",
-    "The eigenvalues tell us then how much we need to stretch the\n",
-    "corresponding eigenvectors. Dimensions with large eigenvalues have\n",
-    "thus large variations (large variance) and define therefore useful\n",
-    "dimensions. The data points are more spread out in the direction of\n",
-    "these eigenvectors.  Smaller eigenvalues mean on the other hand that\n",
-    "the corresponding eigenvectors are shrunk accordingly and the data\n",
-    "points are tightly bunched together and there is not much variation in\n",
-    "these specific directions. Hopefully then we could leave it out\n",
-    "dimensions where the eigenvalues are very small. If $p$ is very large,\n",
-    "we could then aim at reducing $p$ to $l << p$ and handle only $l$\n",
-    "features/predictors.\n",
-    "\n",
-    "## The Algorithm before theorem\n",
-    "\n",
-    "Here's how we would proceed in setting up the algorithm for the PCA, see also discussion below here. \n",
-    "* Set up the datapoints for the design/feature matrix $\\boldsymbol{X}$ with $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$, with the predictors/features $p$  referring to the column numbers and the entries $n$ being the row elements."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{X}=\\begin{bmatrix}\n",
-    "x_{0,0} & x_{0,1} & x_{0,2}& \\dots & \\dots x_{0,p-1}\\\\\n",
-    "x_{1,0} & x_{1,1} & x_{1,2}& \\dots & \\dots x_{1,p-1}\\\\\n",
-    "x_{2,0} & x_{2,1} & x_{2,2}& \\dots & \\dots x_{2,p-1}\\\\\n",
-    "\\dots & \\dots & \\dots & \\dots \\dots & \\dots \\\\\n",
-    "x_{n-2,0} & x_{n-2,1} & x_{n-2,2}& \\dots & \\dots x_{n-2,p-1}\\\\\n",
-    "x_{n-1,0} & x_{n-1,1} & x_{n-1,2}& \\dots & \\dots x_{n-1,p-1}\\\\\n",
-    "\\end{bmatrix},\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "* Center the data by subtracting the mean value for each column. This leads to a new matrix $\\boldsymbol{X}\\rightarrow \\overline{\\boldsymbol{X}}$.\n",
-    "\n",
-    "* Compute then the covariance/correlation matrix $\\mathbb{E}[\\overline{\\boldsymbol{X}}\\overline{\\boldsymbol{X}}^T]$.\n",
-    "\n",
-    "* Find the eigenpairs of $\\boldsymbol{C}$ with eigenvalues $[\\lambda_0,\\lambda_1,\\dots,\\lambda_{p-1}]$ and eigenvectors $[\\boldsymbol{s}_0,\\boldsymbol{s}_1,\\dots,\\boldsymbol{s}_{p-1}]$.\n",
-    "\n",
-    "* Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.\n",
-    "\n",
-    "* Keep only those $l$ eigenvalues larger than a selected threshold value, discarding thus $p-l$ features since we expect small variations in the data here.\n",
-    "\n",
-    "## Writing our own PCA code\n",
-    "\n",
-    "We will use a simple example first with two-dimensional data\n",
-    "drawn from a multivariate normal distribution with the following mean and covariance matrix:"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mu = (-1,2) \\qquad \\Sigma = \\begin{bmatrix} 4 & 2 \\\\\n",
-    "2 & 2\n",
-    "\\end{bmatrix}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that the mean refers to each column of data. \n",
-    "We will generate $n = 1000$ points $X = \\{ x_1, \\ldots, x_N \\}$ from\n",
-    "this distribution, and store them in the $1000 \\times 2$ matrix $\\boldsymbol{X}$.\n",
-    "\n",
-    "The following Python code aids in setting up the data and writing out the design matrix.\n",
-    "Note that the function **multivariate** returns also the covariance discussed above and that it is defined by dividing by $n-1$ instead of $n$."
-   ]
-  },
-  {
-   "cell_type": "code",
-<<<<<<< HEAD
-   "execution_count": 15,
-=======
-   "execution_count": 5,
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import pandas as pd\n",
-    "import matplotlib.pyplot as plt\n",
-    "from IPython.display import display\n",
-    "n = 10000\n",
-    "mean = (-1, 2)\n",
-    "cov = [[4, 2], [2, 2]]\n",
-    "X = np.random.multivariate_normal(mean, cov, n)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now we are going to implement the PCA algorithm. We will break it down into various substeps.\n",
-    "\n",
-    "### Compute the sample mean and center the data\n",
-    "\n",
-    "The first step of PCA is to compute the sample mean of the data and use it to center the data. Recall that the sample mean is"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mu_n = \\frac{1}{n} \\sum_{i=1}^n x_i\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "and the mean-centered data $\\bar{X} = \\{ \\bar{x}_1, \\ldots, \\bar{x}_n \\}$ takes the form"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\bar{x}_i = x_i - \\mu_n.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "When you are done with these steps, print out $\\mu_n$ to verify it is\n",
-    "close to $\\mu$ and plot your mean centered data to verify it is\n",
-    "centered at the origin! Compare your code with the functionality from **Scikit-Learn** discussed above.\n",
-    "The following code elements perform these operations using **pandas** or using our own functionality for doing so. The latter, using **numpy** is rather simple through the **mean()** function."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "df = pd.DataFrame(X)\n",
-    "# Pandas does the centering for us\n",
-    "df = df -df.mean()\n",
-    "# we center it ourselves\n",
-    "X_centered = X - X.mean(axis=0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Alternatively, we could use the functions we discussed\n",
-    "earlier for scaling the data set.  That is, we could have used the\n",
-    "**StandardScaler** function in **Scikit-Learn**, a function which ensures\n",
-    "that for each feature/predictor we study the mean value is zero and\n",
-    "the variance is one (every column in the design/feature matrix).  You\n",
-    "would then not get the same results, since we divide by the\n",
