From 1605d87b70b7dc965d96141a39a0f5b0ec18987b Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Thu, 14 Oct 2021 11:13:00 +0200 Subject: [PATCH] typos correction --- doc/pub/week40/ipynb/week40.ipynb | 115 ++---- doc/pub/week41/html/._week41-bs000.html | 89 +++-- doc/pub/week41/html/._week41-bs001.html | 89 +++-- doc/pub/week41/html/._week41-bs002.html | 89 +++-- doc/pub/week41/html/._week41-bs003.html | 101 +++-- doc/pub/week41/html/._week41-bs004.html | 95 +++-- doc/pub/week41/html/._week41-bs005.html | 113 +++--- doc/pub/week41/html/._week41-bs006.html | 101 +++-- doc/pub/week41/html/._week41-bs007.html | 89 +++-- doc/pub/week41/html/._week41-bs008.html | 89 +++-- doc/pub/week41/html/._week41-bs009.html | 89 +++-- doc/pub/week41/html/._week41-bs010.html | 89 +++-- doc/pub/week41/html/._week41-bs011.html | 89 +++-- doc/pub/week41/html/._week41-bs012.html | 95 +++-- doc/pub/week41/html/._week41-bs013.html | 91 +++-- doc/pub/week41/html/._week41-bs014.html | 89 +++-- doc/pub/week41/html/._week41-bs015.html | 97 +++-- doc/pub/week41/html/._week41-bs016.html | 97 +++-- doc/pub/week41/html/._week41-bs017.html | 89 +++-- doc/pub/week41/html/._week41-bs018.html | 91 +++-- doc/pub/week41/html/._week41-bs019.html | 99 +++-- doc/pub/week41/html/._week41-bs020.html | 89 +++-- doc/pub/week41/html/._week41-bs021.html | 89 +++-- doc/pub/week41/html/._week41-bs022.html | 93 +++-- doc/pub/week41/html/._week41-bs023.html | 89 +++-- doc/pub/week41/html/._week41-bs024.html | 89 +++-- doc/pub/week41/html/._week41-bs025.html | 89 +++-- doc/pub/week41/html/._week41-bs026.html | 89 +++-- doc/pub/week41/html/._week41-bs027.html | 89 +++-- doc/pub/week41/html/._week41-bs028.html | 93 +++-- doc/pub/week41/html/._week41-bs029.html | 89 +++-- doc/pub/week41/html/._week41-bs030.html | 150 +++++--- doc/pub/week41/html/._week41-bs031.html | 172 ++++----- doc/pub/week41/html/._week41-bs032.html | 156 +++----- doc/pub/week41/html/._week41-bs033.html | 143 ++++--- doc/pub/week41/html/._week41-bs034.html | 138 +++---- doc/pub/week41/html/._week41-bs035.html | 234 +++++++++--- doc/pub/week41/html/._week41-bs036.html | 370 ++++++++++--------- doc/pub/week41/html/._week41-bs037.html | 273 +++----------- doc/pub/week41/html/._week41-bs038.html | 123 +++--- doc/pub/week41/html/._week41-bs039.html | 124 ++++--- doc/pub/week41/html/._week41-bs040.html | 128 ++++--- doc/pub/week41/html/._week41-bs041.html | 137 +++---- doc/pub/week41/html/._week41-bs042.html | 132 +++---- doc/pub/week41/html/._week41-bs043.html | 120 +++--- doc/pub/week41/html/._week41-bs044.html | 111 +++--- doc/pub/week41/html/._week41-bs045.html | 110 +++--- doc/pub/week41/html/._week41-bs046.html | 107 +++--- doc/pub/week41/html/._week41-bs047.html | 105 +++--- doc/pub/week41/html/._week41-bs048.html | 102 +++-- doc/pub/week41/html/._week41-bs049.html | 129 ++++--- doc/pub/week41/html/._week41-bs050.html | 139 +++---- doc/pub/week41/html/._week41-bs051.html | 128 +++---- doc/pub/week41/html/._week41-bs052.html | 116 +++--- doc/pub/week41/html/._week41-bs053.html | 124 ++++--- doc/pub/week41/html/._week41-bs054.html | 136 +++---- doc/pub/week41/html/._week41-bs055.html | 131 +++---- doc/pub/week41/html/._week41-bs056.html | 138 +++---- doc/pub/week41/html/._week41-bs057.html | 119 +++--- doc/pub/week41/html/._week41-bs058.html | 115 +++--- doc/pub/week41/html/._week41-bs059.html | 112 +++--- doc/pub/week41/html/._week41-bs060.html | 105 +++--- doc/pub/week41/html/._week41-bs061.html | 107 +++--- doc/pub/week41/html/._week41-bs062.html | 108 +++--- doc/pub/week41/html/._week41-bs063.html | 114 +++--- doc/pub/week41/html/._week41-bs064.html | 115 +++--- doc/pub/week41/html/._week41-bs065.html | 141 ++++--- doc/pub/week41/html/._week41-bs066.html | 146 +++----- doc/pub/week41/html/._week41-bs067.html | 137 ++++--- doc/pub/week41/html/._week41-bs068.html | 132 +++---- doc/pub/week41/html/._week41-bs069.html | 134 +++---- doc/pub/week41/html/._week41-bs070.html | 128 +++---- doc/pub/week41/html/week41-bs.html | 89 +++-- doc/pub/week41/html/week41-reveal.html | 131 +++---- doc/pub/week41/html/week41-solarized.html | 134 +++---- doc/pub/week41/html/week41.html | 134 +++---- doc/pub/week41/ipynb/ipynb-week41-src.tar.gz | Bin 534110 -> 534110 bytes doc/pub/week41/ipynb/week41.ipynb | 139 +++---- doc/src/week41/week41.do.txt | 129 +++---- 79 files changed, 4424 insertions(+), 4904 deletions(-) diff --git a/doc/pub/week40/ipynb/week40.ipynb b/doc/pub/week40/ipynb/week40.ipynb index c357a751a..d2a86b7c9 100644 --- a/doc/pub/week40/ipynb/week40.ipynb +++ b/doc/pub/week40/ipynb/week40.ipynb @@ -192,10 +192,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -257,10 +254,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -302,10 +296,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", @@ -859,10 +850,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -918,10 +906,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -957,10 +942,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1011,10 +993,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1054,10 +1033,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1089,10 +1065,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1151,10 +1124,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1178,10 +1148,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1228,10 +1195,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1259,10 +1223,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1290,10 +1251,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1323,10 +1281,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "a += b\n", @@ -1557,10 +1512,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "\"\"\"\n", @@ -1607,10 +1559,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "\"\"\"\n", @@ -1676,10 +1625,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "\n", @@ -2091,10 +2037,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "\"\"\"The sigmoid function (or the logistic curve) is a \n", @@ -2802,7 +2745,25 @@ ] } ], - "metadata": {}, + "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", + "version": "3.8.5" + } + }, "nbformat": 4, "nbformat_minor": 4 } diff --git a/doc/pub/week41/html/._week41-bs000.html b/doc/pub/week41/html/._week41-bs000.html index d8bab1fc1..17ac62bf8 100644 --- a/doc/pub/week41/html/._week41-bs000.html +++ b/doc/pub/week41/html/._week41-bs000.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -394,7 +389,7 @@ MathJax.Hub.Config({
  • 9
  • 10
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs001.html b/doc/pub/week41/html/._week41-bs001.html index 0cda5c4f1..b4cfb208f 100644 --- a/doc/pub/week41/html/._week41-bs001.html +++ b/doc/pub/week41/html/._week41-bs001.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -379,7 +374,7 @@ For a more in depth discussion on neural networks we recommend Goodfellow et al
  • 10
  • 11
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs002.html b/doc/pub/week41/html/._week41-bs002.html index bd344ac7b..2daf01027 100644 --- a/doc/pub/week41/html/._week41-bs002.html +++ b/doc/pub/week41/html/._week41-bs002.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -375,7 +370,7 @@ MathJax.Hub.Config({
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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -360,9 +355,9 @@ The four equations derived last week provide us with a way of computing the gra

    -First, we set up the input data \( \hat{x} \) and the activations -\( \hat{z}_1 \) of the input layer and compute the activation function and -the pertinent outputs \( \hat{a}^1 \). +First, we set up the input data \( \boldsymbol{x} \) and the activations +\( \boldsymbol{z}_1 \) of the input layer and compute the activation function and +the pertinent outputs \( \boldsymbol{a}^1 \).

    @@ -372,8 +367,8 @@ the pertinent outputs \( \hat{a}^1 \).

    Secondly, we perform then the feed forward till we reach the output -layer and compute all \( \hat{z}_l \) of the input layer and compute the -activation function and the pertinent outputs \( \hat{a}^l \) for +layer and compute all \( \boldsymbol{z}_l \) of the input layer and compute the +activation function and the pertinent outputs \( \boldsymbol{a}^l \) for \( l=2,3,\dots,L \).

    @@ -383,7 +378,7 @@ activation function and the pertinent outputs \( \hat{a}^l \) for

    -Thereafter we compute the ouput error \( \hat{\delta}^L \) by computing all +Thereafter we compute the ouput error \( \boldsymbol{\delta}^L \) by computing all $$ \delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}. $$ @@ -443,7 +438,7 @@ Here it is convenient to use stochastic gradient descent (see the examples below

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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -374,16 +369,16 @@ For an input \( \boldsymbol{a} \) from the hidden layer, the probability that th 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 \( x \) represents our activation values \( z \). We have $$ -P(y = 0 \mid \hat{x}, \hat{\theta}) = \frac{1}{1 + \exp{(- \hat{x}})} , +P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) = \frac{1}{1 + \exp{(- \boldsymbol{x}})} , $$ and $$ -P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) , +P(y = 1 \mid \boldsymbol{x}, \boldsymbol{\theta}) = 1 - P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) , $$

    -where \( y \in \{0, 1\} \) and \( \hat{\theta} \) represents the weights and biases +where \( y \in \{0, 1\} \) and \( \boldsymbol{\theta} \) represents the weights and biases of our network.

    @@ -406,7 +401,7 @@ of our network.

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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -356,13 +351,13 @@ MathJax.Hub.Config({

    Our cost function is given as (see the Logistic regression lectures) $$ -\mathcal{C}(\hat{\theta}) = - \ln P(\mathcal{D} \mid \hat{\theta}) = - \sum_{i=1}^n -y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\hat{\theta}) . +\mathcal{C}(\boldsymbol{\theta}) = - \ln P(\mathcal{D} \mid \boldsymbol{\theta}) = - \sum_{i=1}^n +y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\boldsymbol{\theta}) . $$

    This last equality means that we can interpret our cost function as a sum over the loss function -for each point in the dataset \( \mathcal{L}_i(\hat{\theta}) \). +for each point in the dataset \( \mathcal{L}_i(\boldsymbol{\theta}) \). The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather than maximizing a negative number. @@ -370,22 +365,22 @@ than maximizing a negative number. In multiclass classification it is common to treat each integer label as a so called one-hot vector:

    -\( y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and +\( y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and

    -\( y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \) +\( y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)

    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 \( 9 \))..

    -If \( \hat{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th -output vector \( \hat{y}_i \). -The probability of \( \hat{x}_i \) being in class \( c \) will be given by the softmax function: +If \( \boldsymbol{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th +output vector \( \boldsymbol{y}_i \). +The probability of \( \boldsymbol{x}_i \) being in class \( c \) will be given by the softmax function: $$ -P(y_{ic} = 1 \mid \hat{x}_i, \hat{\theta}) = \frac{\exp{((\hat{a}_i^{hidden})^T \hat{w}_c)}} -{\sum_{c'=0}^{C-1} \exp{((\hat{a}_i^{hidden})^T \hat{w}_{c'})}} , +P(y_{ic} = 1 \mid \boldsymbol{x}_i, \boldsymbol{\theta}) = \frac{\exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_c)}} +{\sum_{c'=0}^{C-1} \exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_{c'})}} , $$

    @@ -394,13 +389,13 @@ The likelihood of this \( C \)-class classifier is now given as: $$ -P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} . +P(\mathcal{D} \mid \boldsymbol{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} . $$ Again we take the negative log-likelihood to define our cost function: $$ -\mathcal{C}(\hat{\theta}) = - \log{P(\mathcal{D} \mid \hat{\theta})}. +\mathcal{C}(\boldsymbol{\theta}) = - \log{P(\mathcal{D} \mid \boldsymbol{\theta})}. $$ See the logistic regression lectures for a full definition of the cost function. @@ -429,7 +424,7 @@ The back propagation equations need now only a small change, namely the definiti

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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -356,20 +351,20 @@ MathJax.Hub.Config({

    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 $$ -\mathcal{C}(\hat{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\hat{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\hat{\beta})}\right), +\mathcal{C}(\boldsymbol{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\boldsymbol{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\boldsymbol{\beta})}\right), $$ where we had defined the logistic (sigmoid) function $$ -p(y_i =1\vert x_i,\hat{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}}, +p(y_i =1\vert x_i,\boldsymbol{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}}, $$ and $$ -p(y_i =0\vert x_i,\hat{\beta})=1-p(y_i =1\vert x_i,\hat{\beta}). +p(y_i =0\vert x_i,\boldsymbol{\beta})=1-p(y_i =1\vert x_i,\boldsymbol{\beta}). $$ -The parameters \( \hat{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method. +The parameters \( \boldsymbol{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.

    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 \( b_i^l \). @@ -386,12 +381,12 @@ $$ where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \). Our cost function at the final layer \( l=L \) is now $$ -\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right), +\mathcal{C}(\boldsymbol{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right), $$ 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 $$ -\frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. +\frac{\partial \mathcal{C}(\boldsymbol{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. $$ In case we use another activation function than the logistic one, we need to evaluate other derivatives. @@ -418,7 +413,7 @@ In case we use another activation function than the logistic one, we need to eva

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    • diff --git a/doc/pub/week41/html/._week41-bs007.html b/doc/pub/week41/html/._week41-bs007.html index 30c95ed2e..a4b8511a8 100644 --- a/doc/pub/week41/html/._week41-bs007.html +++ b/doc/pub/week41/html/._week41-bs007.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -393,7 +388,7 @@ which in case of the simply binary model reduces to having \( i=j \).
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    • diff --git a/doc/pub/week41/html/._week41-bs008.html b/doc/pub/week41/html/._week41-bs008.html index da990568a..eaceb9b46 100644 --- a/doc/pub/week41/html/._week41-bs008.html +++ b/doc/pub/week41/html/._week41-bs008.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -388,7 +383,7 @@ One can identify a set of key steps when using neural networks to solve supervis
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    • diff --git a/doc/pub/week41/html/._week41-bs009.html b/doc/pub/week41/html/._week41-bs009.html index e6bbdc805..3c0402692 100644 --- a/doc/pub/week41/html/._week41-bs009.html +++ b/doc/pub/week41/html/._week41-bs009.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -468,7 +463,7 @@ plt.show()
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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -423,7 +418,7 @@ X_train, X_test, Y_train, Y_test = train_tes
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    • diff --git a/doc/pub/week41/html/._week41-bs011.html b/doc/pub/week41/html/._week41-bs011.html index 2b7d947af..447f39a19 100644 --- a/doc/pub/week41/html/._week41-bs011.html +++ b/doc/pub/week41/html/._week41-bs011.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -420,7 +415,7 @@ which is inspired by probability theory (see logistic regression) and was most c
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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -379,11 +374,11 @@ For a soft binary classifier, we could use a single neuron and interpret the out

    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: -$$ P(\text{class \( j \)} \mid \text{input \( \hat{a} \)}) = \frac{\exp{(\hat{a}^T \hat{w}_j)}} -{\sum_{c=0}^{9} \exp{(\hat{a}^T \hat{w}_c)}} ,$$ +$$ P(\text{class \( j \)} \mid \text{input \( \boldsymbol{a} \)}) = \frac{\exp{(\boldsymbol{a}^T \boldsymbol{w}_j)}} +{\sum_{c=0}^{9} \exp{(\boldsymbol{a}^T \boldsymbol{w}_c)}} ,$$

    -i.e. each neuron \( j \) outputs the probability of being in class \( j \) given an input from the hidden layer \( \hat{a} \), with \( \hat{w}_j \) the weights of neuron \( j \) to the inputs. +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. The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1. The exponent is just the weighted sum of inputs as before: @@ -419,7 +414,7 @@ weights to the output layer.

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    • diff --git a/doc/pub/week41/html/._week41-bs013.html b/doc/pub/week41/html/._week41-bs013.html index 651c8b89f..e8744f3e4 100644 --- a/doc/pub/week41/html/._week41-bs013.html +++ b/doc/pub/week41/html/._week41-bs013.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -364,7 +359,7 @@ of values. Without it, any input with the value 0 will be mapped to zero (before $$ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.$$

    -The bias weights \( \hat{b} \) 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. +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.

    @@ -410,7 +405,7 @@ output_bias = np22

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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -401,7 +396,7 @@ $$ a_{j}^{L} = \frac{\exp{(z_j^{L})}}
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    • diff --git a/doc/pub/week41/html/._week41-bs015.html b/doc/pub/week41/html/._week41-bs015.html index b164bc314..344e291fa 100644 --- a/doc/pub/week41/html/._week41-bs015.html +++ b/doc/pub/week41/html/._week41-bs015.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -366,23 +361,23 @@ and obtain a matrix that holds the weighted sum of inputs to the hidden layer for each input image and each hidden neuron. We also add the bias to obtain a matrix of weighted sums to the hidden layer \( Z^{h} \): -$$ \hat{z}^{l} = \hat{X} \hat{W}^{l} + \hat{b}^{l} ,$$ +$$ \boldsymbol{z}^{l} = \boldsymbol{X} \boldsymbol{W}^{l} + \boldsymbol{b}^{l} ,$$

    meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image. This is then passed through the activation: -$$ \hat{a}^{l} = f(\hat{z}^l) .$$ +$$ \boldsymbol{a}^{l} = f(\boldsymbol{z}^l) .$$

    This is fed to the output layer: -$$ \hat{z}^{L} = \hat{a}^{L} \hat{W}^{L} + \hat{b}^{L} .$$ +$$ \boldsymbol{z}^{L} = \boldsymbol{a}^{L} \boldsymbol{W}^{L} + \boldsymbol{b}^{L} .$$

    Finally we receive our output values for each image and each category by passing it through the softmax function: -$$ output = softmax (\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$ +$$ output = softmax (\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$

    @@ -449,7 +444,7 @@ predictions = predict(X_train)

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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -362,22 +357,22 @@ A typical choice for multiclass classification is the cross-entropy los

    In multiclass classification it is common to treat each integer label as a so called one-hot vector: -$$ y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ +$$ y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ -$$ y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$ +$$ y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$

    i.e. a binary bit string of length \( C \), where \( C = 10 \) is the number of classes in the MNIST dataset.