-    "variance. The diagonal covariance matrix elements will then be one,\n",
-    "while the non-diagonal ones need to be divided by $2\\sqrt{2}$ for our\n",
-    "specific case.\n",
-    "\n",
-    "### Compute the sample covariance\n",
-    "\n",
-    "Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\Sigma_n = \\frac{1}{n-1} \\sum_{i=1}^n \\bar{x}_i^T \\bar{x}_i = \\frac{1}{n-1} \\sum_{i=1}^n (x_i - \\mu_n)^T (x_i - \\mu_n)\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where the data points $x_i \\in \\mathbb{R}^p$ (here in this example $p = 2$) are column vectors and $x^T$ is the transpose of $x$.\n",
-    "We can write our own code or simply use either the functionaly of **numpy** or that of **pandas**, as follows"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(df.cov())\n",
-    "print(np.cov(X_centered.T))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that the way we define the covariance matrix here has a factor $n-1$ instead of $n$. This is included in the **cov()** function by **numpy** and **pandas**. \n",
-    "Our own code here is not very elegant and asks for obvious improvements. It is tailored to this specific $2\\times 2$ covariance matrix."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# extract the relevant columns from the centered design matrix of dim n x 2\n",
-    "x = X_centered[:,0]\n",
-    "y = X_centered[:,1]\n",
-    "Cov = np.zeros((2,2))\n",
-    "Cov[0,1] = np.sum(x.T@y)/(n-1.0)\n",
-    "Cov[0,0] = np.sum(x.T@x)/(n-1.0)\n",
-    "Cov[1,1] = np.sum(y.T@y)/(n-1.0)\n",
-    "Cov[1,0]= Cov[0,1]\n",
-    "print(\"Centered covariance using own code\")\n",
-    "print(Cov)\n",
-    "plt.plot(x, y, 'x')\n",
-    "plt.axis('equal')\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Depending on the number of points $n$, we will get results that are close to the covariance values defined above.\n",
-    "The plot shows how the data are clustered around a line with slope close to one. Is this expected?\n",
-    "\n",
-    "### Diagonalize the sample covariance matrix to obtain the principal components\n",
-    "\n",
-    "Now we are ready to solve for the principal components! To do so we\n",
-    "diagonalize the sample covariance matrix $\\Sigma$. We can use the\n",
-    "function **np.linalg.eig** to do so. It will return the eigenvalues and\n",
-    "eigenvectors of $\\Sigma$. Once we have these we can perform the \n",
-    "following tasks:\n",
-    "\n",
-    "* We compute the percentage of the total variance captured by the first principal component\n",
-    "\n",
-    "* We plot the mean centered data and lines along the first and second principal components\n",
-    "\n",
-    "* Then we project the mean centered data onto the first and second principal components, and plot the projected data. \n",
-    "\n",
-    "* Finally, we approximate the data as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "x_i \\approx \\tilde{x}_i = \\mu_n + \\langle x_i, v_0 \\rangle v_0\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where $v_0$ is the first principal component. \n",
-    "\n",
-    "Collecting all these steps we can write our own PCA function and\n",
-    "compare this with the functionality included in **Scikit-Learn**.  \n",
-    "\n",
-    "The code here outlines some of the elements we could include in the\n",
-    "analysis. Feel free to extend upon this in order to address the above\n",
-    "questions."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# diagonalize and obtain eigenvalues, not necessarily sorted\n",
-    "EigValues, EigVectors = np.linalg.eig(Cov)\n",
-    "# sort eigenvectors and eigenvalues\n",
-    "#permute = EigValues.argsort()\n",
-    "#EigValues = EigValues[permute]\n",
-    "#EigVectors = EigVectors[:,permute]\n",
-    "print(\"Eigenvalues of Covariance matrix\")\n",
-    "for i in range(2):\n",
-    "    print(EigValues[i])\n",
-    "FirstEigvector = EigVectors[:,0]\n",
-    "SecondEigvector = EigVectors[:,1]\n",
-    "print(\"First eigenvector\")\n",
-    "print(FirstEigvector)\n",
-    "print(\"Second eigenvector\")\n",
-    "print(SecondEigvector)\n",
-    "#thereafter we do a PCA with Scikit-learn\n",
-    "from sklearn.decomposition import PCA\n",
-    "pca = PCA(n_components = 2)\n",
-    "X2Dsl = pca.fit_transform(X)\n",
-    "print(\"Eigenvector of largest eigenvalue\")\n",
-    "print(pca.components_.T[:, 0])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This code does not contain all the above elements, but it shows how we can use **Scikit-Learn** to extract the eigenvector which corresponds to the largest eigenvalue. Try to address the questions we pose before the above code.  Try also to change the values of the covariance matrix by making one of the diagonal elements much larger than the other. What do you observe then? \n",
-    "\n",
-    "## Classical PCA Theorem\n",
-    "\n",
-    "We assume now that we have a design matrix $\\boldsymbol{X}$ which has been\n",
-    "centered as discussed above. For the sake of simplicity we skip the\n",
-    "overline symbol. The matrix is defined in terms of the various column\n",
-    "vectors $[\\boldsymbol{x}_0,\\boldsymbol{x}_1,\\dots, \\boldsymbol{x}_{p-1}]$ each with dimension\n",
-    "$\\boldsymbol{x}\\in {\\mathbb{R}}^{n}$.\n",
-    "\n",
-    "We assume also that we have an orthogonal transformation $\\boldsymbol{W}\\in {\\mathbb{R}}^{p\\times p}$.  We define the reconstruction error (which is similar to the mean squared error we have seen before) as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{W},\\boldsymbol{Z}) = \\frac{1}{n}\\sum_i (\\boldsymbol{x}_i - \\overline{\\boldsymbol{x}}_i)^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "with $\\overline{\\boldsymbol{x}}_i = \\boldsymbol{W}\\boldsymbol{z}_i$, where $\\boldsymbol{z}_i$ is a row vector with dimension ${\\mathbb{R}}^{n}$ of the matrix\n",
-    "$\\boldsymbol{Z}\\in{\\mathbb{R}}^{p\\times n}$.  When doing PCA we want to reduce this dimensionality. \n",
-    "\n",
-    "The PCA theorem states that minimizing the above reconstruction error\n",
-    "corresponds to setting $\\boldsymbol{W}=\\boldsymbol{S}$, the orthogonal matrix which\n",
-    "diagonalizes the empirical covariance(correlation) matrix. The optimal\n",
-    "low-dimensional encoding of the data is then given by a set of vectors\n",
-    "$\\boldsymbol{z}_i$ with at most $l$ vectors, with $l << p$, defined by the\n",
-    "orthogonal projection of the data onto the columns spanned by the\n",
-    "eigenvectors of the covariance(correlations matrix).\n",
-    "\n",
-<<<<<<< HEAD
-    "The proof which follows will be updated by mid January 2020.\n",
-=======
-    "\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "## Proof of the PCA Theorem\n",
-    "\n",
-    "To show the PCA theorem let us start with the assumption that there is one vector $\\boldsymbol{w}_0$ which corresponds to a solution which minimized the reconstruction error $J$. This is an orthogonal vector. It means that we now approximate the reconstruction error in terms of $\\boldsymbol{w}_0$ and $\\boldsymbol{z}_0$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0,\\boldsymbol{z}_0)= \\frac{1}{n}\\sum_i (\\boldsymbol{x}_i - z_{i0}\\boldsymbol{w}_0)^2=\\frac{1}{n}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - 2z_{i0}\\boldsymbol{w}_0^T\\boldsymbol{x}_i+z_{i0}^2\\boldsymbol{w}_0^T\\boldsymbol{w}_0),\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which we can rewrite due to the orthogonality of $\\boldsymbol{w}_i$ as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0,\\boldsymbol{z}_0)=\\frac{1}{n}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - 2z_{i0}\\boldsymbol{w}_0^T\\boldsymbol{x}_i+z_{i0}^2).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Minimizing $J$ with respect to the unknown parameters $z_{0i}$ we obtain that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "z_{i0}=\\boldsymbol{w}_0^T\\boldsymbol{x}_i,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where the vectors on the rhs are known. \n",
-    "\n",
-    "\n",
-    "## PCA Proof continued\n",
-    "\n",
-    "We have now found the unknown parameters $z_{i0}$. These correspond to the projected coordinates and we can write"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0)= \\frac{1}{p}\\sum_i (\\boldsymbol{x}_i^T\\boldsymbol{x}_i - z_{i0}^2)=\\mathrm{const}-\\frac{1}{n}\\sum_i z_{i0}^2.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can show that the variance of the projected coordinates defined by $\\boldsymbol{w}_0^T\\boldsymbol{x}_i$ are given by"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{var}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\frac{1}{n}\\sum_i z_{i0}^2,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "since the expectation value of"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathbb{E}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\mathbb{E}[z_{i0}]= \\boldsymbol{w}_0^T\\mathbb{E}[\\boldsymbol{x}_i]=0,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "where we have used the fact that our data are centered.\n",
-    "\n",
-    "Recalling our definition of the covariance as"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}] = \\frac{1}{n}\\boldsymbol{X}\\boldsymbol{X}^T=\\mathbb{E}[\\boldsymbol{X}\\boldsymbol{X}^T],\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "we have thus that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\mathrm{var}[\\boldsymbol{w}_0^T\\boldsymbol{x}_i] = \\frac{1}{n}\\sum_i z_{i0}^2=\\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We are almost there, we have obtained a relation between minimizing\n",
-    "the reconstruction error and the variance and the covariance\n",
-    "matrix. Minimizing the error is equivalent to maximizing the variance\n",
-    "of the projected data.\n",
-    "\n",
-    "## The final step\n",
-    "\n",
-    "We could trivially maximize the variance of the projection (and\n",
-    "thereby minimize the error in the reconstruction function) by letting\n",
-    "the norm-2 of $\\boldsymbol{w}_0$ go to infinity. However, this norm since we\n",
-    "want the matrix $\\boldsymbol{W}$ to be an orthogonal matrix, is constrained by\n",
-    "$\\vert\\vert \\boldsymbol{w}_0 \\vert\\vert_2^2=1$. Imposing this condition via a\n",
-    "Lagrange multiplier we can then in turn maximize"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "J(\\boldsymbol{w}_0)= \\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0+\\lambda_0(1-\\boldsymbol{w}_0^T\\boldsymbol{w}_0).\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Taking the derivative with respect to $\\boldsymbol{w}_0$ we obtain"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\frac{\\partial J(\\boldsymbol{w}_0)}{\\partial \\boldsymbol{w}_0}= 2\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0-2\\lambda_0\\boldsymbol{w}_0=0,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "meaning that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0=\\lambda_0\\boldsymbol{w}_0.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**The direction that maximizes the variance (or minimizes the construction error) is an eigenvector of the covariance matrix**! If we left multiply with $\\boldsymbol{w}_0^T$ we have the variance of the projected data is"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\boldsymbol{w}_0^T\\boldsymbol{C}[\\boldsymbol{x}]\\boldsymbol{w}_0=\\lambda_0.\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If we want to maximize the variance (minimize the construction error)\n",