    Let \( y_{ic} \) denote the \( c \)-th component of the \( i \)-th one-hot vector. -We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \hat{x}_i \) in the dataset. +We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \boldsymbol{x}_i \) in the dataset.

    In the one-hot representation only one of the terms in the loss function is non-zero, namely the probability of the correct category \( c' \) (i.e. the category \( c' \) such that \( y_{ic'} = 1 \)). This means that the cross entropy loss only punishes you for how wrong -you got the correct label. The probability of category \( c \) is given by the softmax function. The vector \( \hat{\theta} \) represents the parameters of our network, i.e. all the weights and biases. +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.

    @@ -405,7 +400,7 @@ you got the correct label. The probability of category \( c \) is given by the s

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    • diff --git a/doc/pub/week41/html/._week41-bs017.html b/doc/pub/week41/html/._week41-bs017.html index f7722d844..0ac175db5 100644 --- a/doc/pub/week41/html/._week41-bs017.html +++ b/doc/pub/week41/html/._week41-bs017.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -414,7 +409,7 @@ The various optmization methods, with codes and algorithms, are discussed in o
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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -365,7 +360,7 @@ reduces overfitting. We will measure the size of the weights using the so called L2-norm, meaning our cost function becomes: $$ \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad -\frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) + \lambda \lvert \lvert \hat{w} \rvert \rvert_2^2 +\frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) + \lambda \lvert \lvert \boldsymbol{w} \rvert \rvert_2^2 = \frac{1}{N} \sum_{i=1}^N \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,$$

    @@ -407,7 +402,7 @@ calculate the gradient efficently.

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  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -355,23 +350,23 @@ MathJax.Hub.Config({

    To more efficently train our network these equations are implemented using matrix operations. -The error in the output layer is calculated simply as, with \( \hat{t} \) being our targets, +The error in the output layer is calculated simply as, with \( \boldsymbol{t} \) being our targets, -$$ \delta_L = \hat{t} - \hat{y} = (n_{inputs}, n_{categories}) .$$ +$$ \delta_L = \boldsymbol{t} - \boldsymbol{y} = (n_{inputs}, n_{categories}) .$$

    The gradient for the output weights is calculated as -$$ \nabla W_{L} = \hat{a}^T \delta_L = (n_{hidden}, n_{categories}) ,$$ +$$ \nabla W_{L} = \boldsymbol{a}^T \delta_L = (n_{hidden}, n_{categories}) ,$$

    -where \( \hat{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input. +where \( \boldsymbol{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input. Since we are going backwards we have to transpose the activation matrix.

    The gradient with respect to the output bias is then -$$ \nabla \hat{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$ +$$ \nabla \boldsymbol{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$

    The error in the hidden layer is @@ -488,7 +483,7 @@ lmbd = 0.0128

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    • diff --git a/doc/pub/week41/html/._week41-bs020.html b/doc/pub/week41/html/._week41-bs020.html index 8a97ee7f9..e9b25a61f 100644 --- a/doc/pub/week41/html/._week41-bs020.html +++ b/doc/pub/week41/html/._week41-bs020.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -394,7 +389,7 @@ Andrew Ng goes through some of these considerations in this 29
  • 30
  • ...
    • -
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    • +
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  • »
    • diff --git a/doc/pub/week41/html/._week41-bs021.html b/doc/pub/week41/html/._week41-bs021.html index 478609862..53417e61f 100644 --- a/doc/pub/week41/html/._week41-bs021.html +++ b/doc/pub/week41/html/._week41-bs021.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -486,7 +481,7 @@ being realizations of this object with different hyperparameters. An implementat
  • 30
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  • ...
    • -
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    • diff --git a/doc/pub/week41/html/._week41-bs022.html b/doc/pub/week41/html/._week41-bs022.html index 6ef9640b2..686f86059 100644 --- a/doc/pub/week41/html/._week41-bs022.html +++ b/doc/pub/week41/html/._week41-bs022.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -358,10 +353,10 @@ To measure the performance of our network we evaluate how well it does it data i We measure the performance of the network using the accuracy score. 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 \( 1 \). -$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\hat{y}_i = y_i)}{n} ,$$ +$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,$$

    -where \( I \) is the indicator function, \( 1 \) if \( \hat{y}_i = y_i \) and \( 0 \) otherwise. +where \( I \) is the indicator function, \( 1 \) if \( \tilde{y}_i = y_i \) and \( 0 \) otherwise.

    @@ -409,7 +404,7 @@ test_predict = dnn31

  • 32
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    • diff --git a/doc/pub/week41/html/._week41-bs023.html b/doc/pub/week41/html/._week41-bs023.html index 75043a422..208ad949b 100644 --- a/doc/pub/week41/html/._week41-bs023.html +++ b/doc/pub/week41/html/._week41-bs023.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -407,7 +402,7 @@ DNN_numpy = np.
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    • diff --git a/doc/pub/week41/html/._week41-bs024.html b/doc/pub/week41/html/._week41-bs024.html index 1983ba752..26e514b59 100644 --- a/doc/pub/week41/html/._week41-bs024.html +++ b/doc/pub/week41/html/._week41-bs024.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -416,7 +411,7 @@ plt.show()
  • 33
  • 34
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs025.html b/doc/pub/week41/html/._week41-bs025.html index a478fba80..1edb3b5b1 100644 --- a/doc/pub/week41/html/._week41-bs025.html +++ b/doc/pub/week41/html/._week41-bs025.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -413,7 +408,7 @@ DNN_scikit = np
  • 34
  • 35
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs026.html b/doc/pub/week41/html/._week41-bs026.html index 7e2e43331..f2a116136 100644 --- a/doc/pub/week41/html/._week41-bs026.html +++ b/doc/pub/week41/html/._week41-bs026.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -416,7 +411,7 @@ plt.show()
  • 35
  • 36
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs027.html b/doc/pub/week41/html/._week41-bs027.html index 68ab49652..2ef1b4862 100644 --- a/doc/pub/week41/html/._week41-bs027.html +++ b/doc/pub/week41/html/._week41-bs027.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -402,7 +397,7 @@ inputs \( x_1 \) and \( x_2 \) and outputs \( y \):
  • 36
  • 37
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs028.html b/doc/pub/week41/html/._week41-bs028.html index 9fa7def64..5dbbe1df8 100644 --- a/doc/pub/week41/html/._week41-bs028.html +++ b/doc/pub/week41/html/._week41-bs028.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -354,7 +349,7 @@ MathJax.Hub.Config({

    The AND and XOR Gates

    -The AND gate is defined as +The AND gate is defined as

    @@ -374,7 +369,7 @@ The AND gate is defined as

    -And finally we have the XOR gate +And finally we have the XOR gate

    @@ -419,7 +414,7 @@ And finally we have the XOR gate

  • 37
  • 38
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs029.html b/doc/pub/week41/html/._week41-bs029.html index 9cd4dc68d..a5a0d6cff 100644 --- a/doc/pub/week41/html/._week41-bs029.html +++ b/doc/pub/week41/html/._week41-bs029.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -391,7 +386,7 @@ while the vector of outputs is \( \boldsymbol{y}^T=[0,1,1,0] \) for the XOR gate
  • 38
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  • ...
    • -
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    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs030.html b/doc/pub/week41/html/._week41-bs030.html index 9a8cb511d..1bb254eed 100644 --- a/doc/pub/week41/html/._week41-bs030.html +++ b/doc/pub/week41/html/._week41-bs030.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -362,21 +357,72 @@ We define first our design matrix and the various output vectors for the differe 
    """
 Simple code that tests XOR, OR and AND gates with linear regression
 """
+
 # import necessary packages
 import numpy as np
 import matplotlib.pyplot as plt
 from sklearn import datasets
 
-# Design matrix
-X = np.array([ [1, 0, 0], [1, 0, 1], [1, 1, 0],[1, 1, 1]],dtype=np.float64)
+def sigmoid(x):
+    return 1/(1 + np.exp(-x))
 
-# The XOR gate 
+def feed_forward(X):
+    # weighted sum of inputs to the hidden layer
+    z_h = np.matmul(X, hidden_weights) + hidden_bias
+    # activation in the hidden layer
+    a_h = sigmoid(z_h)
+    
+    # weighted sum of inputs to the output layer
+    z_o = np.matmul(a_h, output_weights) + output_bias
+    # softmax output
+    # axis 0 holds each input and axis 1 the probabilities of each category
+    probabilities = sigmoid(z_o)
+    return probabilities
+
+# we obtain a prediction by taking the class with the highest likelihood
+def predict(X):
+    probabilities = feed_forward(X)
+    return np.argmax(probabilities, axis=1)
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
 yXOR = np.array( [ 0, 1 ,1, 0])
-# The OR gate 
+# The OR gate
 yOR = np.array( [ 0, 1 ,1, 1])
-# The AND gate 
+# The AND gate
 yAND = np.array( [ 0, 0 ,0, 1])
+
+# Defining the neural network
+n_inputs, n_features = X.shape
+n_hidden_neurons = 2
+n_categories = 2
+n_features = 2
+
+# we make the weights normally distributed using numpy.random.randn
+
+# weights and bias in the hidden layer
+hidden_weights = np.random.randn(n_features, n_hidden_neurons)
+hidden_bias = np.zeros(n_hidden_neurons) + 0.01
+
+# weights and bias in the output layer
+output_weights = np.random.randn(n_hidden_neurons, n_categories)
+output_bias = np.zeros(n_categories) + 0.01
+
+probabilities = feed_forward(X)
+print(probabilities)
+
+
+predictions = predict(X)
+print(predictions)
    +

    +Not an impressive result, but this was our first forward pass with randomly assigned weights. Let us now add the full network with the back-propagation algorithm discussed above. +

    @@ -403,7 +449,7 @@ yAND = np.39

  • 40
  • ...
    • -
  • 72
    • +
  • 71
  • »
    • diff --git a/doc/pub/week41/html/._week41-bs031.html b/doc/pub/week41/html/._week41-bs031.html index cfbe44a9c..69ad7476d 100644 --- a/doc/pub/week41/html/._week41-bs031.html +++ b/doc/pub/week41/html/._week41-bs031.html @@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source 2, None, 'setting-up-the-neural-network'), - ('Then the first Feed Forward pass', - 2, - None, - 'then-the-first-feed-forward-pass'), ('The Code using Scikit-Learn', 2, None, @@ -273,7 +269,7 @@ MathJax.Hub.Config({
  • Example: binary classification problem
  • The Softmax function
  • Developing a code for doing neural networks with back propagation
    • -
  • Collect and pre-process data
    • +
  • Collect and pre-process data
  • Train and test datasets
  • Define model and architecture
  • Layers
    • @@ -295,47 +291,46 @@ MathJax.Hub.Config({
  • The AND and XOR Gates
  • Representing the Data Sets
  • Setting up the Neural Network
    • -
  • Then the first Feed Forward pass
    • -
  • The Code using Scikit-Learn
    • -
  • Building neural networks in Tensorflow and Keras
    • -
  • Tensorflow
    • -
  • Using Keras
    • -
  • Collect and pre-process data
    • -
  • The Breast Cancer Data, now with Keras
    • -
  • Fine-tuning neural network hyperparameters
    • -
  • Hidden layers
    • -
  • Which activation function should I use?
    • -
  • Is the Logistic activation function (Sigmoid) our choice?
    • -
  • The derivative of the Logistic funtion
    • -
  • The RELU function family
    • -
  • Which activation function should we use?
    • -
  • More on activation functions, output layers
    • -
  • Batch Normalization
    • -
  • Dropout
    • -
  • Gradient Clipping
    • -
  • A very nice website on Neural Networks
    • -
  • A top-down perspective on Neural networks
    • -
  • Limitations of supervised learning with deep networks
    • -
  • Overarching Views, a personal note
    • -
  • From a Spherical Cow to a real one
    • -
  • Convolutional Neural Networks (recognizing images)
    • -
  • Regular NNs don’t scale well to full images
    • -
  • 3D volumes of neurons
    • -
  • Layers used to build CNNs
    • -
  • Transforming images
    • -
  • CNNs in brief
    • -
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • -
  • Setting it up
    • -
  • The MNIST dataset again
    • -
  • Strong correlations
    • -
  • Layers of a CNN
    • -
  • Systematic reduction
    • -
  • Prerequisites: Collect and pre-process data
    • -
  • Importing Keras and Tensorflow
    • -
  • Running with Keras
    • -
  • Final part
    • -
  • Final visualization
    • -
  • Fun links
    • +
  • The Code using Scikit-Learn
    • +
  • Building neural networks in Tensorflow and Keras
    • +
  • Tensorflow
    • +
  • Using Keras
    • +
  • Collect and pre-process data
    • +
  • The Breast Cancer Data, now with Keras
    • +
  • Fine-tuning neural network hyperparameters
    • +
  • Hidden layers
    • +
  • Which activation function should I use?
    • +
  • Is the Logistic activation function (Sigmoid) our choice?
    • +
  • The derivative of the Logistic funtion
    • +
  • The RELU function family
    • +
  • Which activation function should we use?
    • +
  • More on activation functions, output layers
    • +
  • Batch Normalization
    • +
  • Dropout
    • +
  • Gradient Clipping
    • +
  • A very nice website on Neural Networks
    • +
  • A top-down perspective on Neural networks
    • +
  • Limitations of supervised learning with deep networks
    • +
  • Overarching Views, a personal note
    • +
  • From a Spherical Cow to a real one
    • +
  • Convolutional Neural Networks (recognizing images)
    • +
  • Regular NNs don’t scale well to full images
    • +
  • 3D volumes of neurons
    • +
  • Layers used to build CNNs
    • +
  • Transforming images
    • +
  • CNNs in brief
    • +
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • +
  • Setting it up
    • +
  • The MNIST dataset again
    • +
  • Strong correlations
    • +
  • Layers of a CNN
    • +
  • Systematic reduction
    • +
  • Prerequisites: Collect and pre-process data
    • +
  • Importing Keras and Tensorflow
    • +
  • Running with Keras
    • +
  • Final part
    • +
  • Final visualization
    • +
  • Fun links
    • @@ -351,37 +346,30 @@ MathJax.Hub.Config({ -

    Then the first Feed Forward pass

    +

    The Code using Scikit-Learn

    -

    def sigmoid(x):
-    return 1/(1 + np.exp(-x))
-
-def feed_forward(X):
-    # weighted sum of inputs to the hidden layer
-    z_h = np.matmul(X, hidden_weights) + hidden_bias
-    # activation in the hidden layer
-    a_h = sigmoid(z_h)
-    
-    # weighted sum of inputs to the output layer
-    z_o = np.matmul(a_h, output_weights) + output_bias
-    # softmax output
-    # axis 0 holds each input and axis 1 the probabilities of each category
-    probabilities = sigmoid(z_o)
-    return probabilities
-
-# we obtain a prediction by taking the class with the highest likelihood
-def predict(X):
-    probabilities = feed_forward(X)
-    return np.argmax(probabilities, axis=1)
-
-
+
    # import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.neural_network import MLPClassifier
+from sklearn.metrics import accuracy_score
+import seaborn as sns
 
 # ensure the same random numbers appear every time
 np.random.seed(0)
 
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
 
 # Defining the neural network
 n_inputs, n_features = X.shape
@@ -389,26 +377,38 @@ n_hidden_neurons = = 2
 n_features = 2
 
-# we make the weights normally distributed using numpy.random.randn
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+# store models for later use
+DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+epochs = 100
 
-# weights and bias in the hidden layer
-hidden_weights = np.random.randn(n_features, n_hidden_neurons)
-hidden_bias = np.zeros(n_hidden_neurons) + 0.01
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
+                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
+        dnn.fit(X, yXOR)
+        DNN_scikit[i][j] = dnn
+        print("Learning rate  = ", eta)
+        print("Lambda = ", lmbd)
+        print("Accuracy score on data set: ", dnn.score(X, yXOR))
+        print()
 
-# weights and bias in the output layer
-output_weights = np.random.randn(n_hidden_neurons, n_categories)
-output_bias = np.zeros(n_categories) + 0.01
+sns.set()
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        dnn = DNN_scikit[i][j]
+        test_pred = dnn.predict(X)
+        test_accuracy[i][j] = accuracy_score(yXOR, test_pred)
 
-probabilities = feed_forward(X)
-print(probabilities)
-
-
-predictions = predict(X)
-print(predictions)
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
 
    
-
    
-Not an impressive result, but this was our first forward pass with randomly assigned weights. Let us now add the full network with the back-propagation algorithm discussed above.
-
 
    
 
    
 
@@ -435,7 +435,7 @@ Not an impressive result, but this was our first forward pass with randomly assi
   
  • 40
    • 
   
  • 41
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
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    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs032.html b/doc/pub/week41/html/._week41-bs032.html
index b88392b97..983e593d4 100644
--- a/doc/pub/week41/html/._week41-bs032.html
+++ b/doc/pub/week41/html/._week41-bs032.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,69 +346,18 @@ MathJax.Hub.Config({
 
 
 
-
    The Code using Scikit-Learn 
    
+
    Building neural networks in Tensorflow and Keras 
    
 
 
    
+Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn
+and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
+and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
 
-
-
    # import necessary packages
-import numpy as np
-import matplotlib.pyplot as plt
-from sklearn.neural_network import MLPClassifier
-from sklearn.metrics import accuracy_score
-import seaborn as sns
+
    
+In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
+clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
+NumPy arrays.
 