-    "we simply pick the eigenvector of the covariance matrix with the\n",
-    "largest eigenvalue. This establishes the link between the minimization\n",
-    "of the reconstruction function $J$ in terms of an orthogonal matrix\n",
-    "and the maximization of the variance and thereby the covariance of our\n",
-    "observations encoded in the design/feature matrix $\\boldsymbol{X}$.\n",
-    "\n",
-    "The proof\n",
-    "for the other eigenvectors $\\boldsymbol{w}_1,\\boldsymbol{w}_2,\\dots$ can be\n",
-    "established by applying the above arguments and using the fact that\n",
-    "our basis of eigenvectors is orthogonal, see [Murphy chapter\n",
-    "12.2](https://mitpress.mit.edu/books/machine-learning-1).  The\n",
-    "discussion in chapter 12.2 of Murphy's text has also a nice link with\n",
-    "the Singular Value Decomposition theorem. For categorical data, see\n",
-    "chapter 12.4 and discussion therein.\n",
-    "\n",
-<<<<<<< HEAD
-    "Additional part of the proof for the other eigenvectors will be added by mid January 2020.\n",
-    "\n",
-    "## Geometric Interpretation and link with Singular Value Decomposition\n",
-    "\n",
-    "This material will be added by mid January 2020.\n",
-=======
-    "For more details, see for example [Vidal, Ma and Sastry, chapter 2](https://www.springer.com/gp/book/9780387878102).\n",
-    "\n",
-    "## Geometric Interpretation and link with Singular Value Decomposition\n",
-    "\n",
-    "For a detailed demonstration of the geometric interpretation, see [Vidal, Ma and Sastry, section 2.1.2](https://www.springer.com/gp/book/9780387878102).\n",
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
-    "\n",
-    "\n",
-    "## Principal Component Analysis\n",
-    "\n",
-    "Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.\n",
-    "First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.\n",
-    "\n",
-    "The following Python code uses NumPy’s **svd()** function to obtain all the principal components of the\n",
-    "training set, then extracts the first two principal components. First we center the data using either **pandas** or our own code"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import pandas as pd\n",
-    "from IPython.display import display\n",
-    "np.random.seed(100)\n",
-    "# setting up a 10 x 5 vanilla matrix \n",
-    "rows = 10\n",
-    "cols = 5\n",
-    "X = np.random.randn(rows,cols)\n",
-    "df = pd.DataFrame(X)\n",
-    "# Pandas does the centering for us\n",
-    "df = df -df.mean()\n",
-    "display(df)\n",
-    "\n",
-    "# we center it ourselves\n",
-    "X_centered = X - X.mean(axis=0)\n",
-    "# Then check the difference between pandas and our own set up\n",
-    "print(X_centered-df)\n",
-    "#Now we do an SVD\n",
-    "U, s, V = np.linalg.svd(X_centered)\n",
-    "c1 = V.T[:, 0]\n",
-    "c2 = V.T[:, 1]\n",
-    "W2 = V.T[:, :2]\n",
-    "X2D = X_centered.dot(W2)\n",
-    "print(X2D)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering\n",
-    "the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t\n",
-    "forget to center the data first.\n",
-    "\n",
-    "Once you have identified all the principal components, you can reduce the dimensionality of the dataset\n",
-    "down to $d$ dimensions by projecting it onto the hyperplane defined by the first $d$ principal components.\n",
-    "Selecting this hyperplane ensures that the projection will preserve as much variance as possible."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "W2 = V.T[:, :2]\n",
-    "X2D = X_centered.dot(W2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<!-- !split  -->\n",
-    "## PCA and scikit-learn\n",
-    "\n",
-    "Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The\n",
-    "following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note\n",
-    "that it automatically takes care of centering the data):"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#thereafter we do a PCA with Scikit-learn\n",
-    "from sklearn.decomposition import PCA\n",
-    "pca = PCA(n_components = 2)\n",
-    "X2D = pca.fit_transform(X)\n",
-    "print(X2D)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "After fitting the PCA transformer to the dataset, you can access the principal components using the\n",
-    "components variable (note that it contains the PCs as horizontal vectors, so, for example, the first\n",
-    "principal component is equal to"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "pca.components_.T[:, 0]."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Another very useful piece of information is the explained variance ratio of each principal component,\n",
-    "available via the $explained\\_variance\\_ratio$ variable. It indicates the proportion of the dataset’s\n",
-    "variance that lies along the axis of each principal component. \n",
-    "\n",
-    "## Back to the Cancer Data\n",
-    "We can now repeat the above but applied to real data, in this case our breast cancer data.\n",
-    "Here we compute performance scores on the training data using logistic regression."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "from sklearn.model_selection import  train_test_split \n",
-    "from sklearn.datasets import load_breast_cancer\n",
-    "from sklearn.linear_model import LogisticRegression\n",
-    "cancer = load_breast_cancer()\n",
-    "\n",
-    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
-    "\n",
-    "logreg = LogisticRegression()\n",
-    "logreg.fit(X_train, y_train)\n",
-    "print(\"Train set accuracy from Logistic Regression: {:.2f}\".format(logreg.score(X_train,y_train)))\n",
-    "# We scale the data\n",
-    "from sklearn.preprocessing import StandardScaler\n",
-    "scaler = StandardScaler()\n",
-    "scaler.fit(X_train)\n",
-    "X_train_scaled = scaler.transform(X_train)\n",
-    "X_test_scaled = scaler.transform(X_test)\n",
-    "# Then perform again a log reg fit\n",
-    "logreg.fit(X_train_scaled, y_train)\n",
-    "print(\"Train set accuracy scaled data: {:.2f}\".format(logreg.score(X_train_scaled,y_train)))\n",
-    "#thereafter we do a PCA with Scikit-learn\n",
-    "from sklearn.decomposition import PCA\n",
-    "pca = PCA(n_components = 2)\n",
-    "X2D_train = pca.fit_transform(X_train_scaled)\n",
-    "# and finally compute the log reg fit and the score on the training data\t\n",
-    "logreg.fit(X2D_train,y_train)\n",
-    "print(\"Train set accuracy scaled and PCA data: {:.2f}\".format(logreg.score(X2D_train,y_train)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We see that our training data after the PCA decomposition has a performance similar to the non-scaled data. \n",
-    "\n",
-    "## More on the PCA\n",
-    "\n",
-    "Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to\n",
-    "choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).\n",
-    "Unless, of course, you are reducing dimensionality for data visualization — in that case you will\n",
-    "generally want to reduce the dimensionality down to 2 or 3.\n",
-    "The following code computes PCA without reducing dimensionality, then computes the minimum number\n",
-    "of dimensions required to preserve 95% of the training set’s variance:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "pca = PCA()\n",
-    "pca.fit(X)\n",
-    "cumsum = np.cumsum(pca.explained_variance_ratio_)\n",
-    "d = np.argmax(cumsum >= 0.95) + 1"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You could then set $n\\_components=d$ and run PCA again. However, there is a much better option: instead\n",
-    "of specifying the number of principal components you want to preserve, you can set $n\\_components$ to be\n",
-    "a float between 0.0 and 1.0, indicating the ratio of variance you wish to preserve:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "pca = PCA(n_components=0.95)\n",
-    "X_reduced = pca.fit_transform(X)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Incremental PCA\n",
-    "\n",
-    "One problem with the preceding implementation of PCA is that it requires the whole training set to fit in\n",
-    "memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have\n",
-    "been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch\n",
-    "at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new\n",
-    "instances arrive).\n",
-    "\n",
-    "## Randomized PCA\n",
-    "\n",
-    "Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic\n",
-    "algorithm that quickly finds an approximation of the first d principal components. Its computational\n",
-    "complexity is $O(m \\times d^2)+O(d^3)$, instead of $O(m \\times n^2) + O(n^3)$, so it is dramatically faster than the\n",
-    "previous algorithms when $d$ is much smaller than $n$.\n",
-    "\n",
-    "\n",
-    "\n",
-    "\n",
-    "## Kernel PCA\n",
-    "\n",
-    "The kernel trick is a mathematical technique that implicitly maps instances into a\n",
-    "very high-dimensional space (called the feature space), enabling nonlinear classification and regression\n",
-    "with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature\n",
-    "space corresponds to a complex nonlinear decision boundary in the original space.\n",
-    "It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear\n",
-    "projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at\n",
-    "preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a\n",
-    "twisted manifold.\n",
-    "For example, the following code uses Scikit-Learn’s KernelPCA class to perform kPCA with an"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from sklearn.decomposition import KernelPCA\n",
-    "rbf_pca = KernelPCA(n_components = 2, kernel=\"rbf\", gamma=0.04)\n",
-    "X_reduced = rbf_pca.fit_transform(X)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## LLE\n",
-    "\n",
-    "Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction\n",
-    "(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous\n",
-    "algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its\n",
-    "closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where\n",
-    "these local relationships are best preserved (more details shortly). \n",
-    "\n",
-    "\n",
-    "\n",
-    "## Other techniques\n",
-    "\n",
-    "\n",
-    "There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.\n",
-    "\n",
-    "Here are some of the most popular:\n",
-    "* **Multidimensional Scaling (MDS)** reduces dimensionality while trying to preserve the distances between the instances.\n",
-    "\n",
-    "* **Isomap** creates a graph by connecting each instance to its nearest neighbors, then reduces dimensionality while trying to preserve the geodesic distances between the instances.\n",
-    "\n",
-    "* **t-Distributed Stochastic Neighbor Embedding** (t-SNE) reduces dimensionality while trying to keep similar instances close and dissimilar instances apart. It is mostly used for visualization, in particular to visualize clusters of instances in high-dimensional space (e.g., to visualize the MNIST images in 2D).\n",
-    "\n",
-    "* Linear Discriminant Analysis (LDA) is actually a classification algorithm, but during training it learns the most discriminative axes between the classes, and these axes can then be used to define a hyperplane onto which to project the data. The benefit is that the projection will keep classes as far apart as possible, so LDA is a good technique to reduce dimensionality before running another classification algorithm such as a Support Vector Machine (SVM) classifier discussed in the SVM lectures."