-# ensure the same random numbers appear every time
-np.random.seed(0)
-
-# Design matrix
-X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
-
-# The XOR gate
-yXOR = np.array( [ 0, 1 ,1, 0])
-# The OR gate
-yOR = np.array( [ 0, 1 ,1, 1])
-# The AND gate
-yAND = np.array( [ 0, 0 ,0, 1])
-
-# Defining the neural network
-n_inputs, n_features = X.shape
-n_hidden_neurons = 2
-n_categories = 2
-n_features = 2
-
-eta_vals = np.logspace(-5, 1, 7)
-lmbd_vals = np.logspace(-5, 1, 7)
-# store models for later use
-DNN_scikit = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
-epochs = 100
-
-for i, eta in enumerate(eta_vals):
-    for j, lmbd in enumerate(lmbd_vals):
-        dnn = MLPClassifier(hidden_layer_sizes=(n_hidden_neurons), activation='logistic',
-                            alpha=lmbd, learning_rate_init=eta, max_iter=epochs)
-        dnn.fit(X, yXOR)
-        DNN_scikit[i][j] = dnn
-        print("Learning rate  = ", eta)
-        print("Lambda = ", lmbd)
-        print("Accuracy score on data set: ", dnn.score(X, yXOR))
-        print()
-
-sns.set()
-test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
-for i in range(len(eta_vals)):
-    for j in range(len(lmbd_vals)):
-        dnn = DNN_scikit[i][j]
-        test_pred = dnn.predict(X)
-        test_accuracy[i][j] = accuracy_score(yXOR, test_pred)
-
-fig, ax = plt.subplots(figsize = (10, 10))
-sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
-ax.set_title("Test Accuracy")
-ax.set_ylabel("$\eta$")
-ax.set_xlabel("$\lambda$")
-plt.show()
-
    
 
    
 
    
 
@@ -440,7 +384,7 @@ plt.show()
   
  • 41
    • 
   
  • 42
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs033.html b/doc/pub/week41/html/._week41-bs033.html
index 5fff6fed7..f10773c39 100644
--- a/doc/pub/week41/html/._week41-bs033.html
+++ b/doc/pub/week41/html/._week41-bs033.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,18 +346,58 @@ MathJax.Hub.Config({
 
 
 
-
    Building neural networks in Tensorflow and Keras 
    
+
    Tensorflow 
    
 
 
    
-Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn
-and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
-and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
+Tensorflow is an open source library machine learning library
+developed by the Google Brain team for internal use. It was released
+under the Apache 2.0 open source license in November 9, 2015.
 
 
    
-In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
-clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
-NumPy arrays.
+Tensorflow is a computational framework that allows you to construct
+machine learning models at different levels of abstraction, from
+high-level, object-oriented APIs like Keras, down to the C++ kernels
+that Tensorflow is built upon. The higher levels of abstraction are
+simpler to use, but less flexible, and our choice of implementation
+should reflect the problems we are trying to solve.
 
+
    
+Tensorflow uses so-called graphs to represent your computation
+in terms of the dependencies between individual operations, such that you first build a Tensorflow graph
+to represent your model, and then create a Tensorflow session to run the graph.
+
+
    
+In this guide we will analyze the same data as we did in our NumPy and
+scikit-learn tutorial, gathered from the MNIST database of images. We
+will give an introduction to the lower level Python Application
+Program Interfaces (APIs), and see how we use them to build our graph.
+Then we will build (effectively) the same graph in Keras, to see just
+how simple solving a machine learning problem can be.
+
+
    
+To install tensorflow on Unix/Linux systems, use pip as
+
    
+
+
+
    pip3 install tensorflow
+
    
+
    
+and/or if you use anaconda, just write (or install from the graphical user interface)
+(current release of CPU-only TensorFlow)
+
    
+
+
+
    conda create -n tf tensorflow
+conda activate tf
+
    
+
    
+To install the current release of GPU TensorFlow
+
    
+
+
+
    conda create -n tf-gpu tensorflow-gpu
+conda activate tf-gpu
+
    
 
    
 
    
 
@@ -389,7 +424,7 @@ NumPy arrays.
   
  • 42
    • 
   
  • 43
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs034.html b/doc/pub/week41/html/._week41-bs034.html
index 83f0c0797..cb154d807 100644
--- a/doc/pub/week41/html/._week41-bs034.html
+++ b/doc/pub/week41/html/._week41-bs034.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,58 +346,23 @@ MathJax.Hub.Config({
 
 
 
-
    Tensorflow 
    
+
    Using Keras 
    
 
 
    
-Tensorflow is an open source library machine learning library
-developed by the Google Brain team for internal use. It was released
-under the Apache 2.0 open source license in November 9, 2015.
-
-
    
-Tensorflow is a computational framework that allows you to construct
-machine learning models at different levels of abstraction, from
-high-level, object-oriented APIs like Keras, down to the C++ kernels
-that Tensorflow is built upon. The higher levels of abstraction are
-simpler to use, but less flexible, and our choice of implementation
-should reflect the problems we are trying to solve.
-
-
    
-Tensorflow uses so-called graphs to represent your computation
-in terms of the dependencies between individual operations, such that you first build a Tensorflow graph
-to represent your model, and then create a Tensorflow session to run the graph.
-
-
    
-In this guide we will analyze the same data as we did in our NumPy and
-scikit-learn tutorial, gathered from the MNIST database of images. We
-will give an introduction to the lower level Python Application
-Program Interfaces (APIs), and see how we use them to build our graph.
-Then we will build (effectively) the same graph in Keras, to see just
-how simple solving a machine learning problem can be.
-
-
    
-To install tensorflow on Unix/Linux systems, use pip as
+Keras is a high level neural network
+that supports Tensorflow, CTNK and Theano as backends.  
+If you have Anaconda installed you may run the following command
 
    
 
 
-
    pip3 install tensorflow
+
    conda install keras
 
    
 
    
-and/or if you use anaconda, just write (or install from the graphical user interface)
-(current release of CPU-only TensorFlow)
-
    
+You can look up the instructions here for more information.
 
-
-
    conda create -n tf tensorflow
-conda activate tf
-
    
-
    
-To install the current release of GPU TensorFlow
 
    
+We will to a large extent use keras in this course.
 
-
-
    conda create -n tf-gpu tensorflow-gpu
-conda activate tf-gpu
-
    
 
    
 
    
 
@@ -429,7 +389,7 @@ conda activate tf-gpu
   
  • 43
    • 
   
  • 44
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs035.html b/doc/pub/week41/html/._week41-bs035.html
index b8faddb6e..23e2c3f3a 100644
--- a/doc/pub/week41/html/._week41-bs035.html
+++ b/doc/pub/week41/html/._week41-bs035.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,23 +346,154 @@ MathJax.Hub.Config({
 
 
 
-
    Using Keras 
    
+
    Collect and pre-process data 
    
 
 
    
-Keras is a high level neural network
-that supports Tensorflow, CTNK and Theano as backends.  
-If you have Anaconda installed you may run the following command
+Let us look again at the MINST data set.
+
 
    
 
 
-
    conda install keras
+
    # import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+import tensorflow as tf
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+%matplotlib inline
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# flatten the image
+# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64
+n_inputs = len(inputs)
+inputs = inputs.reshape(n_inputs, -1)
+print("X = (n_inputs, n_features) = " + str(inputs.shape))
+
+
+# choose some random images to display
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
 
    
 
    
-You can look up the instructions here for more information.
 
+
+
    from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+
+from sklearn.model_selection import train_test_split
+
+# one-hot representation of labels
+labels = to_categorical(labels)
+
+# split into train and test data
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
    
 
    
-We will to a large extent use keras in this course.
 
+
+
    epochs = 100
+batch_size = 100
+n_neurons_layer1 = 100
+n_neurons_layer2 = 50
+n_categories = 10
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
+    model = Sequential()
+    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(Dense(n_categories, activation='softmax'))
+    
+    sgd = optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
+    
+    return model
+
    
+
    
+
+
+
    DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+        
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
+                                         eta=eta, lmbd=lmbd)
+        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+        scores = DNN.evaluate(X_test, Y_test)
+        
+        DNN_keras[i][j] = DNN
+        
+        print("Learning rate = ", eta)
+        print("Lambda = ", lmbd)
+        print("Test accuracy: %.3f" % scores[1])
+        print()
+
    
+
    
+
+
+
    # optional
+# visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        DNN = DNN_keras[i][j]
+
+        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]
+        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
    
 
    
 
    
 
@@ -394,7 +520,7 @@ We will to a large extent use keras in this course.
   
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    • 
-  
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diff --git a/doc/pub/week41/html/._week41-bs036.html b/doc/pub/week41/html/._week41-bs036.html
index df8628ed0..ce122c2f5 100644
--- a/doc/pub/week41/html/._week41-bs036.html
+++ b/doc/pub/week41/html/._week41-bs036.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,153 +346,176 @@ MathJax.Hub.Config({
 
 
 
-
    Collect and pre-process data 
    
-
-
    
-Let us look again at the MINST data set.
+
    The Breast Cancer Data, now with Keras 
    
 
 
    
 
 
-
    # import necessary packages
-import numpy as np
-import matplotlib.pyplot as plt
-import tensorflow as tf
-from sklearn import datasets
-
-
-# ensure the same random numbers appear every time
-np.random.seed(0)
-
-# display images in notebook
-%matplotlib inline
-plt.rcParams['figure.figsize'] = (12,12)
-
-
-# download MNIST dataset
-digits = datasets.load_digits()
-
-# define inputs and labels
-inputs = digits.images
-labels = digits.target
-
-print("inputs = (n_inputs, pixel_width, pixel_height) = " + str(inputs.shape))
-print("labels = (n_inputs) = " + str(labels.shape))
-
-
-# flatten the image
-# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64
-n_inputs = len(inputs)
-inputs = inputs.reshape(n_inputs, -1)
-print("X = (n_inputs, n_features) = " + str(inputs.shape))
-
-
-# choose some random images to display
-indices = np.arange(n_inputs)
-random_indices = np.random.choice(indices, size=5)
-
-for i, image in enumerate(digits.images[random_indices]):
-    plt.subplot(1, 5, i+1)
-    plt.axis('off')
-    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
-    plt.title("Label: %d" % digits.target[random_indices[i]])
-plt.show()
-
    
-
    
-
-
-
    from tensorflow.keras.layers import Input
+
    import tensorflow as tf
+from tensorflow.keras.layers import Input
 from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
 from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
 from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
 from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
 from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
-
-from sklearn.model_selection import train_test_split
-
-# one-hot representation of labels
-labels = to_categorical(labels)
-
-# split into train and test data
-train_size = 0.8
-test_size = 1 - train_size
-X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
-                                                    test_size=test_size)
-
    
-
    
-
-
-
    epochs = 100
-batch_size = 100
-n_neurons_layer1 = 100
-n_neurons_layer2 = 50
-n_categories = 10
-eta_vals = np.logspace(-5, 1, 7)
-lmbd_vals = np.logspace(-5, 1, 7)
-def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
-    model = Sequential()
-    model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
-    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
-    model.add(Dense(n_categories, activation='softmax'))
-    
-    sgd = optimizers.SGD(lr=eta)
-    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
-    
-    return model
-
    
-
    
-
-
-
    DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
-        
-for i, eta in enumerate(eta_vals):
-    for j, lmbd in enumerate(lmbd_vals):
-        DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
-                                         eta=eta, lmbd=lmbd)
-        DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
-        scores = DNN.evaluate(X_test, Y_test)
-        
-        DNN_keras[i][j] = DNN
-        
-        print("Learning rate = ", eta)
-        print("Lambda = ", lmbd)
-        print("Test accuracy: %.3f" % scores[1])
-        print()
-
    
-
    
-
-
-
    # optional
-# visual representation of grid search
-# uses seaborn heatmap, could probably do this in matplotlib
+import numpy as np
+import matplotlib.pyplot as plt
 import seaborn as sns
+from sklearn.model_selection import train_test_split as splitter
+from sklearn.datasets import load_breast_cancer
+import pickle
+import os 
 
-sns.set()
 
-train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
-test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+"""Load breast cancer dataset"""
 
-for i in range(len(eta_vals)):
-    for j in range(len(lmbd_vals)):
-        DNN = DNN_keras[i][j]
+np.random.seed(0)        #create same seed for random number every time
 
-        train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]
-        test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]
+cancer=load_breast_cancer()      #Download breast cancer dataset
 
-        
-fig, ax = plt.subplots(figsize = (10, 10))
-sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
-ax.set_title("Training Accuracy")
-ax.set_ylabel("$\eta$")
-ax.set_xlabel("$\lambda$")
+inputs=cancer.data                     #Feature matrix of 569 rows (samples) and 30 columns (parameters)
+outputs=cancer.target                  #Label array of 569 rows (0 for benign and 1 for malignant)
+labels=cancer.feature_names[0:30]
+
+print('The content of the breast cancer dataset is:')      #Print information about the datasets
+print(labels)
+print('-------------------------')
+print("inputs =  " + str(inputs.shape))
+print("outputs =  " + str(outputs.shape))
+print("labels =  "+ str(labels.shape))
+
+x=inputs      #Reassign the Feature and Label matrices to other variables
+y=outputs
+
+#%% 
+
+# Visualisation of dataset (for correlation analysis)
+
+plt.figure()
+plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean radius',fontweight='bold')
+plt.ylabel('Mean perimeter',fontweight='bold')
 plt.show()
 
-fig, ax = plt.subplots(figsize = (10, 10))
-sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
-ax.set_title("Test Accuracy")
-ax.set_ylabel("$\eta$")
-ax.set_xlabel("$\lambda$")
+plt.figure()
+plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)
+plt.xlabel('Mean compactness',fontweight='bold')
+plt.ylabel('Mean concavity',fontweight='bold')
 plt.show()
+
+
+plt.figure()
+plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean radius',fontweight='bold')
+plt.ylabel('Mean texture',fontweight='bold')
+plt.show()
+
+plt.figure()
+plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
+plt.xlabel('Mean perimeter',fontweight='bold')
+plt.ylabel('Mean compactness',fontweight='bold')
+plt.show()
+
+
+# Generate training and testing datasets
+
+#Select features relevant to classification (texture,perimeter,compactness and symmetery) 
+#and add to input matrix
+
+temp1=np.reshape(x[:,1],(len(x[:,1]),1))
+temp2=np.reshape(x[:,2],(len(x[:,2]),1))
+X=np.hstack((temp1,temp2))      
+temp=np.reshape(x[:,5],(len(x[:,5]),1))
+X=np.hstack((X,temp))       
+temp=np.reshape(x[:,8],(len(x[:,8]),1))
+X=np.hstack((X,temp))       
+
+X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1)   #Split datasets into training and testing
+
+y_train=to_categorical(y_train)     #Convert labels to categorical when using categorical cross entropy
+y_test=to_categorical(y_test)
+
+del temp1,temp2,temp
+
+# %%
+
+# Define tunable parameters"
+
+eta=np.logspace(-3,-1,3)                    #Define vector of learning rates (parameter to SGD optimiser)
+lamda=0.01                                  #Define hyperparameter
+n_layers=2                                  #Define number of hidden layers in the model
+n_neuron=np.logspace(0,3,4,dtype=int)       #Define number of neurons per layer
+epochs=100                                   #Number of reiterations over the input data
+batch_size=100                              #Number of samples per gradient update
+
+# %%
+
+"""Define function to return Deep Neural Network model"""
+
+def NN_model(inputsize,n_layers,n_neuron,eta,lamda):
+    model=Sequential()      
+    for i in range(n_layers):       #Run loop to add hidden layers to the model
+        if (i==0):                  #First layer requires input dimensions
+            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))
+        else:                       #Subsequent layers are capable of automatic shape inferencing
+            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))
+    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)
+    sgd=optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])
+    return model
+
+    
+Train_accuracy=np.zeros((len(n_neuron),len(eta)))      #Define matrices to store accuracy scores as a function
+Test_accuracy=np.zeros((len(n_neuron),len(eta)))       #of learning rate and number of hidden neurons for 
+
+for i in range(len(n_neuron)):     #run loops over hidden neurons and learning rates to calculate 
+    for j in range(len(eta)):      #accuracy scores 
+        DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)
+        DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)
+        Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]
+        Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]
+               
+
+def plot_data(x,y,data,title=None):
+
+    # plot results
+    fontsize=16
+
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)
+    
+    cbar=fig.colorbar(cax)
+    cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)
+    cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])
+    cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])
+
+    # put text on matrix elements
+    for i, x_val in enumerate(np.arange(len(x))):
+        for j, y_val in enumerate(np.arange(len(y))):
+            c = "${0:.1f}\\%$".format( 100*data[j,i])  
+            ax.text(x_val, y_val, c, va='center', ha='center')
+
+    # convert axis vaues to to string labels
+    x=[str(i) for i in x]
+    y=[str(i) for i in y]
+
+
+    ax.set_xticklabels(['']+x)
+    ax.set_yticklabels(['']+y)
+
+    ax.set_xlabel('$\\mathrm{learning\\ rate}$',fontsize=fontsize)
+    ax.set_ylabel('$\\mathrm{hidden\\ neurons}$',fontsize=fontsize)
+    if title is not None:
+        ax.set_title(title)
+
+    plt.tight_layout()
+
+    plt.show()
+    
+plot_data(eta,n_neuron,Train_accuracy, 'training')
+plot_data(eta,n_neuron,Test_accuracy, 'testing')
 
    
 
    
 
    
@@ -525,7 +543,7 @@ plt.show()
   
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    • 
   
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    • 
   
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    • 
-  
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    • 
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    • 
   
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diff --git a/doc/pub/week41/html/._week41-bs037.html b/doc/pub/week41/html/._week41-bs037.html
index a6f527030..f46d0fa4b 100644
--- a/doc/pub/week41/html/._week41-bs037.html
+++ b/doc/pub/week41/html/._week41-bs037.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,178 +346,30 @@ MathJax.Hub.Config({
 
 
 
-
    The Breast Cancer Data, now with Keras 
    
+
    Fine-tuning neural network hyperparameters 
    
 
 
    
+The flexibility of neural networks is also one of their main
+drawbacks: there are many hyperparameters to tweak. Not only can you
+use any imaginable network topology (how neurons/nodes are interconnected),
+but even in a simple FFNN you can change the number of layers, the
+number of neurons per layer, the type of activation function to use in
+each layer, the weight initialization logic, the stochastic gradient optmized and much more. How do you
+know what combination of hyperparameters is the best for your task?
 
-
-
    import tensorflow as tf
-from tensorflow.keras.layers import Input
-from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
-from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
-from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
-from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
-from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
-import numpy as np
-import matplotlib.pyplot as plt
-import seaborn as sns
-from sklearn.model_selection import train_test_split as splitter
-from sklearn.datasets import load_breast_cancer
-import pickle
-import os 
+
      
+
    •  You can use grid search with cross-validation to find the right hyperparameters.
      • 
+
    
 
+However,since there are many hyperparameters to tune, and since
+training a neural network on a large dataset takes a lot of time, you
+will only be able to explore a tiny part of the hyperparameter space.
 