+    "4. [Introduction to Partial Differential Equations by A. Tveito, R. Winther](https://www.springer.com/us/book/9783540225515)"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -4747,13 +7320,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-<<<<<<< HEAD
-   "version": "3.6.8"
-=======
-   "version": "3.8.3"
->>>>>>> 9b0e2e75096cc1acee65bfac25f4eff818140252
+   "version": "3.9.15"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 4
+ "nbformat_minor": 5
 }
diff --git a/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz b/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz
index 408b30685..daf852197 100644
Binary files a/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz and b/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz differ
diff --git a/doc/pub/week43/ipynb/week43.ipynb b/doc/pub/week43/ipynb/week43.ipynb
index 8d5235416..b190102b6 100644
--- a/doc/pub/week43/ipynb/week43.ipynb
+++ b/doc/pub/week43/ipynb/week43.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "b10156d4",
+   "id": "5e07edf2",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f85baa2f",
+   "id": "44b465a0",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "543fad4a",
+   "id": "9d7bd8c9",
    "metadata": {
     "editable": true
    },
@@ -43,13 +43,15 @@
     "3. Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13.. \n",
     "\n",
     "4. Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.\n",
-    "<!-- * Video of lecture at <https://youtu.be/vkBNTn-MLqs> -->\n",
-    "<!-- * Whiteboard notes on solving differential equations at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf> -->"
+    "\n",
+    "5. Video of lecture at <https://youtu.be/Gi6mzxAT0Ew>\n",
+    "\n",
+    "6. Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf>"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "72acb4e9",
+   "id": "c50cff0f",
    "metadata": {
     "editable": true
    },
@@ -64,7 +66,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "361768dc",
+   "id": "fe8d32ed",
    "metadata": {
     "editable": true
    },
@@ -77,7 +79,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e058671",
+   "id": "99999ab4",
    "metadata": {
     "editable": true
    },
@@ -94,7 +96,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cbbf2bf",
+   "id": "b4489372",
    "metadata": {
     "editable": true
    },
@@ -104,7 +106,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78e2de21",
+   "id": "f7435e4a",
    "metadata": {
     "editable": true
    },
@@ -131,7 +133,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41a3dc23",
+   "id": "e2561576",
    "metadata": {
     "editable": true
    },
@@ -154,7 +156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e4ac2c0",
+   "id": "39ed46ed",
    "metadata": {
     "editable": true
    },
@@ -166,7 +168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9fd2f83",
+   "id": "776b50ac",
    "metadata": {
     "editable": true
    },
@@ -178,7 +180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16e2b900",
+   "id": "b0ad385d",
    "metadata": {
     "editable": true
    },
@@ -188,7 +190,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9f4b9d8",
+   "id": "bb592830",
    "metadata": {
     "editable": true
    },
@@ -200,7 +202,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01be6441",
+   "id": "41259526",
    "metadata": {
     "editable": true
    },
@@ -214,7 +216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce898b85",
+   "id": "47eaff91",
    "metadata": {
     "editable": true
    },
@@ -226,7 +228,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e2e7314",
+   "id": "05b74533",
    "metadata": {
     "editable": true
    },
@@ -238,7 +240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7114295",
+   "id": "6edb8648",
    "metadata": {
     "editable": true
    },
@@ -248,7 +250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69dfa048",
+   "id": "a663fc08",
    "metadata": {
     "editable": true
    },
@@ -260,7 +262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6efa469c",
+   "id": "479150e0",
    "metadata": {
     "editable": true
    },
@@ -272,7 +274,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "076e4937",
+   "id": "41b9b1ea",
    "metadata": {
     "editable": true
    },
@@ -282,7 +284,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1072f5a1",
+   "id": "590c403a",
    "metadata": {
     "editable": true
    },
@@ -294,7 +296,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f77a7074",
+   "id": "3db8cbb4",
    "metadata": {
     "editable": true
    },
@@ -306,7 +308,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f12effab",
+   "id": "a204182a",
    "metadata": {
     "editable": true
    },
@@ -329,7 +331,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31eb54b1",
+   "id": "4fe58cce",
    "metadata": {
     "editable": true
    },
@@ -341,7 +343,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a549168",
+   "id": "a14f6d08",
    "metadata": {
     "editable": true
    },
@@ -353,7 +355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce35ae73",
+   "id": "4c290410",
    "metadata": {
     "editable": true
    },
@@ -363,7 +365,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6cdfc89",
+   "id": "ca1ac514",
    "metadata": {
     "editable": true
    },
@@ -375,7 +377,7 @@
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@@ -396,7 +398,7 @@
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@@ -410,7 +412,7 @@
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@@ -422,7 +424,7 @@
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@@ -444,7 +446,7 @@
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@@ -466,7 +468,7 @@
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@@ -484,7 +486,7 @@
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@@ -519,7 +521,7 @@
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@@ -531,7 +533,7 @@
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@@ -543,7 +545,7 @@
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@@ -556,7 +558,7 @@
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@@ -567,7 +569,7 @@
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@@ -580,7 +582,7 @@
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@@ -595,7 +597,7 @@
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@@ -607,7 +609,7 @@
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@@ -619,7 +621,7 @@
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@@ -632,7 +634,7 @@
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@@ -689,7 +691,7 @@
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@@ -718,7 +720,7 @@
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@@ -748,7 +750,7 @@
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@@ -775,7 +777,7 @@
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@@ -817,7 +819,7 @@
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@@ -828,7 +830,7 @@
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@@ -915,7 +917,7 @@
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@@ -926,7 +928,7 @@
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@@ -986,7 +988,7 @@
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@@ -1005,7 +1007,7 @@
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@@ -1027,7 +1029,7 @@
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@@ -1168,7 +1170,7 @@
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@@ -1184,7 +1186,7 @@
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@@ -1197,7 +1199,7 @@
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@@ -1209,7 +1211,7 @@
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@@ -1231,7 +1233,7 @@
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@@ -1247,7 +1249,7 @@
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@@ -1285,7 +1287,7 @@
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@@ -1298,7 +1300,7 @@
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@@ -1319,7 +1321,7 @@
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@@ -1335,7 +1337,7 @@
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-   "id": "90045474",
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@@ -1393,7 +1395,7 @@
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@@ -1408,7 +1410,7 @@
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@@ -1429,7 +1431,7 @@
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@@ -1453,7 +1455,7 @@
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-   "id": "9dd0b112",
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@@ -1925,7 +1927,7 @@
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@@ -1937,7 +1939,7 @@
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@@ -1981,7 +1983,7 @@
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@@ -1997,7 +1999,7 @@
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-   "id": "3de4263c",
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@@ -2012,7 +2014,7 @@
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@@ -2023,7 +2025,7 @@
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@@ -2038,7 +2040,7 @@
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@@ -2054,7 +2056,7 @@
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-   "id": "96f9f1ab",
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@@ -2068,7 +2070,7 @@
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@@ -2083,7 +2085,7 @@
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-   "id": "98f0055d",
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@@ -2109,7 +2111,7 @@
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-   "id": "fbd2675f",
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@@ -2124,7 +2126,7 @@
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@@ -2135,7 +2137,7 @@
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-   "id": "1cdc9d23",
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@@ -2150,7 +2152,7 @@
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@@ -2161,7 +2163,7 @@
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-   "id": "c28f2181",
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@@ -2181,7 +2183,7 @@
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-   "id": "3150b724",
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@@ -2196,7 +2198,7 @@
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@@ -2211,7 +2213,7 @@
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-   "id": "997c5001",
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@@ -2248,7 +2250,7 @@
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@@ -2261,7 +2263,7 @@
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@@ -2284,7 +2286,7 @@
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@@ -2294,7 +2296,7 @@
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@@ -2321,7 +2323,7 @@
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@@ -2335,7 +2337,7 @@
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@@ -2352,7 +2354,7 @@
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@@ -2368,7 +2370,7 @@
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@@ -2380,7 +2382,7 @@
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@@ -2398,7 +2400,7 @@
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@@ -2419,7 +2421,7 @@
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@@ -2436,7 +2438,7 @@
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@@ -2448,7 +2450,7 @@
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@@ -2459,7 +2461,7 @@
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@@ -2476,7 +2478,7 @@
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@@ -2487,7 +2489,7 @@
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@@ -2503,7 +2505,7 @@
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@@ -2515,7 +2517,7 @@
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@@ -2532,7 +2534,7 @@
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@@ -2544,7 +2546,7 @@
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@@ -2562,7 +2564,7 @@
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@@ -2572,7 +2574,7 @@
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@@ -2584,7 +2586,7 @@
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@@ -2601,7 +2603,7 @@
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@@ -2613,7 +2615,7 @@
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@@ -2624,7 +2626,7 @@
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@@ -2636,7 +2638,7 @@
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@@ -2646,7 +2648,7 @@
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@@ -2666,7 +2668,7 @@
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@@ -2683,7 +2685,7 @@
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@@ -2702,7 +2704,7 @@
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@@ -2714,7 +2716,7 @@
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@@ -2724,7 +2726,7 @@
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@@ -2741,7 +2743,7 @@
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@@ -2751,7 +2753,7 @@
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@@ -2767,7 +2769,7 @@
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@@ -2779,7 +2781,7 @@
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@@ -2791,7 +2793,7 @@
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@@ -2803,7 +2805,7 @@
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@@ -2813,7 +2815,7 @@
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@@ -2825,7 +2827,7 @@
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@@ -2842,7 +2844,7 @@
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@@ -2852,7 +2854,7 @@
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@@ -2864,7 +2866,7 @@
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@@ -2878,7 +2880,7 @@
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@@ -2894,7 +2896,7 @@
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@@ -2906,7 +2908,7 @@
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@@ -2928,7 +2930,7 @@
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@@ -2940,7 +2942,7 @@
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@@ -2963,7 +2965,7 @@
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@@ -2979,7 +2981,7 @@
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@@ -2991,7 +2993,7 @@
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@@ -3015,7 +3017,7 @@
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@@ -3027,7 +3029,7 @@
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@@ -3048,7 +3050,7 @@
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@@ -3060,7 +3062,7 @@
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@@ -3079,7 +3081,7 @@
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@@ -3089,7 +3091,7 @@
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@@ -3103,7 +3105,7 @@
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@@ -3115,7 +3117,7 @@
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@@ -3127,7 +3129,7 @@
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@@ -3144,7 +3146,7 @@
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@@ -3156,7 +3158,7 @@
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@@ -3178,7 +3180,7 @@
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@@ -3193,7 +3195,7 @@
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@@ -3204,7 +3206,7 @@
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@@ -3359,7 +3361,7 @@
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@@ -3374,7 +3376,7 @@
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@@ -3543,7 +3545,7 @@
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@@ -3556,7 +3558,7 @@
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@@ -3573,7 +3575,7 @@
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@@ -3589,7 +3591,7 @@
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@@ -3602,7 +3604,7 @@
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@@ -3619,7 +3621,7 @@
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@@ -3631,7 +3633,7 @@
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@@ -3658,7 +3660,7 @@
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@@ -3671,7 +3673,7 @@
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@@ -3850,7 +3852,7 @@
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@@ -3870,7 +3872,7 @@
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@@ -3885,7 +3887,7 @@