-"""Load breast cancer dataset"""
+
      
+
    •  You can use randomized search.
      • 
+
    •  Or use tools like Oscar, which implements more complex algorithms to help you find a good set of hyperparameters quickly.
      •   
+
    
 
-np.random.seed(0)        #create same seed for random number every time
-
-cancer=load_breast_cancer()      #Download breast cancer dataset
-
-inputs=cancer.data                     #Feature matrix of 569 rows (samples) and 30 columns (parameters)
-outputs=cancer.target                  #Label array of 569 rows (0 for benign and 1 for malignant)
-labels=cancer.feature_names[0:30]
-
-print('The content of the breast cancer dataset is:')      #Print information about the datasets
-print(labels)
-print('-------------------------')
-print("inputs =  " + str(inputs.shape))
-print("outputs =  " + str(outputs.shape))
-print("labels =  "+ str(labels.shape))
-
-x=inputs      #Reassign the Feature and Label matrices to other variables
-y=outputs
-
-#%% 
-
-# Visualisation of dataset (for correlation analysis)
-
-plt.figure()
-plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)
-plt.xlabel('Mean radius',fontweight='bold')
-plt.ylabel('Mean perimeter',fontweight='bold')
-plt.show()
-
-plt.figure()
-plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)
-plt.xlabel('Mean compactness',fontweight='bold')
-plt.ylabel('Mean concavity',fontweight='bold')
-plt.show()
-
-
-plt.figure()
-plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
-plt.xlabel('Mean radius',fontweight='bold')
-plt.ylabel('Mean texture',fontweight='bold')
-plt.show()
-
-plt.figure()
-plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
-plt.xlabel('Mean perimeter',fontweight='bold')
-plt.ylabel('Mean compactness',fontweight='bold')
-plt.show()
-
-
-# Generate training and testing datasets
-
-#Select features relevant to classification (texture,perimeter,compactness and symmetery) 
-#and add to input matrix
-
-temp1=np.reshape(x[:,1],(len(x[:,1]),1))
-temp2=np.reshape(x[:,2],(len(x[:,2]),1))
-X=np.hstack((temp1,temp2))      
-temp=np.reshape(x[:,5],(len(x[:,5]),1))
-X=np.hstack((X,temp))       
-temp=np.reshape(x[:,8],(len(x[:,8]),1))
-X=np.hstack((X,temp))       
-
-X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1)   #Split datasets into training and testing
-
-y_train=to_categorical(y_train)     #Convert labels to categorical when using categorical cross entropy
-y_test=to_categorical(y_test)
-
-del temp1,temp2,temp
-
-# %%
-
-# Define tunable parameters"
-
-eta=np.logspace(-3,-1,3)                    #Define vector of learning rates (parameter to SGD optimiser)
-lamda=0.01                                  #Define hyperparameter
-n_layers=2                                  #Define number of hidden layers in the model
-n_neuron=np.logspace(0,3,4,dtype=int)       #Define number of neurons per layer
-epochs=100                                   #Number of reiterations over the input data
-batch_size=100                              #Number of samples per gradient update
-
-# %%
-
-"""Define function to return Deep Neural Network model"""
-
-def NN_model(inputsize,n_layers,n_neuron,eta,lamda):
-    model=Sequential()      
-    for i in range(n_layers):       #Run loop to add hidden layers to the model
-        if (i==0):                  #First layer requires input dimensions
-            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))
-        else:                       #Subsequent layers are capable of automatic shape inferencing
-            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))
-    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)
-    sgd=optimizers.SGD(lr=eta)
-    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])
-    return model
-
-    
-Train_accuracy=np.zeros((len(n_neuron),len(eta)))      #Define matrices to store accuracy scores as a function
-Test_accuracy=np.zeros((len(n_neuron),len(eta)))       #of learning rate and number of hidden neurons for 
-
-for i in range(len(n_neuron)):     #run loops over hidden neurons and learning rates to calculate 
-    for j in range(len(eta)):      #accuracy scores 
-        DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)
-        DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)
-        Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]
-        Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]
-               
-
-def plot_data(x,y,data,title=None):
-
-    # plot results
-    fontsize=16
-
-
-    fig = plt.figure()
-    ax = fig.add_subplot(111)
-    cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)
-    
-    cbar=fig.colorbar(cax)
-    cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)
-    cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])
-    cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])
-
-    # put text on matrix elements
-    for i, x_val in enumerate(np.arange(len(x))):
-        for j, y_val in enumerate(np.arange(len(y))):
-            c = "${0:.1f}\\%$".format( 100*data[j,i])  
-            ax.text(x_val, y_val, c, va='center', ha='center')
-
-    # convert axis vaues to to string labels
-    x=[str(i) for i in x]
-    y=[str(i) for i in y]
-
-
-    ax.set_xticklabels(['']+x)
-    ax.set_yticklabels(['']+y)
-
-    ax.set_xlabel('$\\mathrm{learning\\ rate}$',fontsize=fontsize)
-    ax.set_ylabel('$\\mathrm{hidden\\ neurons}$',fontsize=fontsize)
-    if title is not None:
-        ax.set_title(title)
-
-    plt.tight_layout()
-
-    plt.show()
-    
-plot_data(eta,n_neuron,Train_accuracy, 'training')
-plot_data(eta,n_neuron,Test_accuracy, 'testing')
-
    
-
    
 
    
 
 
      
@@ -548,7 +395,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing&
   
    • 46
      • 
   
    • 47
      • 
   
    • ...
      • 
-  
    • 72
      • 
+  
    • 71
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week41/html/._week41-bs038.html b/doc/pub/week41/html/._week41-bs038.html
index 446f022a7..02df96a12 100644
--- a/doc/pub/week41/html/._week41-bs038.html
+++ b/doc/pub/week41/html/._week41-bs038.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,30 +346,24 @@ MathJax.Hub.Config({
 
 
 
-
    Fine-tuning neural network hyperparameters 
    
+
    Hidden layers 
    
 
 
    
-The flexibility of neural networks is also one of their main
-drawbacks: there are many hyperparameters to tweak. Not only can you
-use any imaginable network topology (how neurons/nodes are interconnected),
-but even in a simple FFNN you can change the number of layers, the
-number of neurons per layer, the type of activation function to use in
-each layer, the weight initialization logic, the stochastic gradient optmized and much more. How do you
-know what combination of hyperparameters is the best for your task?
+For many problems you can start with just one or two hidden layers and it will work just fine.
+For the MNIST data set you ca easily get a high accuracy using just one hidden layer with a
+few hundred neurons.
+You can reach for this data set above 98% accuracy using two hidden layers with the same total amount of
+neurons, in roughly the same amount of training time.
 
-
      
-
    •  You can use grid search with cross-validation to find the right hyperparameters.
      • 
-
    
-
-However,since there are many hyperparameters to tune, and since
-training a neural network on a large dataset takes a lot of time, you
-will only be able to explore a tiny part of the hyperparameter space.
-
-
      
-
    •  You can use randomized search.
      • 
-
    •  Or use tools like Oscar, which implements more complex algorithms to help you find a good set of hyperparameters quickly.
      •   
-
    
+
    
+For more complex problems, you can gradually
+ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such
+as large image classification or speech recognition, typically require networks with dozens of layers
+and they need a huge amount
+of training data. However, you will rarely have to train such networks from scratch: it is much more
+common to reuse parts of a pretrained state-of-the-art network that performs a similar task.
 
+
    
 
    
 
 
      
@@ -400,7 +389,7 @@ will only be able to explore a tiny part of the hyperparameter space.
   
    • 47
      • 
   
    • 48
      • 
   
    • ...
      • 
-  
    • 72
      • 
+  
    • 71
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week41/html/._week41-bs039.html b/doc/pub/week41/html/._week41-bs039.html
index 1a66a1d1a..f7532038c 100644
--- a/doc/pub/week41/html/._week41-bs039.html
+++ b/doc/pub/week41/html/._week41-bs039.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,24 +344,33 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    Hidden layers 
    
+
    Which activation function should I use? 
    
 
 
    
-For many problems you can start with just one or two hidden layers and it will work just fine.
-For the MNIST data set you ca easily get a high accuracy using just one hidden layer with a
-few hundred neurons.
-You can reach for this data set above 98% accuracy using two hidden layers with the same total amount of
-neurons, in roughly the same amount of training time.
+The Back propagation algorithm we derived above works by going from
+the output layer to the input layer, propagating the error gradient on
+the way. Once the algorithm has computed the gradient of the cost
+function with regards to each parameter in the network, it uses these
+gradients to update each parameter with a Gradient Descent (GD) step.
 
 
    
-For more complex problems, you can gradually
-ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such
-as large image classification or speech recognition, typically require networks with dozens of layers
-and they need a huge amount
-of training data. However, you will rarely have to train such networks from scratch: it is much more
-common to reuse parts of a pretrained state-of-the-art network that performs a similar task.
+Unfortunately for us, the gradients often get smaller and smaller as the
+algorithm progresses down to the first hidden layers. As a result, the
+GD update leaves the lower layer connection weights
+virtually unchanged, and training never converges to a good
+solution. This is known in the literature as 
+the vanishing gradients problem.
+
+
    
+In other cases, the opposite can happen, namely the the gradients can grow bigger and
+bigger. The result is that many of the layers get large updates of the 
+weights the
+algorithm diverges. This is the exploding gradients problem, which is
+mostly encountered in recurrent neural networks. More generally, deep
+neural networks suffer from unstable gradients, different layers may
+learn at widely different speeds
 
 
    
 
    
@@ -394,7 +398,7 @@ common to reuse parts of a pretrained state-of-the-art network that performs a s
   
  • 48
    • 
   
  • 49
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs040.html b/doc/pub/week41/html/._week41-bs040.html
index 3085e63e6..6291bdac3 100644
--- a/doc/pub/week41/html/._week41-bs040.html
+++ b/doc/pub/week41/html/._week41-bs040.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,31 +346,32 @@ MathJax.Hub.Config({
 
 
 
-
    Which activation function should I use? 
    
+
    Is the Logistic activation function (Sigmoid)  our choice? 
    
 
 
    
-The Back propagation algorithm we derived above works by going from
-the output layer to the input layer, propagating the error gradient on
-the way. Once the algorithm has computed the gradient of the cost
-function with regards to each parameter in the network, it uses these
-gradients to update each parameter with a Gradient Descent (GD) step.
+Although this unfortunate behavior has been empirically observed for
+quite a while (it was one of the reasons why deep neural networks were
+mostly abandoned for a long time), it is only around 2010 that
+significant progress was made in understanding it.
 
 
    
-Unfortunately for us, the gradients often get smaller and smaller as the
-algorithm progresses down to the first hidden layers. As a result, the
-GD update leaves the lower layer connection weights
-virtually unchanged, and training never converges to a good
-solution. This is known in the literature as 
-the vanishing gradients problem.
+A paper titled Understanding the Difficulty of Training Deep
+Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio found that
+the problems with the popular logistic
+sigmoid activation function and the weight initialization technique
+that was most popular at the time, namely random initialization using
+a normal distribution with a mean of 0 and a standard deviation of
+1.
 
 
    
-In other cases, the opposite can happen, namely the the gradients can grow bigger and
-bigger. The result is that many of the layers get large updates of the 
-weights the
-algorithm diverges. This is the exploding gradients problem, which is
-mostly encountered in recurrent neural networks. More generally, deep
-neural networks suffer from unstable gradients, different layers may
-learn at widely different speeds
+They showed that with this activation function and this
+initialization scheme, the variance of the outputs of each layer is
+much greater than the variance of its inputs. Going forward in the
+network, the variance keeps increasing after each layer until the
+activation function saturates at the top layers. This is actually made
+worse by the fact that the logistic function has a mean of 0.5, not 0
+(the hyperbolic tangent function has a mean of 0 and behaves slightly
+better than the logistic function in deep networks).
 
 
    
 
    
@@ -403,7 +399,7 @@ learn at widely different speeds
   
  • 49
    • 
   
  • 50
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs041.html b/doc/pub/week41/html/._week41-bs041.html
index 66ed92a09..866d561b5 100644
--- a/doc/pub/week41/html/._week41-bs041.html
+++ b/doc/pub/week41/html/._week41-bs041.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,34 +344,40 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    Is the Logistic activation function (Sigmoid)  our choice? 
    
+
    The derivative of the Logistic funtion 
    
 
 
    
-Although this unfortunate behavior has been empirically observed for
-quite a while (it was one of the reasons why deep neural networks were
-mostly abandoned for a long time), it is only around 2010 that
-significant progress was made in understanding it.
+Looking at the logistic activation function, when inputs become large
+(negative or positive), the function saturates at 0 or 1, with a
+derivative extremely close to 0. Thus when backpropagation kicks in,
+it has virtually no gradient to propagate back through the network,
+and what little gradient exists keeps getting diluted as
+backpropagation progresses down through the top layers, so there is
+really nothing left for the lower layers.
 
 
    
-A paper titled Understanding the Difficulty of Training Deep
-Feedforward Neural Networks by Xavier Glorot and Yoshua Bengio found that
-the problems with the popular logistic
-sigmoid activation function and the weight initialization technique
-that was most popular at the time, namely random initialization using
-a normal distribution with a mean of 0 and a standard deviation of
-1.
+In their paper, Glorot and Bengio propose a way to significantly
+alleviate this problem. We need the signal to flow properly in both
+directions: in the forward direction when making predictions, and in
+the reverse direction when backpropagating gradients. We don’t want
+the signal to die out, nor do we want it to explode and saturate. For
+the signal to flow properly, the authors argue that we need the
+variance of the outputs of each layer to be equal to the variance of
+its inputs, and we also need the gradients to have equal variance
+before and after flowing through a layer in the reverse direction.
 
 
    
-They showed that with this activation function and this
-initialization scheme, the variance of the outputs of each layer is
-much greater than the variance of its inputs. Going forward in the
-network, the variance keeps increasing after each layer until the
-activation function saturates at the top layers. This is actually made
-worse by the fact that the logistic function has a mean of 0.5, not 0
-(the hyperbolic tangent function has a mean of 0 and behaves slightly
-better than the logistic function in deep networks).
+One of the insights in the 2010 paper by Glorot and Bengio was that
+the vanishing/exploding gradients problems were in part due to a poor
+choice of activation function. Until then most people had assumed that
+if Nature had chosen to use roughly sigmoid activation functions in
+biological neurons, they must be an excellent choice. But it turns out
+that other activation functions behave much better in deep neural
+networks, in particular the ReLU activation function, mostly because
+it does not saturate for positive values (and also because it is quite
+fast to compute).
 
 
    
 
    
@@ -404,7 +405,7 @@ better than the logistic function in deep networks).
   
  • 50
    • 
   
  • 51
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs042.html b/doc/pub/week41/html/._week41-bs042.html
index 03ffc726c..f45d1bb66 100644
--- a/doc/pub/week41/html/._week41-bs042.html
+++ b/doc/pub/week41/html/._week41-bs042.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,38 +346,29 @@ MathJax.Hub.Config({
 
 
 
-
    The derivative of the Logistic funtion 
    
+
    The RELU function family 
    
 
 
    
-Looking at the logistic activation function, when inputs become large
-(negative or positive), the function saturates at 0 or 1, with a
-derivative extremely close to 0. Thus when backpropagation kicks in,
-it has virtually no gradient to propagate back through the network,
-and what little gradient exists keeps getting diluted as
-backpropagation progresses down through the top layers, so there is
-really nothing left for the lower layers.
+The ReLU activation function suffers from a problem known as the dying
+ReLUs: during training, some neurons effectively die, meaning they
+stop outputting anything other than 0.
 
 
    
-In their paper, Glorot and Bengio propose a way to significantly
-alleviate this problem. We need the signal to flow properly in both
-directions: in the forward direction when making predictions, and in
-the reverse direction when backpropagating gradients. We don’t want
-the signal to die out, nor do we want it to explode and saturate. For
-the signal to flow properly, the authors argue that we need the
-variance of the outputs of each layer to be equal to the variance of
-its inputs, and we also need the gradients to have equal variance
-before and after flowing through a layer in the reverse direction.
+In some cases, you may find that half of your network’s neurons are
+dead, especially if you used a large learning rate. During training,
+if a neuron’s weights get updated such that the weighted sum of the
+neuron’s inputs is negative, it will start outputting 0. When this
+happen, the neuron is unlikely to come back to life since the gradient
+of the ReLU function is 0 when its input is negative.
 
 
    
-One of the insights in the 2010 paper by Glorot and Bengio was that
-the vanishing/exploding gradients problems were in part due to a poor
-choice of activation function. Until then most people had assumed that
-if Nature had chosen to use roughly sigmoid activation functions in
-biological neurons, they must be an excellent choice. But it turns out
-that other activation functions behave much better in deep neural
-networks, in particular the ReLU activation function, mostly because
-it does not saturate for positive values (and also because it is quite
-fast to compute).
+To solve this problem, nowadays practitioners use a  variant of the ReLU
+function, such as the leaky ReLU discussed above or the so-called
+exponential linear unit (ELU) function
+
+$$
+ELU(z) = \left\{\begin{array}{cc} \alpha\left( \exp{(z)}-1\right) & z < 0,\\  z & z \ge 0.\end{array}\right. 
+$$
 
 
    
 
    
@@ -410,7 +396,7 @@ fast to compute).
   
  • 51
    • 
   
  • 52
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs043.html b/doc/pub/week41/html/._week41-bs043.html
index 28bbf9fbe..eeaa92b45 100644
--- a/doc/pub/week41/html/._week41-bs043.html
+++ b/doc/pub/week41/html/._week41-bs043.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,29 +346,22 @@ MathJax.Hub.Config({
 
 
 
-
    The RELU function family 
    
+
    Which activation function should we use? 
    
 
 
    
-The ReLU activation function suffers from a problem known as the dying
-ReLUs: during training, some neurons effectively die, meaning they
-stop outputting anything other than 0.
+In general it seems that the ELU activation function is better than
+the leaky ReLU function (and its variants), which is better than
+ReLU. ReLU performs better than \( \tanh \) which in turn performs better
+than the logistic function.
 
 
    
-In some cases, you may find that half of your network’s neurons are
-dead, especially if you used a large learning rate. During training,
-if a neuron’s weights get updated such that the weighted sum of the
-neuron’s inputs is negative, it will start outputting 0. When this
-happen, the neuron is unlikely to come back to life since the gradient
-of the ReLU function is 0 when its input is negative.
-
-
    
-To solve this problem, nowadays practitioners use a  variant of the ReLU
-function, such as the leaky ReLU discussed above or the so-called
-exponential linear unit (ELU) function
-
-$$
-ELU(z) = \left\{\begin{array}{cc} \alpha\left( \exp{(z)}-1\right) & z < 0,\\  z & z \ge 0.\end{array}\right. 
-$$
+If runtime
+performance is an issue, then you may opt for the  leaky ReLU function  over the 
+ELU function If you don’t
+want to tweak yet another hyperparameter, you may just use the default
+\( \alpha \) of \( 0.01 \) for the leaky ReLU, and \( 1 \) for ELU. If you have
+spare time and computing power, you can use cross-validation or
+bootstrap to evaluate other activation functions.
 