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@@ -3899,7 +3901,7 @@
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@@ -3915,7 +3917,7 @@
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@@ -3925,7 +3927,7 @@
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@@ -3947,7 +3949,7 @@
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@@ -3961,7 +3963,7 @@
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@@ -4037,7 +4039,7 @@
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@@ -4049,7 +4051,7 @@
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@@ -4066,7 +4068,7 @@
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@@ -4078,7 +4080,7 @@
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@@ -4093,7 +4095,7 @@
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@@ -4105,7 +4107,7 @@
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@@ -4117,7 +4119,7 @@
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@@ -4129,7 +4131,7 @@
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@@ -4139,7 +4141,7 @@
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@@ -4156,7 +4158,7 @@
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@@ -4168,7 +4170,7 @@
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@@ -4180,7 +4182,7 @@
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@@ -4190,7 +4192,7 @@
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@@ -4202,7 +4204,7 @@
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@@ -4213,7 +4215,7 @@
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@@ -4378,7 +4380,7 @@
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@@ -4400,7 +4402,7 @@
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@@ -4417,7 +4419,7 @@
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@@ -4427,7 +4429,7 @@
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@@ -4442,7 +4444,7 @@
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@@ -4452,7 +4454,7 @@
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@@ -4467,7 +4469,7 @@
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@@ -4478,7 +4480,7 @@
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@@ -4498,7 +4500,7 @@
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@@ -4510,7 +4512,7 @@
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@@ -4547,7 +4549,7 @@
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@@ -4557,7 +4559,7 @@
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@@ -4570,7 +4572,7 @@
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@@ -4775,7 +4777,7 @@
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@@ -4792,7 +4794,7 @@
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@@ -4809,7 +4811,7 @@
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@@ -4819,7 +4821,7 @@
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@@ -4834,7 +4836,7 @@
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@@ -4848,7 +4850,7 @@
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@@ -4861,7 +4863,7 @@
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@@ -4881,7 +4883,7 @@
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@@ -4893,7 +4895,7 @@
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@@ -4905,7 +4907,7 @@
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@@ -4917,7 +4919,7 @@
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@@ -4927,7 +4929,7 @@
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@@ -4939,7 +4941,7 @@
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@@ -4951,7 +4953,7 @@
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@@ -4963,7 +4965,7 @@
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@@ -4973,7 +4975,7 @@
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@@ -4989,7 +4991,7 @@
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@@ -4999,7 +5001,7 @@
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@@ -5011,7 +5013,7 @@
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@@ -5028,7 +5030,7 @@
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@@ -5038,7 +5040,7 @@
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@@ -5054,7 +5056,7 @@
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@@ -5068,7 +5070,7 @@
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@@ -5087,7 +5089,7 @@
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@@ -5142,7 +5144,7 @@
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@@ -5172,7 +5174,7 @@
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@@ -5201,7 +5203,7 @@
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    "cell_type": "code",
    "execution_count": 38,
-   "id": "4192bf3d",
+   "id": "7b494481",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5248,7 +5250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87f8417d",
+   "id": "9f4b4939",
    "metadata": {
     "editable": true
    },
@@ -5274,7 +5276,7 @@
   {
    "cell_type": "code",
    "execution_count": 39,
-   "id": "1572e93b",
+   "id": "83d6eb7d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5508,7 +5510,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf7afd74",
+   "id": "ada13a48",
    "metadata": {
     "editable": true
    },
@@ -5520,7 +5522,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fdef78b2",
+   "id": "e4727d73",
    "metadata": {
     "editable": true
    },
@@ -5532,7 +5534,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be570613",
+   "id": "0b86d555",
    "metadata": {
     "editable": true
    },
@@ -5544,7 +5546,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f81e04f",
+   "id": "216948d5",
    "metadata": {
     "editable": true
    },
@@ -5561,7 +5563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91171d8b",
+   "id": "44c25fdc",
    "metadata": {
     "editable": true
    },
@@ -5571,7 +5573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbbbb8a5",
+   "id": "98f919eb",
    "metadata": {
     "editable": true
    },
@@ -5583,7 +5585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f1be58e",
+   "id": "01299767",
    "metadata": {
     "editable": true
    },
@@ -5600,7 +5602,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d54c4188",
+   "id": "556587c5",
    "metadata": {
     "editable": true
    },
@@ -5611,7 +5613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "952c58e8",
+   "id": "c9eb4f3a",
    "metadata": {
     "editable": true
    },
@@ -5631,7 +5633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a650bae2",
+   "id": "63128ef6",
    "metadata": {
     "editable": true
    },
@@ -5641,7 +5643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e0b8996",
+   "id": "ff568c81",
    "metadata": {
     "editable": true
    },
@@ -5667,7 +5669,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f3f1985",
+   "id": "7b32c8dd",
    "metadata": {
     "editable": true
    },
@@ -5683,7 +5685,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbd35329",
+   "id": "fc33e683",
    "metadata": {
     "editable": true
    },
@@ -5694,7 +5696,7 @@
   {
    "cell_type": "code",
    "execution_count": 40,
-   "id": "6ccf9344",
+   "id": "2f923958",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5925,7 +5927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "988e09cf",
+   "id": "95dea76f",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week43/week43.do.txt b/doc/src/week43/week43.do.txt
index 529cd1bdc..c7701fa35 100644
--- a/doc/src/week43/week43.do.txt
+++ b/doc/src/week43/week43.do.txt
@@ -10,8 +10,8 @@ o Reminder from last week, see also lecture notes from week 42 at URL:"https://c
 o Building our own Feed-forward Neural Network.
 o Coding examples using Tensorflow/Keras and Pytorch examples. The Pytorch examples are adapted from Rashcka's text, see chapters 11-13.. 
 o Start discussions on how to use neural networks for solving  differential equations (ordinary and partial ones). This topic continues next week as well.
-#  * Video of lecture at URL:"https://youtu.be/vkBNTn-MLqs"
-#  * Whiteboard notes on solving differential equations at URL:"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf"  
+o Video of lecture at URL:"https://youtu.be/Gi6mzxAT0Ew"
+o Whiteboard notes at URL:"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2025/FYSSTKweek43.pdf"  
 !eblock