 
    
 
    
@@ -401,7 +389,7 @@ $$
   
  • 52
    • 
   
  • 53
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs044.html b/doc/pub/week41/html/._week41-bs044.html
index b56603731..ab1ffa6fc 100644
--- a/doc/pub/week41/html/._week41-bs044.html
+++ b/doc/pub/week41/html/._week41-bs044.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,24 +346,22 @@ MathJax.Hub.Config({
 
 
 
-
    Which activation function should we use? 
    
+
    More on activation functions, output layers 
    
 
 
    
-In general it seems that the ELU activation function is better than
-the leaky ReLU function (and its variants), which is better than
-ReLU. ReLU performs better than \( \tanh \) which in turn performs better
-than the logistic function.
+In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).
 
 
    
-If runtime
-performance is an issue, then you may opt for the  leaky ReLU function  over the 
-ELU function If you don’t
-want to tweak yet another hyperparameter, you may just use the default
-\( \alpha \) of \( 0.01 \) for the leaky ReLU, and \( 1 \) for ELU. If you have
-spare time and computing power, you can use cross-validation or
-bootstrap to evaluate other activation functions.
+It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.
 
 
    
+For the output layer:
+
+
      
+
    •  For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).
      • 
+
    •  For regression tasks, you can simply use no activation function at all.
      • 
+
    
+
 
    
 
 
      
@@ -394,7 +387,7 @@ bootstrap to evaluate other activation functions.
   
    • 53
      • 
   
    • 54
      • 
   
    • ...
      • 
-  
    • 72
      • 
+  
    • 71
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week41/html/._week41-bs045.html b/doc/pub/week41/html/._week41-bs045.html
index b63a009ce..d8204f266 100644
--- a/doc/pub/week41/html/._week41-bs045.html
+++ b/doc/pub/week41/html/._week41-bs045.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,22 +346,23 @@ MathJax.Hub.Config({
 
 
 
-
    More on activation functions, output layers 
    
+
    Batch Normalization 
    
 
 
    
-In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).
+Batch Normalization
+aims to address the vanishing/exploding gradients problems, and more generally the problem that the
+distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.
 
 
    
-It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.
+The technique consists of adding an operation in the model just before the activation function of each
+layer, simply zero-centering and normalizing the inputs, then scaling and shifting the result using two new
+parameters per layer (one for scaling, the other for shifting). In other words, this operation lets the model
+learn the optimal scale and mean of the inputs for each layer.
+In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and
+standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current
+mini-batch, from this the name batch normalization.
 
 
    
-For the output layer:
-
-
      
-
    •  For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).
      • 
-
    •  For regression tasks, you can simply use no activation function at all.
      • 
-
    
-
 
    
 
 
      
@@ -392,7 +388,7 @@ It is a bit faster to compute than other activation functions, and the gradient
   
    • 54
      • 
   
    • 55
      • 
   
    • ...
      • 
-  
    • 72
      • 
+  
    • 71
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week41/html/._week41-bs046.html b/doc/pub/week41/html/._week41-bs046.html
index 8dc593fe3..efcd2e0d6 100644
--- a/doc/pub/week41/html/._week41-bs046.html
+++ b/doc/pub/week41/html/._week41-bs046.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,21 +346,17 @@ MathJax.Hub.Config({
 
 
 
-
    Batch Normalization 
    
+
    Dropout 
    
 
 
    
-Batch Normalization
-aims to address the vanishing/exploding gradients problems, and more generally the problem that the
-distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.
+It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but
+excluding the output neurons) has a probability \( p \) of being temporarily dropped out, meaning it will be
+entirely ignored during this training step, but it may be active during the next step.
 
 
    
-The technique consists of adding an operation in the model just before the activation function of each
-layer, simply zero-centering and normalizing the inputs, then scaling and shifting the result using two new
-parameters per layer (one for scaling, the other for shifting). In other words, this operation lets the model
-learn the optimal scale and mean of the inputs for each layer.
-In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and
-standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current
-mini-batch, from this the name batch normalization.
+The
+hyperparameter \( p \) is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.
+ It is viewed as one of the most popular regularization techniques.
 
 
    
 
    
@@ -393,7 +384,7 @@ mini-batch, from this the name batch normalization.
   
  • 55
    • 
   
  • 56
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs047.html b/doc/pub/week41/html/._week41-bs047.html
index f0ed7337c..05543b7ad 100644
--- a/doc/pub/week41/html/._week41-bs047.html
+++ b/doc/pub/week41/html/._week41-bs047.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,17 +346,19 @@ MathJax.Hub.Config({
 
 
 
-
    Dropout 
    
+
    Gradient Clipping 
    
 
 
    
-It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but
-excluding the output neurons) has a probability \( p \) of being temporarily dropped out, meaning it will be
-entirely ignored during this training step, but it may be active during the next step.
+A popular technique to lessen the exploding gradients problem is to simply clip the gradients during
+backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural
+networks).
 
 
    
-The
-hyperparameter \( p \) is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.
- It is viewed as one of the most popular regularization techniques.
+This technique is called Gradient Clipping.
+
+
    
+In general however, Batch
+Normalization is preferred.
 
 
    
 
    
@@ -389,7 +386,7 @@ hyperparameter \( p \) is called the dropout rate, and it is typically set to 50
   
  • 56
    • 
   
  • 57
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs048.html b/doc/pub/week41/html/._week41-bs048.html
index 251b1b3b6..6f80b50f8 100644
--- a/doc/pub/week41/html/._week41-bs048.html
+++ b/doc/pub/week41/html/._week41-bs048.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,19 +346,10 @@ MathJax.Hub.Config({
 
 
 
-
    Gradient Clipping 
    
+
    A very nice website on Neural Networks 
    
 
 
    
-A popular technique to lessen the exploding gradients problem is to simply clip the gradients during
-backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural
-networks).
-
-
    
-This technique is called Gradient Clipping.
-
-
    
-In general however, Batch
-Normalization is preferred.
+You may find this website very useful. Thx a million to Ghadi for sharing.
 
 
    
 
    
@@ -391,7 +377,7 @@ Normalization is preferred.
   
  • 57
    • 
   
  • 58
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs049.html b/doc/pub/week41/html/._week41-bs049.html
index c0c309a7a..94d1a56b5 100644
--- a/doc/pub/week41/html/._week41-bs049.html
+++ b/doc/pub/week41/html/._week41-bs049.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,12 +344,46 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    A very nice website on Neural Networks 
    
+
    A top-down perspective on Neural networks 
    
 
 
    
-You may find this website very useful. Thx a million to Ghadi for sharing.
+The first thing we would like to do is divide the data into two or three
+parts. A training set, a validation or dev (development) set, and a
+test set. The test set is the data on which we want to make
+predictions. The dev set is a subset of the training data we use to
+check how well we are doing out-of-sample, after training the model on
+the training dataset. We use the validation error as a proxy for the
+test error in order to make tweaks to our model. It is crucial that we
+do not use any of the test data to train the algorithm. This is a
+cardinal sin in ML. Then:
+
+
      
+
    •  Estimate optimal error rate
      • 
+
    •  Minimize underfitting (bias) on training data set.
      • 
+
    •  Make sure you are not overfitting.
      • 
+
    
+
+If the validation and test sets are drawn from the same distributions,
+then a good performance on the validation set should lead to similarly
+good performance on the test set.
+
+
    
+However, sometimes
+the training data and test data differ in subtle ways because, for
+example, they are collected using slightly different methods, or
+because it is cheaper to collect data in one way versus another. In
+this case, there can be a mismatch between the training and test
+data. This can lead to the neural network overfitting these small
+differences between the test and training sets, and a poor performance
+on the test set despite having a good performance on the validation
+set. To rectify this, Andrew Ng suggests making two validation or dev
+sets, one constructed from the training data and one constructed from
+the test data. The difference between the performance of the algorithm
+on these two validation sets quantifies the train-test mismatch. This
+can serve as another important diagnostic when using DNNs for
+supervised learning.
 
 
    
 
    
@@ -382,7 +411,7 @@ You may find this 58
   
  • 59
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs050.html b/doc/pub/week41/html/._week41-bs050.html
index 7d87ae6e6..3cd34142d 100644
--- a/doc/pub/week41/html/._week41-bs050.html
+++ b/doc/pub/week41/html/._week41-bs050.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,46 +344,30 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    A top-down perspective on Neural networks 
    
+
    Limitations of supervised learning with deep networks 
    
 
 
    
-The first thing we would like to do is divide the data into two or three
-parts. A training set, a validation or dev (development) set, and a
-test set. The test set is the data on which we want to make
-predictions. The dev set is a subset of the training data we use to
-check how well we are doing out-of-sample, after training the model on
-the training dataset. We use the validation error as a proxy for the
-test error in order to make tweaks to our model. It is crucial that we
-do not use any of the test data to train the algorithm. This is a
-cardinal sin in ML. Then:
+Like all statistical methods, supervised learning using neural
+networks has important limitations. This is especially important when
+one seeks to apply these methods, especially to physics problems. Like
+all tools, DNNs are not a universal solution. Often, the same or
+better performance on a task can be achieved by using a few
+hand-engineered features (or even a collection of random
+features).
+
+
    
+Here we list some of the important limitations of supervised neural network based models. 
 
 
      
-
    •  Estimate optimal error rate
      • 
-
    •  Minimize underfitting (bias) on training data set.
      • 
-
    •  Make sure you are not overfitting.
      • 
+
    •  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).
      • 
+
    •  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.
      • 
+
    •  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.
      • 
+
    •  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.
      • 
 
    
 
-If the validation and test sets are drawn from the same distributions,
-then a good performance on the validation set should lead to similarly
-good performance on the test set.
-
-
    
-However, sometimes
-the training data and test data differ in subtle ways because, for
-example, they are collected using slightly different methods, or
-because it is cheaper to collect data in one way versus another. In
-this case, there can be a mismatch between the training and test
-data. This can lead to the neural network overfitting these small
-differences between the test and training sets, and a poor performance
-on the test set despite having a good performance on the validation
-set. To rectify this, Andrew Ng suggests making two validation or dev
-sets, one constructed from the training data and one constructed from
-the test data. The difference between the performance of the algorithm
-on these two validation sets quantifies the train-test mismatch. This
-can serve as another important diagnostic when using DNNs for
-supervised learning.
+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.
 
 
    
 
    
@@ -416,7 +395,7 @@ supervised learning.
   
  • 59
    • 
   
  • 60
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs051.html b/doc/pub/week41/html/._week41-bs051.html
index a9aff07bd..d6a53bade 100644
--- a/doc/pub/week41/html/._week41-bs051.html
+++ b/doc/pub/week41/html/._week41-bs051.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,28 +346,33 @@ MathJax.Hub.Config({
 
 
 
-
    Limitations of supervised learning with deep networks 
    
+
    Overarching Views, a personal  note 
    
 
 
    
-Like all statistical methods, supervised learning using neural
-networks has important limitations. This is especially important when
-one seeks to apply these methods, especially to physics problems. Like
-all tools, DNNs are not a universal solution. Often, the same or
-better performance on a task can be achieved by using a few
-hand-engineered features (or even a collection of random
-features).
+The author of these lecture notes has an overarching take on many of
+the machine learning algorithms we discuss here.
 
 
    
-Here we list some of the important limitations of supervised neural network based models. 
+If we wish to understand complex systems, we need to find some
+effective degrees of freedom or features that we find essential,
+simply in order to reduce the complexity of the systems we are
+studying.  This leads, in one way or the other to dimensionality
+reductions. Most of the Machine Learning methods we encounter deal
+with this, whether we opt for a principal component analysis, or
+clustering, or convolutional neural networks, or Ridge or Lasso
+regression or random forest, yes, perhaps most machine learning
+methods at large.
 
-
      
-
    •  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).
      • 
-
    •  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.
      • 
-
    •  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.
      • 
-
    •  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.
      • 
-
    
-
-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.
+
    
+For neural networks and our previous discussion, we have seen that we
+in essence end up with matrix-matrix and matrix-vector
+multiplications. In all cases, our matrices are dense ones, and the
+more data we deal with the larger the dimensionalities of the matrices
+and vectors. How can we reduce such dimensionalities?  One possible
+answer is offered by convolutional neural networks (CNN), as
+discussed below. The figure here shows a typical situation of the
+reduction of information in an image and is typical of what CNNs
+actually end up doing.
 
 
    
 
    
@@ -400,7 +400,7 @@ Some of these remarks are particular to DNNs, others are shared by all supervise
   
  • 60
    • 
   
  • 61
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs052.html b/doc/pub/week41/html/._week41-bs052.html
index 7284c6e40..32be09bc1 100644
--- a/doc/pub/week41/html/._week41-bs052.html
+++ b/doc/pub/week41/html/._week41-bs052.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,33 +346,10 @@ MathJax.Hub.Config({
 
 
 
-
    Overarching Views, a personal  note 
    
+
    From a Spherical Cow to a real one 
    
 
 
    
-The author of these lecture notes has an overarching take on many of
-the machine learning algorithms we discuss here.
-
-
    
-If we wish to understand complex systems, we need to find some
-effective degrees of freedom or features that we find essential,
-simply in order to reduce the complexity of the systems we are
-studying.  This leads, in one way or the other to dimensionality
-reductions. Most of the Machine Learning methods we encounter deal
-with this, whether we opt for a principal component analysis, or
-clustering, or convolutional neural networks, or Ridge or Lasso
-regression or random forest, yes, perhaps most machine learning
-methods at large.
-
-
    
-For neural networks and our previous discussion, we have seen that we
-in essence end up with matrix-matrix and matrix-vector
-multiplications. In all cases, our matrices are dense ones, and the
-more data we deal with the larger the dimensionalities of the matrices
-and vectors. How can we reduce such dimensionalities?  One possible
-answer is offered by convolutional neural networks (CNN), as
-discussed below. The figure here shows a typical situation of the
-reduction of information in an image and is typical of what CNNs
-actually end up doing.
+



    
 
 
    
 
    
@@ -405,7 +377,7 @@ actually end up doing.
   
  • 61
    • 
   
  • 62
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs053.html b/doc/pub/week41/html/._week41-bs053.html
index 159f89504..5dae64630 100644
--- a/doc/pub/week41/html/._week41-bs053.html
+++ b/doc/pub/week41/html/._week41-bs053.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,10 +346,41 @@ MathJax.Hub.Config({
 
 
 
-
    From a Spherical Cow to a real one 
    
+
    Convolutional Neural Networks (recognizing images) 
    
 
 
    
-



    
+Convolutional neural networks (CNNs) were developed during the last
+decade of the previous century, with a focus on character recognition
+tasks. Nowadays, CNNs are a central element in the spectacular success
+of deep learning methods. The success in for example image
+classifications have made them a central tool for most machine
+learning practitioners.
+
+
    
+CNNs are very similar to ordinary Neural Networks.
+They are made up of neurons that have learnable weights and
+biases. Each neuron receives some inputs, performs a dot product and
+optionally follows it with a non-linearity. The whole network still
+expresses a single differentiable score function: from the raw image
+pixels on one end to class scores at the other. And they still have a
+loss function (for example Softmax) on the last (fully-connected) layer
+and all the tips/tricks we developed for learning regular Neural
+Networks still apply (back propagation, gradient descent etc etc).
+
+
    
+What is the difference? CNN architectures make the explicit assumption that
+the inputs are images, which allows us to encode certain properties
+into the architecture. These then make the forward function more
+efficient to implement and vastly reduce the amount of parameters in
+the network.
+
+
    
+Here we provide only a superficial overview, for the more interested, we recommend highly the course
+IN5400 – Machine Learning for Image Analysis
+and the slides of CS231.
+
+
    
+Another good read is the article here https://arxiv.org/pdf/1603.07285.pdf.
 
 
    
 
    
@@ -382,7 +408,7 @@ MathJax.Hub.Config({
   
  • 62
    • 
   
  • 63
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs054.html b/doc/pub/week41/html/._week41-bs054.html
index ef57825ae..cbbe8a780 100644
--- a/doc/pub/week41/html/._week41-bs054.html
+++ b/doc/pub/week41/html/._week41-bs054.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,41 +346,30 @@ MathJax.Hub.Config({
 
 
 
-
    Convolutional Neural Networks (recognizing images) 
    
+
    Regular NNs don’t scale well to full images 
    
 
 
    
-Convolutional neural networks (CNNs) were developed during the last
-decade of the previous century, with a focus on character recognition
-tasks. Nowadays, CNNs are a central element in the spectacular success
-of deep learning methods. The success in for example image
-classifications have made them a central tool for most machine
-learning practitioners.
+As an example, consider
+an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a
+single fully-connected neuron in a first hidden layer of a regular
+Neural Network would have \( 32\times 32\times 3 = 3072 \) weights. This amount still
+seems manageable, but clearly this fully-connected structure does not
+scale to larger images. For example, an image of more respectable
+size, say \( 200\times 200\times 3 \), would lead to neurons that have 
+\( 200\times 200\times 3 = 120,000 \) weights.
 
 
    
-CNNs are very similar to ordinary Neural Networks.
-They are made up of neurons that have learnable weights and
-biases. Each neuron receives some inputs, performs a dot product and
-optionally follows it with a non-linearity. The whole network still
-expresses a single differentiable score function: from the raw image
-pixels on one end to class scores at the other. And they still have a
-loss function (for example Softmax) on the last (fully-connected) layer
-and all the tips/tricks we developed for learning regular Neural
-Networks still apply (back propagation, gradient descent etc etc).
+We could have
+several such neurons, and the parameters would add up quickly! Clearly,
+this full connectivity is wasteful and the huge number of parameters
+would quickly lead to possible overfitting.
 
 
    
-What is the difference? CNN architectures make the explicit assumption that
-the inputs are images, which allows us to encode certain properties
-into the architecture. These then make the forward function more
-efficient to implement and vastly reduce the amount of parameters in
-the network.
-
-
    
-Here we provide only a superficial overview, for the more interested, we recommend highly the course
-IN5400 – Machine Learning for Image Analysis
-and the slides of CS231.
-
-
    
-Another good read is the article here https://arxiv.org/pdf/1603.07285.pdf.
+
      
+
    
+
    Figure 1:  A regular 3-layer Neural Network. 
    
+
    
+
    
 
 
    
 
    
@@ -413,7 +397,7 @@ Another good read is the article here 63
   
  • 64
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs055.html b/doc/pub/week41/html/._week41-bs055.html
index eb7e8b222..78efc2836 100644
--- a/doc/pub/week41/html/._week41-bs055.html
+++ b/doc/pub/week41/html/._week41-bs055.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,29 +346,41 @@ MathJax.Hub.Config({
 
 
 
-
    Regular NNs don’t scale well to full images 
    
+
    3D volumes of neurons 
    
 
 
    
-As an example, consider
-an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a
-single fully-connected neuron in a first hidden layer of a regular
-Neural Network would have \( 32\times 32\times 3 = 3072 \) weights. This amount still
-seems manageable, but clearly this fully-connected structure does not
-scale to larger images. For example, an image of more respectable
-size, say \( 200\times 200\times 3 \), would lead to neurons that have 
-\( 200\times 200\times 3 = 120,000 \) weights.
+Convolutional Neural Networks take advantage of the fact that the
+input consists of images and they constrain the architecture in a more
+sensible way.
 
 
    
-We could have
-several such neurons, and the parameters would add up quickly! Clearly,
-this full connectivity is wasteful and the huge number of parameters
-would quickly lead to possible overfitting.
+In particular, unlike a regular Neural Network, the
+layers of a CNN have neurons arranged in 3 dimensions: width,
+height, depth. (Note that the word depth here refers to the third
+dimension of an activation volume, not to the depth of a full Neural
+Network, which can refer to the total number of layers in a network.)
+
+
    
+To understand it better, the above example of an image 
+with an input volume of
+activations has dimensions \( 32\times 32\times 3 \) (width, height,
+depth respectively).
+
+
    
+The neurons in a layer will
+only be connected to a small region of the layer before it, instead of
+all of the neurons in a fully-connected manner. Moreover, the final
+output layer could  for this specific image have dimensions \( 1\times 1 \times 10 \), 
+because by the
+end of the CNN architecture we will reduce the full image into a
+single vector of class scores, arranged along the depth
+dimension.
 
 
    
 
      
 
    
-
    Figure 1:  A regular 3-layer Neural Network. 
    
-
    
+
    Figure 2:  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). 
    
+
    
 
    
 
 
    
@@ -402,7 +409,7 @@ would quickly lead to possible overfitting.
   
  • 64
    • 
   
  • 65
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs056.html b/doc/pub/week41/html/._week41-bs056.html
index 30eca8248..a05471e85 100644
--- a/doc/pub/week41/html/._week41-bs056.html
+++ b/doc/pub/week41/html/._week41-bs056.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,46 +344,29 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    3D volumes of neurons 
    
+
    Layers used to build CNNs 
    
 
 
    
-Convolutional Neural Networks take advantage of the fact that the
-input consists of images and they constrain the architecture in a more
-sensible way.
+A simple CNN is a sequence of layers, and every layer of a CNN
+transforms one volume of activations to another through a
+differentiable function. We use three main types of layers to build
+CNN architectures: Convolutional Layer, Pooling Layer, and
+Fully-Connected Layer (exactly as seen in regular Neural Networks). We
+will stack these layers to form a full CNN architecture.
 
 
    
-In particular, unlike a regular Neural Network, the
-layers of a CNN have neurons arranged in 3 dimensions: width,
-height, depth. (Note that the word depth here refers to the third
-dimension of an activation volume, not to the depth of a full Neural
-Network, which can refer to the total number of layers in a network.)
+A simple CNN for image classification could have the architecture:
 
-
    
-To understand it better, the above example of an image 
-with an input volume of
-activations has dimensions \( 32\times 32\times 3 \) (width, height,
-depth respectively).
+
      
+
    •  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.
      • 
+
    •  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.
      • 
+
    •  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 (\( [32\times 32\times 12] \)).
      • 
+
    •  POOL (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).
      • 
+
    •  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.
      • 
+
    
 
-
    
-The neurons in a layer will
-only be connected to a small region of the layer before it, instead of
-all of the neurons in a fully-connected manner. Moreover, the final
-output layer could  for this specific image have dimensions \( 1\times 1 \times 10 \), 
-because by the
-end of the CNN architecture we will reduce the full image into a
-single vector of class scores, arranged along the depth
-dimension.
-
-
    
-
      
-
    
-
    Figure 2:  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). 
    
-
    
-
    
-
-
    
 
    
 
 
    
 
diff --git a/doc/pub/week41/html/._week41-bs057.html b/doc/pub/week41/html/._week41-bs057.html
index f9c1175ec..8c65b57c1 100644
--- a/doc/pub/week41/html/._week41-bs057.html
+++ b/doc/pub/week41/html/._week41-bs057.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,29 +344,25 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    Layers used to build CNNs 
    
+
    Transforming images 
    
 
 
    
-A simple CNN is a sequence of layers, and every layer of a CNN
-transforms one volume of activations to another through a
-differentiable function. We use three main types of layers to build
-CNN architectures: Convolutional Layer, Pooling Layer, and
-Fully-Connected Layer (exactly as seen in regular Neural Networks). We
-will stack these layers to form a full CNN architecture.
+CNNs transform the original image layer by layer from the original
+pixel values to the final class scores.
 
 
    
-A simple CNN for image classification could have the architecture:
-
-
      
-
    •  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.
      • 
-
    •  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.
      • 
-
    •  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 (\( [32\times 32\times 12] \)).
      • 
-
    •  POOL (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \( [16\times 16\times 12] \).
      • 
-
    •  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.
      • 
-
    
+Observe that some layers contain
+parameters and other don’t. In particular, the CNN layers perform
+transformations that are a function of not only the activations in the
+input volume, but also of the parameters (the weights and biases of
+the neurons). On the other hand, the RELU/POOL layers will implement a
+fixed function. The parameters in the CONV/FC layers will be trained
+with gradient descent so that the class scores that the CNN computes
+are consistent with the labels in the training set for each image.
 
+
    
 
    
 
 
      
@@ -397,7 +388,7 @@ A simple CNN for image classification could have the architecture:
   
    • 66
      • 
   
    • 67
      • 
   
    • ...
      • 
-  
    • 72
      • 
+  
    • 71
      • 
   
    • »
      • 
 
    
 
diff --git a/doc/pub/week41/html/._week41-bs058.html b/doc/pub/week41/html/._week41-bs058.html
index ca1dba208..16cb65065 100644
--- a/doc/pub/week41/html/._week41-bs058.html
+++ b/doc/pub/week41/html/._week41-bs058.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,21 +346,23 @@ MathJax.Hub.Config({
 
 
 
-
    Transforming images 
    
+
    CNNs in brief 
    
 
 
    
-CNNs transform the original image layer by layer from the original
-pixel values to the final class scores.
+In summary:
 
-
    
-Observe that some layers contain
-parameters and other don’t. In particular, the CNN layers perform
-transformations that are a function of not only the activations in the
-input volume, but also of the parameters (the weights and biases of
-the neurons). On the other hand, the RELU/POOL layers will implement a
-fixed function. The parameters in the CONV/FC layers will be trained
-with gradient descent so that the class scores that the CNN computes
-are consistent with the labels in the training set for each image.
+
      
+
    •  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)
      • 
+
    •  There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • 
+
    •  Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • 
+
    •  Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • 
+
    •  Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • 
+
    
+
+For more material on convolutional networks, we strongly recommend
+the course
+IN5400 – Machine Learning for Image Analysis
+and the slides of CS231 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.
 
 
    
 
    
@@ -393,7 +390,7 @@ are consistent with the labels in the training set for each image.
   
  • 67
    • 
   
  • 68
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs059.html b/doc/pub/week41/html/._week41-bs059.html
index 5881c8fa4..aec6e4aaf 100644
--- a/doc/pub/week41/html/._week41-bs059.html
+++ b/doc/pub/week41/html/._week41-bs059.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,23 +346,18 @@ MathJax.Hub.Config({
 
 
 
-
    CNNs in brief 
    
+
    CNNs in more detail, building convolutional neural networks in Tensorflow and Keras 
    
 
 
    
-In summary:
+As discussed above, CNNs are neural networks built from the assumption that the inputs
+to the network are 2D images. This is important because the number of features or pixels in images
+grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
 
-
      
-
    •  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)
      • 
-
    •  There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • 
-
    •  Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • 
-
    •  Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • 
-
    •  Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • 
-
    
-
-For more material on convolutional networks, we strongly recommend
-the course
-IN5400 – Machine Learning for Image Analysis
-and the slides of CS231 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.
+
    
+As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
+are the convolutional and pooling layers stacked in pairs between the input and the hidden layer.
+In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
+matrices, typically 1 for each color dimension (Red, Green, Blue).
 
 
    
 
    
@@ -395,7 +385,7 @@ and the slides of 68
   
  • 69
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs060.html b/doc/pub/week41/html/._week41-bs060.html
index cba28cf54..9c59513ba 100644
--- a/doc/pub/week41/html/._week41-bs060.html
+++ b/doc/pub/week41/html/._week41-bs060.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,18 +346,14 @@ MathJax.Hub.Config({
 
 
 
-
    CNNs in more detail, building convolutional neural networks in Tensorflow and Keras 
    
+
    Setting it up 
    
 
 
    
-As discussed above, CNNs are neural networks built from the assumption that the inputs
-to the network are 2D images. This is important because the number of features or pixels in images
-grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
-
-
    
-As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
-are the convolutional and pooling layers stacked in pairs between the input and the hidden layer.
-In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
-matrices, typically 1 for each color dimension (Red, Green, Blue).
+It means that to represent the entire
+dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions:  
+$$  
+(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
+$$
 
 
    
 
    
@@ -390,7 +381,7 @@ matrices, typically 1 for each color dimension (Red, Green, Blue).
   
  • 69
    • 
   
  • 70
    • 
   
  • ...
    • 
-  
  • 72
    • 
+  
  • 71
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs061.html b/doc/pub/week41/html/._week41-bs061.html
index 189f3d738..2b358770b 100644
--- a/doc/pub/week41/html/._week41-bs061.html
+++ b/doc/pub/week41/html/._week41-bs061.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,14 +346,20 @@ MathJax.Hub.Config({
 
 
 
-
    Setting it up 
    
+
    The MNIST dataset again 
    
 
 
    
-It means that to represent the entire
-dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions:  
-$$  
-(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
-$$
+The MNIST dataset consists of grayscale images with a pixel size of
+\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
+neuron in the first hidden layer.
+
+
    
+If we were to analyze images of size \( 128\times 128 \) we would require
+\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
+dealing with color images, as most images are, we have an image matrix
+of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
+meaning 3 times the number of weights \( = 49152 \) are required for every
+single neuron in the first hidden layer.
 
 
    
 
    
@@ -385,8 +386,6 @@ $$
   
  • 69
    • 
   
  • 70
    • 
   
  • 71
    • 
-  
  • ...
    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs062.html b/doc/pub/week41/html/._week41-bs062.html
index 85abe81eb..22259def4 100644
--- a/doc/pub/week41/html/._week41-bs062.html
+++ b/doc/pub/week41/html/._week41-bs062.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,20 +346,20 @@ MathJax.Hub.Config({
 
 
 
-
    The MNIST dataset again 
    
+
    Strong correlations 
    
 
 
    
-The MNIST dataset consists of grayscale images with a pixel size of
-\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
-neuron in the first hidden layer.
+Images typically have strong local correlations, meaning that a small
+part of the image varies little from its neighboring regions. If for
+example we have an image of a blue car, we can roughly assume that a
+small blue part of the image is surrounded by other blue regions.
 
 
    
-If we were to analyze images of size \( 128\times 128 \) we would require
-\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
-dealing with color images, as most images are, we have an image matrix
-of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
-meaning 3 times the number of weights \( = 49152 \) are required for every
-single neuron in the first hidden layer.
+Therefore, instead of connecting every single pixel to a neuron in the
+first hidden layer, as we have previously done with deep neural
+networks, we can instead connect each neuron to a small part of the
+image (in all 3 RGB depth dimensions).  The size of each small area is
+fixed, and known as a receptive.
 
 
    
 
    
@@ -390,7 +385,6 @@ single neuron in the first hidden layer.
   
  • 69
    • 
   
  • 70
    • 
   
  • 71
    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs063.html b/doc/pub/week41/html/._week41-bs063.html
index 5060cfa27..946d7cf74 100644
--- a/doc/pub/week41/html/._week41-bs063.html
+++ b/doc/pub/week41/html/._week41-bs063.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,22 +344,26 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    Strong correlations 
    
+
    Layers of a CNN 
    
+The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.  
+The input image is typically a square matrix of depth 3.
 
 
    
-Images typically have strong local correlations, meaning that a small
-part of the image varies little from its neighboring regions. If for
-example we have an image of a blue car, we can roughly assume that a
-small blue part of the image is surrounded by other blue regions.
+A convolution is performed on the image which outputs
+a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as filters.
 
 
    
-Therefore, instead of connecting every single pixel to a neuron in the
-first hidden layer, as we have previously done with deep neural
-networks, we can instead connect each neuron to a small part of the
-image (in all 3 RGB depth dimensions).  The size of each small area is
-fixed, and known as a receptive.
+Each filter slides along the input image, taking the dot product
+between each small part of the image and the filter, in all depth
+dimensions. This is then passed through a non-linear function,
+typically the Rectified Linear (ReLu) function, which serves as the
+activation of the neurons in the first convolutional layer. This is
+further passed through a pooling layer, which reduces the size of the
+convolutional layer, e.g. by taking the maximum or average across some
+small regions, and this serves as input to the next convolutional
+layer.
 
 
    
 
    
@@ -389,7 +388,6 @@ fixed, and known as a 69
   
  • 70
    • 
   
  • 71
    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs064.html b/doc/pub/week41/html/._week41-bs064.html
index 0dddc3d13..236ebd639 100644
--- a/doc/pub/week41/html/._week41-bs064.html
+++ b/doc/pub/week41/html/._week41-bs064.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,26 +344,19 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    Layers of a CNN 
    
-The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.  
-The input image is typically a square matrix of depth 3.
+
    Systematic reduction 
    
 
 
    
-A convolution is performed on the image which outputs
-a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as filters.
-
-
    
-Each filter slides along the input image, taking the dot product
-between each small part of the image and the filter, in all depth
-dimensions. This is then passed through a non-linear function,
-typically the Rectified Linear (ReLu) function, which serves as the
-activation of the neurons in the first convolutional layer. This is
-further passed through a pooling layer, which reduces the size of the
-convolutional layer, e.g. by taking the maximum or average across some
-small regions, and this serves as input to the next convolutional
-layer.
+By systematically reducing the size of the input volume, through
+convolution and pooling, the network should create representations of
+small parts of the input, and then from them assemble representations
+of larger areas.  The final pooling layer is flattened to serve as
+input to a hidden layer, such that each neuron in the final pooling
+layer is connected to every single neuron in the hidden layer. This
+then serves as input to the output layer, e.g. a softmax output for
+classification.
 
 
    
 
    
@@ -392,7 +380,6 @@ layer.
   
  • 69
    • 
   
  • 70
    • 
   
  • 71
    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs065.html b/doc/pub/week41/html/._week41-bs065.html
index f80acae0e..6f6c6d5ee 100644
--- a/doc/pub/week41/html/._week41-bs065.html
+++ b/doc/pub/week41/html/._week41-bs065.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,18 +346,51 @@ MathJax.Hub.Config({
 
 
 
-
    Systematic reduction 
    
-
+
    Prerequisites: Collect and pre-process data 
    
 
    
-By systematically reducing the size of the input volume, through
-convolution and pooling, the network should create representations of
-small parts of the input, and then from them assemble representations
-of larger areas.  The final pooling layer is flattened to serve as
-input to a hidden layer, such that each neuron in the final pooling
-layer is connected to every single neuron in the hidden layer. This
-then serves as input to the output layer, e.g. a softmax output for
-classification.
 
+
+
    # import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+%matplotlib inline
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+# RGB images have a depth of 3
+# our images are grayscale so they should have a depth of 1
+inputs = inputs[:,:,:,np.newaxis]
+
+print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# choose some random images to display
+n_inputs = len(inputs)
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
    
 
    
 
    
 
@@ -384,7 +412,6 @@ classification.
   
  • 69
    • 
   
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    • 
   
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    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs066.html b/doc/pub/week41/html/._week41-bs066.html
index 65ec5b87c..27698f04b 100644
--- a/doc/pub/week41/html/._week41-bs066.html
+++ b/doc/pub/week41/html/._week41-bs066.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,50 +346,32 @@ MathJax.Hub.Config({
 
 
 
-
    Prerequisites: Collect and pre-process data 
    
+
    Importing Keras and Tensorflow 
    
 
    
 
 
-
    # import necessary packages
-import numpy as np
-import matplotlib.pyplot as plt
-from sklearn import datasets
+
    from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+#from tensorflow.keras import Conv2D
+#from tensorflow.keras import MaxPooling2D
+#from tensorflow.keras import Flatten
 
+from sklearn.model_selection import train_test_split
 
-# ensure the same random numbers appear every time
-np.random.seed(0)
+# representation of labels
+labels = to_categorical(labels)
 
-# display images in notebook
-%matplotlib inline
-plt.rcParams['figure.figsize'] = (12,12)
-
-
-# download MNIST dataset
-digits = datasets.load_digits()
-
-# define inputs and labels
-inputs = digits.images
-labels = digits.target
-
-# RGB images have a depth of 3
-# our images are grayscale so they should have a depth of 1
-inputs = inputs[:,:,:,np.newaxis]
-
-print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
-print("labels = (n_inputs) = " + str(labels.shape))
-
-
-# choose some random images to display
-n_inputs = len(inputs)
-indices = np.arange(n_inputs)
-random_indices = np.random.choice(indices, size=5)
-
-for i, image in enumerate(digits.images[random_indices]):
-    plt.subplot(1, 5, i+1)
-    plt.axis('off')
-    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
-    plt.title("Label: %d" % digits.target[random_indices[i]])
-plt.show()
+# split into train and test data
+# one-liner from scikit-learn library
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
 
    
 
    
 
    
@@ -416,7 +393,6 @@ plt.show()
   
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    • 
   
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    • 
-  
  • 72
    • 
   
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    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs067.html b/doc/pub/week41/html/._week41-bs067.html
index 2d55582f3..400cad5da 100644
--- a/doc/pub/week41/html/._week41-bs067.html
+++ b/doc/pub/week41/html/._week41-bs067.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,34 +344,39 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
+
+
    Running with Keras 
    
 
-
    Importing Keras and Tensorflow 
    
 
    
 
 
-
    from tensorflow.keras import datasets, layers, models
-from tensorflow.keras.layers import Input
-from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
-from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
-from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
-from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
-from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
-#from tensorflow.keras import Conv2D
-#from tensorflow.keras import MaxPooling2D
-#from tensorflow.keras import Flatten
+
    def create_convolutional_neural_network_keras(input_shape, receptive_field,
+                                              n_filters, n_neurons_connected, n_categories,
+                                              eta, lmbd):
+    model = Sequential()
+    model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
+              activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(layers.MaxPooling2D(pool_size=(2, 2)))
+    model.add(layers.Flatten())
+    model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))
+    
+    sgd = optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
+    
+    return model
 
-from sklearn.model_selection import train_test_split
+epochs = 100
+batch_size = 100
+input_shape = X_train.shape[1:4]
+receptive_field = 3
+n_filters = 10
+n_neurons_connected = 50
+n_categories = 10
 
-# representation of labels
-labels = to_categorical(labels)
-
-# split into train and test data
-# one-liner from scikit-learn library
-train_size = 0.8
-test_size = 1 - train_size
-X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
-                                                    test_size=test_size)
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
 
    
 
    
 
    
@@ -397,7 +397,6 @@ X_train, X_test, Y_train, Y_test = train_tes
   
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    • 
   
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    • 
   
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    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs068.html b/doc/pub/week41/html/._week41-bs068.html
index 2e4b9ede2..c3c593f82 100644
--- a/doc/pub/week41/html/._week41-bs068.html
+++ b/doc/pub/week41/html/._week41-bs068.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -349,39 +344,29 @@ MathJax.Hub.Config({
 
     
     
     
     
 
 
-
+
 
-
    Running with Keras 
    
+
    Final part 
    
 
 
    
 
 
-
    def create_convolutional_neural_network_keras(input_shape, receptive_field,
+
    CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+        
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
                                               n_filters, n_neurons_connected, n_categories,
-                                              eta, lmbd):
-    model = Sequential()
-    model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
-              activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
-    model.add(layers.MaxPooling2D(pool_size=(2, 2)))
-    model.add(layers.Flatten())
-    model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
-    model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))
-    
-    sgd = optimizers.SGD(lr=eta)
-    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
-    
-    return model
-
-epochs = 100
-batch_size = 100
-input_shape = X_train.shape[1:4]
-receptive_field = 3
-n_filters = 10
-n_neurons_connected = 50
-n_categories = 10
-
-eta_vals = np.logspace(-5, 1, 7)
-lmbd_vals = np.logspace(-5, 1, 7)
+                                              eta, lmbd)
+        CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+        scores = CNN.evaluate(X_test, Y_test)
+        
+        CNN_keras[i][j] = CNN
+        
+        print("Learning rate = ", eta)
+        print("Lambda = ", lmbd)
+        print("Test accuracy: %.3f" % scores[1])
+        print()
 
    
 
    
 
    
@@ -401,7 +386,6 @@ lmbd_vals = np.
   
  • 69
    • 
   
  • 70
    • 
   
  • 71
    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs069.html b/doc/pub/week41/html/._week41-bs069.html
index e4b6ae363..cdbfba8df 100644
--- a/doc/pub/week41/html/._week41-bs069.html
+++ b/doc/pub/week41/html/._week41-bs069.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,27 +346,41 @@ MathJax.Hub.Config({
 
 
 
-
    Final part 
    
+
    Final visualization 
    
 
 
    
 
 
-
    CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+
    # visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        CNN = CNN_keras[i][j]
+
+        train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]
+        test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]
+
         
-for i, eta in enumerate(eta_vals):
-    for j, lmbd in enumerate(lmbd_vals):
-        CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
-                                              n_filters, n_neurons_connected, n_categories,
-                                              eta, lmbd)
-        CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
-        scores = CNN.evaluate(X_test, Y_test)
-        
-        CNN_keras[i][j] = CNN
-        
-        print("Learning rate = ", eta)
-        print("Lambda = ", lmbd)
-        print("Test accuracy: %.3f" % scores[1])
-        print()
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
 
    
 
    
 
    
@@ -390,7 +399,6 @@ MathJax.Hub.Config({
   
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    • 
   
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    • 
   
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    • 
-  
  • 72
    • 
   
  • »
    • 
 
 
diff --git a/doc/pub/week41/html/._week41-bs070.html b/doc/pub/week41/html/._week41-bs070.html
index bbf84ffc8..72cac99ab 100644
--- a/doc/pub/week41/html/._week41-bs070.html
+++ b/doc/pub/week41/html/._week41-bs070.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -351,43 +346,14 @@ MathJax.Hub.Config({
 
 
 
-
    Final visualization 
    
+
 
-
    
+
      
+
    1.  Self-Driving cars using a convolutional neural network
      2. 
+
    2.  Abstract art using convolutional neural networks
      3. 
+
    
 
-
-
    # visual representation of grid search
-# uses seaborn heatmap, could probably do this in matplotlib
-import seaborn as sns
 
-sns.set()
-
-train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
-test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
-
-for i in range(len(eta_vals)):
-    for j in range(len(lmbd_vals)):
-        CNN = CNN_keras[i][j]
-
-        train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]
-        test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]
-
-        
-fig, ax = plt.subplots(figsize = (10, 10))
-sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
-ax.set_title("Training Accuracy")
-ax.set_ylabel("$\eta$")
-ax.set_xlabel("$\lambda$")
-plt.show()
-
-fig, ax = plt.subplots(figsize = (10, 10))
-sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
-ax.set_title("Test Accuracy")
-ax.set_ylabel("$\eta$")
-ax.set_xlabel("$\lambda$")
-plt.show()
-
    
-
    
 
    
 
 
      
@@ -403,8 +369,6 @@ plt.show()
   
    • 69
      • 
   
    • 70
      • 
   
    • 71
      • 
-  
    • 72
      • 
-  
    • »
      • 
 
    
 
 
diff --git a/doc/pub/week41/html/week41-bs.html b/doc/pub/week41/html/week41-bs.html
index d8bab1fc1..17ac62bf8 100644
--- a/doc/pub/week41/html/week41-bs.html
+++ b/doc/pub/week41/html/week41-bs.html
@@ -120,10 +120,6 @@ Automatically generated HTML file from DocOnce source
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -273,7 +269,7 @@ MathJax.Hub.Config({
       
  • Example: binary classification problem
    • 
       
  • The Softmax function
    • 
       
  • Developing a code for doing neural networks with back propagation
    • 
-      
  • Collect and pre-process data
    • 
+      
  • Collect and pre-process data
    • 
       
  • Train and test datasets
    • 
       
  • Define model and architecture
    • 
       
  • Layers
    • 
@@ -295,47 +291,46 @@ MathJax.Hub.Config({
       
  • The AND and XOR Gates
    • 
       
  • Representing the Data Sets
    • 
       
  • Setting up the Neural Network
    • 
-      
  • Then the first Feed Forward pass
    • 
-      
  • The Code using Scikit-Learn
    • 
-      
  • Building neural networks in Tensorflow and Keras
    • 
-      
  • Tensorflow
    • 
-      
  • Using Keras
    • 
-      
  • Collect and pre-process data
    • 
-      
  • The Breast Cancer Data, now with Keras
    • 
-      
  • Fine-tuning neural network hyperparameters
    • 
-      
  • Hidden layers
    • 
-      
  • Which activation function should I use?
    • 
-      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
-      
  • The derivative of the Logistic funtion
    • 
-      
  • The RELU function family
    • 
-      
  • Which activation function should we use?
    • 
-      
  • More on activation functions, output layers
    • 
-      
  • Batch Normalization
    • 
-      
  • Dropout
    • 
-      
  • Gradient Clipping
    • 
-      
  • A very nice website on Neural Networks
    • 
-      
  • A top-down perspective on Neural networks
    • 
-      
  • Limitations of supervised learning with deep networks
    • 
-      
  • Overarching Views, a personal  note
    • 
-      
  • From a Spherical Cow to a real one
    • 
-      
  • Convolutional Neural Networks (recognizing images)
    • 
-      
  • Regular NNs don’t scale well to full images
    • 
-      
  • 3D volumes of neurons
    • 
-      
  • Layers used to build CNNs
    • 
-      
  • Transforming images
    • 
-      
  • CNNs in brief
    • 
-      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
-      
  • Setting it up
    • 
-      
  • The MNIST dataset again
    • 
-      
  • Strong correlations
    • 
-      
  • Layers of a CNN
    • 
-      
  • Systematic reduction
    • 
-      
  • Prerequisites: Collect and pre-process data
    • 
-      
  • Importing Keras and Tensorflow
    • 
-      
  • Running with Keras
    • 
-      
  • Final part
    • 
-      
  • Final visualization
    • 
-      
  • Fun links
    • 
+      
  • The Code using Scikit-Learn
    • 
+      
  • Building neural networks in Tensorflow and Keras
    • 
+      
  • Tensorflow
    • 
+      
  • Using Keras
    • 
+      
  • Collect and pre-process data
    • 
+      
  • The Breast Cancer Data, now with Keras
    • 
+      
  • Fine-tuning neural network hyperparameters
    • 
+      
  • Hidden layers
    • 
+      
  • Which activation function should I use?
    • 
+      
  • Is the Logistic activation function (Sigmoid)  our choice?
    • 
+      
  • The derivative of the Logistic funtion
    • 
+      
  • The RELU function family
    • 
+      
  • Which activation function should we use?
    • 
+      
  • More on activation functions, output layers
    • 
+      
  • Batch Normalization
    • 
+      
  • Dropout
    • 
+      
  • Gradient Clipping
    • 
+      
  • A very nice website on Neural Networks
    • 
+      
  • A top-down perspective on Neural networks
    • 
+      
  • Limitations of supervised learning with deep networks
    • 
+      
  • Overarching Views, a personal  note
    • 
+      
  • From a Spherical Cow to a real one
    • 
+      
  • Convolutional Neural Networks (recognizing images)
    • 
+      
  • Regular NNs don’t scale well to full images
    • 
+      
  • 3D volumes of neurons
    • 
+      
  • Layers used to build CNNs
    • 
+      
  • Transforming images
    • 
+      
  • CNNs in brief
    • 
+      
  • CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
    • 
+      
  • Setting it up
    • 
+      
  • The MNIST dataset again
    • 
+      
  • Strong correlations
    • 
+      
  • Layers of a CNN
    • 
+      
  • Systematic reduction
    • 
+      
  • Prerequisites: Collect and pre-process data
    • 
+      
  • Importing Keras and Tensorflow
    • 
+      
  • Running with Keras
    • 
+      
  • Final part
    • 
+      
  • Final visualization
    • 
+      
  • Fun links
    • 
 
         
       
@@ -394,7 +389,7 @@ MathJax.Hub.Config({
   
  • 9
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    • 
   
  • ...
    • 
-  
  • 72
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+  
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diff --git a/doc/pub/week41/html/week41-reveal.html b/doc/pub/week41/html/week41-reveal.html
index 5209d2955..8ec3b5700 100644
--- a/doc/pub/week41/html/week41-reveal.html
+++ b/doc/pub/week41/html/week41-reveal.html
@@ -193,9 +193,9 @@ The four equations  derived last week provide us with a way of computing the gra
 
    
 
 
    
-First, we set up the input data \( \hat{x} \) and the activations
-\( \hat{z}_1 \) of the input layer and compute the activation function and
-the pertinent outputs \( \hat{a}^1 \).
+First, we set up the input data \( \boldsymbol{x} \) and the activations
+\( \boldsymbol{z}_1 \) of the input layer and compute the activation function and
+the pertinent outputs \( \boldsymbol{a}^1 \).
 
    
 
 
    
@@ -203,8 +203,8 @@ the pertinent outputs \( \hat{a}^1 \).
 
 
    
 Secondly, we perform then the feed forward till we reach the output
-layer and compute all \( \hat{z}_l \) of the input layer and compute the
-activation function and the pertinent outputs \( \hat{a}^l \) for
+layer and compute all \( \boldsymbol{z}_l \) of the input layer and compute the
+activation function and the pertinent outputs \( \boldsymbol{a}^l \) for
 \( l=2,3,\dots,L \).
 
    
 
@@ -212,7 +212,7 @@ activation function and the pertinent outputs \( \hat{a}^l \) for
 
    
 
 
    
-Thereafter we compute the ouput error \( \hat{\delta}^L \) by computing all
+Thereafter we compute the ouput error \( \boldsymbol{\delta}^L \) by computing all
 
     
    
 $$
 \delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}.
@@ -281,19 +281,19 @@ is in class 0 or 1 is just. We let \( \theta \) represent the unknown weights an
 represents our activation values \( z \). We have
 
     
    
 $$
-P(y = 0 \mid \hat{x}, \hat{\theta}) = \frac{1}{1 + \exp{(- \hat{x}})} ,
+P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) = \frac{1}{1 + \exp{(- \boldsymbol{x}})} ,
 $$
 
     
    
 
 and
 
     
    
 $$
-P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) ,
+P(y = 1 \mid \boldsymbol{x}, \boldsymbol{\theta}) = 1 - P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) ,
 $$
 
     
    
 
 
    
-where \( y \in \{0, 1\} \)  and \( \hat{\theta} \) represents the weights and biases
+where \( y \in \{0, 1\} \)  and \( \boldsymbol{\theta} \) represents the weights and biases
 of our network.
 
 
@@ -305,14 +305,14 @@ of our network.
 Our cost function is given as (see the Logistic regression lectures)
 
     
    
 $$
-\mathcal{C}(\hat{\theta}) = - \ln P(\mathcal{D} \mid \hat{\theta}) = - \sum_{i=1}^n
-y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\hat{\theta}) .
+\mathcal{C}(\boldsymbol{\theta}) = - \ln P(\mathcal{D} \mid \boldsymbol{\theta}) = - \sum_{i=1}^n
+y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\boldsymbol{\theta}) .
 $$
 
     
    
 
 
    
 This last equality means that we can interpret our cost function as a sum over the loss function
-for each point in the dataset \( \mathcal{L}_i(\hat{\theta}) \).  
+for each point in the dataset \( \mathcal{L}_i(\boldsymbol{\theta}) \).  
 The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather
 than maximizing a negative number.
 
@@ -320,23 +320,23 @@ than maximizing a negative number.
 In multiclass classification it is common to treat each integer label as a so called one-hot vector:
 
 
    
-\( y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and
+\( y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and
 
 
    
-\( y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)
+\( y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)
 
 
    
 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 \( 9 \))..
 
 
    
-If \( \hat{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th
-output vector \( \hat{y}_i \).  
-The probability of \( \hat{x}_i \) being in class \( c \) will be given by the softmax function:
+If \( \boldsymbol{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th
+output vector \( \boldsymbol{y}_i \).  
+The probability of \( \boldsymbol{x}_i \) being in class \( c \) will be given by the softmax function:
 
 
     
    
 $$
-P(y_{ic} = 1 \mid \hat{x}_i, \hat{\theta}) = \frac{\exp{((\hat{a}_i^{hidden})^T \hat{w}_c)}}
-{\sum_{c'=0}^{C-1} \exp{((\hat{a}_i^{hidden})^T \hat{w}_{c'})}} ,
+P(y_{ic} = 1 \mid \boldsymbol{x}_i, \boldsymbol{\theta}) = \frac{\exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_c)}}
+{\sum_{c'=0}^{C-1} \exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_{c'})}} ,
 $$
 
     
    
 
@@ -347,7 +347,7 @@ is now given as:
 
 
     
    
 $$
-P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
+P(\mathcal{D} \mid \boldsymbol{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
 $$
 
     
    
 
@@ -355,7 +355,7 @@ Again we take the negative log-likelihood to define our cost function:
 
 
     
    
 $$
-\mathcal{C}(\hat{\theta}) = - \log{P(\mathcal{D} \mid \hat{\theta})}.
+\mathcal{C}(\boldsymbol{\theta}) = - \log{P(\mathcal{D} \mid \boldsymbol{\theta})}.
 $$
 
     
    
 
@@ -373,25 +373,25 @@ The back propagation equations need now only a small change, namely the definiti
 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
 
     
    
 $$
-\mathcal{C}(\hat{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\hat{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\hat{\beta})}\right),
+\mathcal{C}(\boldsymbol{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\boldsymbol{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\boldsymbol{\beta})}\right),
 $$
 
     
    
 
 where we had defined the logistic (sigmoid) function
 
     
    
 $$
-p(y_i =1\vert x_i,\hat{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
+p(y_i =1\vert x_i,\boldsymbol{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
 $$
 
     
    
 
 and
 
     
    
 $$
-p(y_i =0\vert x_i,\hat{\beta})=1-p(y_i =1\vert x_i,\hat{\beta}).
+p(y_i =0\vert x_i,\boldsymbol{\beta})=1-p(y_i =1\vert x_i,\boldsymbol{\beta}).
 $$
 
     
    
 
-The parameters \( \hat{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.
+The parameters \( \boldsymbol{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.
 
 
    
 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 \( b_i^l \). 
@@ -413,14 +413,14 @@ where the superscript \( l-1 \) indicates that these are the outputs from layer
 Our cost function at the final layer \( l=L \) is now
 
     
    
 $$
-\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
+\mathcal{C}(\boldsymbol{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
 $$
 
     
    
 
 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
 
     
    
 $$
-\frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
+\frac{\partial \mathcal{C}(\boldsymbol{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
 $$
 
     
    
 
@@ -715,12 +715,12 @@ For a soft binary classifier, we could use a single neuron and interpret the out
 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:
 
 
     
    
-$$ P(\text{class \( j \)} \mid \text{input \( \hat{a} \)}) = \frac{\exp{(\hat{a}^T \hat{w}_j)}}
-{\sum_{c=0}^{9} \exp{(\hat{a}^T \hat{w}_c)}} ,$$
+$$ P(\text{class \( j \)} \mid \text{input \( \boldsymbol{a} \)}) = \frac{\exp{(\boldsymbol{a}^T \boldsymbol{w}_j)}}
+{\sum_{c=0}^{9} \exp{(\boldsymbol{a}^T \boldsymbol{w}_c)}} ,$$
 
     
    
 
 
    
-i.e. each neuron \( j \) outputs the probability of being in class \( j \) given an input from the hidden layer \( \hat{a} \), with \( \hat{w}_j \) the weights of neuron \( j \) to the inputs.  
+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.  
 The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  
 The exponent is just the weighted sum of inputs as before:
 
@@ -750,7 +750,7 @@ $$ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.$$
 
     
    
 
 
    
-The bias weights \( \hat{b} \) 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.
+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.
 
    
 
 
@@ -827,7 +827,7 @@ for each input image and each hidden neuron.
 We also add the bias to obtain a matrix of weighted sums to the hidden layer \( Z^{h} \):
 
 
     
    
-$$ \hat{z}^{l} = \hat{X} \hat{W}^{l} + \hat{b}^{l} ,$$
+$$ \boldsymbol{z}^{l} = \boldsymbol{X} \boldsymbol{W}^{l} + \boldsymbol{b}^{l} ,$$
 
     
    
 
 
    
@@ -835,21 +835,21 @@ meaning the same bias (1D array with size equal number of hidden neurons) is add
 This is then passed through the activation:
 
 
     
    
-$$ \hat{a}^{l} = f(\hat{z}^l) .$$
+$$ \boldsymbol{a}^{l} = f(\boldsymbol{z}^l) .$$
 
     
    
 
 
    
 This is fed to the output layer:
 
 
     
    
-$$ \hat{z}^{L} = \hat{a}^{L} \hat{W}^{L} + \hat{b}^{L} .$$
+$$ \boldsymbol{z}^{L} = \boldsymbol{a}^{L} \boldsymbol{W}^{L} + \boldsymbol{b}^{L} .$$
 
     
    
 
 
    
 Finally we receive our output values for each image and each category by passing it through the softmax function:
 
 
     
    
-$$ output = softmax (\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$
+$$ output = softmax (\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$
 
     
    
 
 
    
@@ -907,11 +907,11 @@ A typical choice for multiclass classification is the cross-entropy los
 In multiclass classification it is common to treat each integer label as a so called one-hot vector:
 
 
     
    
-$$ y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$
+$$ y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$
 
     
    
 
 
     
    
-$$ y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$
+$$ y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$
 
     
    
 
 
    
@@ -919,13 +919,13 @@ i.e. a binary bit string of length \( C \), where \( C = 10 \) is the number of
 
 
    
 Let \( y_{ic} \) denote the \( c \)-th component of the \( i \)-th one-hot vector.  
-We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \hat{x}_i \) in the dataset.
+We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \boldsymbol{x}_i \) in the dataset.
 
 
    
 In the one-hot representation only one of the terms in the loss function is non-zero, namely the
 probability of the correct category \( c' \)  
 (i.e. the category \( c' \) such that \( y_{ic'} = 1 \)). This means that the cross entropy loss only punishes you for how wrong
-you got the correct label. The probability of category \( c \) is given by the softmax function. The vector \( \hat{\theta} \) represents the parameters of our network, i.e. all the weights and biases.
+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.
 
 
 
@@ -991,7 +991,7 @@ We will measure the size of the weights using the so called L2-norm, me
 
 
     
    
 $$  \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad
-\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \hat{w} \rvert \rvert_2^2 
+\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \boldsymbol{w} \rvert \rvert_2^2 
 = \frac{1}{N} \sum_{i=1}^N  \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,$$
 
     
    
 
@@ -1015,28 +1015,28 @@ calculate the gradient efficently.
 
 
    
 To more efficently train our network these equations are implemented using matrix operations.  
-The error in the output layer is calculated simply as, with \( \hat{t} \) being our targets,
+The error in the output layer is calculated simply as, with \( \boldsymbol{t} \) being our targets,
 
 
     
    
-$$ \delta_L = \hat{t} - \hat{y} = (n_{inputs}, n_{categories}) .$$
+$$ \delta_L = \boldsymbol{t} - \boldsymbol{y} = (n_{inputs}, n_{categories}) .$$
 
     
    
 
 
    
 The gradient for the output weights is calculated as
 
 
     
    
-$$ \nabla W_{L} = \hat{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
+$$ \nabla W_{L} = \boldsymbol{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
 
     
    
 
 
    
-where \( \hat{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input.  
+where \( \boldsymbol{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input.  
 Since we are going backwards we have to transpose the activation matrix.
 
 
    
 The gradient with respect to the output bias is then
 
 
     
    
-$$ \nabla \hat{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$
+$$ \nabla \boldsymbol{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$
 
     
    
 
 
    
@@ -1279,11 +1279,11 @@ We measure the performance of the network using the accuracy score.
 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 \( 1 \).
 
 
     
    
-$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\hat{y}_i = y_i)}{n} ,$$
+$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,$$
 
     
    
 
 
    
-where \( I \) is the indicator function, \( 1 \) if \( \hat{y}_i = y_i \) and \( 0 \) otherwise.
+where \( I \) is the indicator function, \( 1 \) if \( \tilde{y}_i = y_i \) and \( 0 \) otherwise.
 
 
    
 
@@ -1496,7 +1496,7 @@ inputs \( x_1 \) and \( x_2 \) and outputs \( y \):
 
    The AND and XOR Gates 
    
 
 
    
-The AND gate is defined as
+The AND gate is defined as
 
 
    
 
@@ -1511,7 +1511,7 @@ The AND gate is defined as
 
    
 
    
 
    
-And finally we have the XOR gate
+And finally we have the XOR gate
 
 
    
 
@@ -1559,31 +1559,13 @@ We define first our design matrix and the various output vectors for the differe
 
    """
 Simple code that tests XOR, OR and AND gates with linear regression
 """
+
 # import necessary packages
 import numpy as np
 import matplotlib.pyplot as plt
 from sklearn import datasets
 
-# Design matrix
-X = np.array([ [1, 0, 0], [1, 0, 1], [1, 1, 0],[1, 1, 1]],dtype=np.float64)
-
-# The XOR gate 
-yXOR = np.array( [ 0, 1 ,1, 0])
-# The OR gate 
-yOR = np.array( [ 0, 1 ,1, 1])
-# The AND gate 
-yAND = np.array( [ 0, 0 ,0, 1])
-
    
-
-
-
-
    
-
    Then the first Feed Forward pass 
    
-
-
    
-
-
-
    def sigmoid(x):
+def sigmoid(x):
     return 1/(1 + np.exp(-x))
 
 def feed_forward(X):
@@ -1604,11 +1586,18 @@ yAND = np.array( [ 0, return np.argmax(probabilities, axis=1)
 
-
-
 # ensure the same random numbers appear every time
 np.random.seed(0)
 
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
 
 # Defining the neural network
 n_inputs, n_features = X.shape
diff --git a/doc/pub/week41/html/week41-solarized.html b/doc/pub/week41/html/week41-solarized.html
index ff15758fa..2d5981bde 100644
--- a/doc/pub/week41/html/week41-solarized.html
+++ b/doc/pub/week41/html/week41-solarized.html
@@ -140,10 +140,6 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -326,9 +322,9 @@ The four equations  derived last week provide us with a way of computing the gra
 
    
 
 
    
-First, we set up the input data \( \hat{x} \) and the activations
-\( \hat{z}_1 \) of the input layer and compute the activation function and
-the pertinent outputs \( \hat{a}^1 \).
+First, we set up the input data \( \boldsymbol{x} \) and the activations
+\( \boldsymbol{z}_1 \) of the input layer and compute the activation function and
+the pertinent outputs \( \boldsymbol{a}^1 \).
 
    
 
 
@@ -337,8 +333,8 @@ the pertinent outputs \( \hat{a}^1 \).
 
 
    
 Secondly, we perform then the feed forward till we reach the output
-layer and compute all \( \hat{z}_l \) of the input layer and compute the
-activation function and the pertinent outputs \( \hat{a}^l \) for
+layer and compute all \( \boldsymbol{z}_l \) of the input layer and compute the
+activation function and the pertinent outputs \( \boldsymbol{a}^l \) for
 \( l=2,3,\dots,L \).
 
    
 
@@ -347,7 +343,7 @@ activation function and the pertinent outputs \( \hat{a}^l \) for
 
    
 
 
    
-Thereafter we compute the ouput error \( \hat{\delta}^L \) by computing all
+Thereafter we compute the ouput error \( \boldsymbol{\delta}^L \) by computing all
 $$
 \delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}.
 $$
@@ -411,16 +407,16 @@ For an input \( \boldsymbol{a} \) from the hidden layer, the probability that th
 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 \( x \)
 represents our activation values \( z \). We have
 $$
-P(y = 0 \mid \hat{x}, \hat{\theta}) = \frac{1}{1 + \exp{(- \hat{x}})} ,
+P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) = \frac{1}{1 + \exp{(- \boldsymbol{x}})} ,
 $$
 
 and
 $$
-P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) ,
+P(y = 1 \mid \boldsymbol{x}, \boldsymbol{\theta}) = 1 - P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) ,
 $$
 
 
    
-where \( y \in \{0, 1\} \)  and \( \hat{\theta} \) represents the weights and biases
+where \( y \in \{0, 1\} \)  and \( \boldsymbol{\theta} \) represents the weights and biases
 of our network.
 
 
    
@@ -431,13 +427,13 @@ of our network.
 
    
 Our cost function is given as (see the Logistic regression lectures)
 $$
-\mathcal{C}(\hat{\theta}) = - \ln P(\mathcal{D} \mid \hat{\theta}) = - \sum_{i=1}^n
-y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\hat{\theta}) .
+\mathcal{C}(\boldsymbol{\theta}) = - \ln P(\mathcal{D} \mid \boldsymbol{\theta}) = - \sum_{i=1}^n
+y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\boldsymbol{\theta}) .
 $$
 
 
    
 This last equality means that we can interpret our cost function as a sum over the loss function
-for each point in the dataset \( \mathcal{L}_i(\hat{\theta}) \).  
+for each point in the dataset \( \mathcal{L}_i(\boldsymbol{\theta}) \).  
 The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather
 than maximizing a negative number.
 
@@ -445,22 +441,22 @@ than maximizing a negative number.
 In multiclass classification it is common to treat each integer label as a so called one-hot vector:
 
 
    
-\( y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and
+\( y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and
 
 
    
-\( y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)
+\( y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)
 
 
    
 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 \( 9 \))..
 
 
    
-If \( \hat{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th
-output vector \( \hat{y}_i \).  
-The probability of \( \hat{x}_i \) being in class \( c \) will be given by the softmax function:  
+If \( \boldsymbol{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th
+output vector \( \boldsymbol{y}_i \).  
+The probability of \( \boldsymbol{x}_i \) being in class \( c \) will be given by the softmax function:  
 
 $$
-P(y_{ic} = 1 \mid \hat{x}_i, \hat{\theta}) = \frac{\exp{((\hat{a}_i^{hidden})^T \hat{w}_c)}}
-{\sum_{c'=0}^{C-1} \exp{((\hat{a}_i^{hidden})^T \hat{w}_{c'})}} ,
+P(y_{ic} = 1 \mid \boldsymbol{x}_i, \boldsymbol{\theta}) = \frac{\exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_c)}}
+{\sum_{c'=0}^{C-1} \exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_{c'})}} ,
 $$
 
 
    
@@ -469,13 +465,13 @@ The likelihood of this \( C \)-class classifier
 is now given as:  
 
 $$
-P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
+P(\mathcal{D} \mid \boldsymbol{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
 $$
 
 Again we take the negative log-likelihood to define our cost function:  
 
 $$
-\mathcal{C}(\hat{\theta}) = - \log{P(\mathcal{D} \mid \hat{\theta})}.
+\mathcal{C}(\boldsymbol{\theta}) = - \log{P(\mathcal{D} \mid \boldsymbol{\theta})}.
 $$
 
 See the logistic regression lectures for a full definition of the cost function.
@@ -491,20 +487,20 @@ The back propagation equations need now only a small change, namely the definiti
 
    
 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
 $$
-\mathcal{C}(\hat{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\hat{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\hat{\beta})}\right),
+\mathcal{C}(\boldsymbol{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\boldsymbol{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\boldsymbol{\beta})}\right),
 $$
 
 where we had defined the logistic (sigmoid) function
 $$
-p(y_i =1\vert x_i,\hat{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
+p(y_i =1\vert x_i,\boldsymbol{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
 $$
 
 and
 $$
-p(y_i =0\vert x_i,\hat{\beta})=1-p(y_i =1\vert x_i,\hat{\beta}).
+p(y_i =0\vert x_i,\boldsymbol{\beta})=1-p(y_i =1\vert x_i,\boldsymbol{\beta}).
 $$
 
-The parameters \( \hat{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.
+The parameters \( \boldsymbol{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.
 
 
    
 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 \( b_i^l \). 
@@ -521,12 +517,12 @@ $$
 where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \).
 Our cost function at the final layer \( l=L \) is now
 $$
-\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
+\mathcal{C}(\boldsymbol{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
 $$
 
 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
 $$
-\frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
+\frac{\partial \mathcal{C}(\boldsymbol{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
 $$
 
 In case we use another activation function than the logistic one, we need to evaluate other derivatives.
@@ -790,11 +786,11 @@ For a soft binary classifier, we could use a single neuron and interpret the out
 
    
 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:  
 
-$$ P(\text{class \( j \)} \mid \text{input \( \hat{a} \)}) = \frac{\exp{(\hat{a}^T \hat{w}_j)}}
-{\sum_{c=0}^{9} \exp{(\hat{a}^T \hat{w}_c)}} ,$$
+$$ P(\text{class \( j \)} \mid \text{input \( \boldsymbol{a} \)}) = \frac{\exp{(\boldsymbol{a}^T \boldsymbol{w}_j)}}
+{\sum_{c=0}^{9} \exp{(\boldsymbol{a}^T \boldsymbol{w}_c)}} ,$$
 
 
    
-i.e. each neuron \( j \) outputs the probability of being in class \( j \) given an input from the hidden layer \( \hat{a} \), with \( \hat{w}_j \) the weights of neuron \( j \) to the inputs.  
+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.  
 The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  
 The exponent is just the weighted sum of inputs as before:  
 
@@ -820,7 +816,7 @@ of values. Without it, any input with the value 0 will be mapped to zero (before
 $$ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.$$
 
 
    
-The bias weights \( \hat{b} \) 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.
+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.
 
    
 
 
@@ -885,23 +881,23 @@ and obtain a matrix that holds the weighted sum of inputs to the hidden layer
 for each input image and each hidden neuron.    
 We also add the bias to obtain a matrix of weighted sums to the hidden layer \( Z^{h} \):  
 
-$$ \hat{z}^{l} = \hat{X} \hat{W}^{l} + \hat{b}^{l} ,$$
+$$ \boldsymbol{z}^{l} = \boldsymbol{X} \boldsymbol{W}^{l} + \boldsymbol{b}^{l} ,$$
 
 
    
 meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.  
 This is then passed through the activation:  
 
-$$ \hat{a}^{l} = f(\hat{z}^l) .$$
+$$ \boldsymbol{a}^{l} = f(\boldsymbol{z}^l) .$$
 
 
    
 This is fed to the output layer:  
 
-$$ \hat{z}^{L} = \hat{a}^{L} \hat{W}^{L} + \hat{b}^{L} .$$
+$$ \boldsymbol{z}^{L} = \boldsymbol{a}^{L} \boldsymbol{W}^{L} + \boldsymbol{b}^{L} .$$
 
 
    
 Finally we receive our output values for each image and each category by passing it through the softmax function:  
 
-$$ output = softmax (\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$
+$$ output = softmax (\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$
 
 
    
 
@@ -956,22 +952,22 @@ A typical choice for multiclass classification is the cross-entropy los
 
    
 In multiclass classification it is common to treat each integer label as a so called one-hot vector:  
 
-$$ y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
+$$ y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
 
-$$ y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$
+$$ y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$
 
 
    
 i.e. a binary bit string of length \( C \), where \( C = 10 \) is the number of classes in the MNIST dataset.
 
 
    
 Let \( y_{ic} \) denote the \( c \)-th component of the \( i \)-th one-hot vector.  
-We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \hat{x}_i \) in the dataset.
+We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \boldsymbol{x}_i \) in the dataset.
 
 
    
 In the one-hot representation only one of the terms in the loss function is non-zero, namely the
 probability of the correct category \( c' \)  
 (i.e. the category \( c' \) such that \( y_{ic'} = 1 \)). This means that the cross entropy loss only punishes you for how wrong
-you got the correct label. The probability of category \( c \) is given by the softmax function. The vector \( \hat{\theta} \) represents the parameters of our network, i.e. all the weights and biases.
+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.
 
 
    
 









    
@@ -1030,7 +1026,7 @@ reduces overfitting.
 We will measure the size of the weights using the so called L2-norm, meaning our cost function becomes:  
 
 $$  \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad
-\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \hat{w} \rvert \rvert_2^2 
+\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \boldsymbol{w} \rvert \rvert_2^2 
 = \frac{1}{N} \sum_{i=1}^N  \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,$$
 
 
    
@@ -1053,23 +1049,23 @@ calculate the gradient efficently.
 
 
    
 To more efficently train our network these equations are implemented using matrix operations.  
-The error in the output layer is calculated simply as, with \( \hat{t} \) being our targets,  
+The error in the output layer is calculated simply as, with \( \boldsymbol{t} \) being our targets,  
 
-$$ \delta_L = \hat{t} - \hat{y} = (n_{inputs}, n_{categories}) .$$
+$$ \delta_L = \boldsymbol{t} - \boldsymbol{y} = (n_{inputs}, n_{categories}) .$$
 
 
    
 The gradient for the output weights is calculated as  
 
-$$ \nabla W_{L} = \hat{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
+$$ \nabla W_{L} = \boldsymbol{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
 
 
    
-where \( \hat{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input.  
+where \( \boldsymbol{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input.  
 Since we are going backwards we have to transpose the activation matrix.
 
 
    
 The gradient with respect to the output bias is then  
 
-$$ \nabla \hat{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$
+$$ \nabla \boldsymbol{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$
 
 
    
 The error in the hidden layer is  
@@ -1302,10 +1298,10 @@ To measure the performance of our network we evaluate how well it does it data i
 We measure the performance of the network using the accuracy score.  
 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 \( 1 \).  
 
-$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\hat{y}_i = y_i)}{n} ,$$
+$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,$$
 
 
    
-where \( I \) is the indicator function, \( 1 \) if \( \hat{y}_i = y_i \) and \( 0 \) otherwise.
+where \( I \) is the indicator function, \( 1 \) if \( \tilde{y}_i = y_i \) and \( 0 \) otherwise.
 
 
    
 
@@ -1512,7 +1508,7 @@ inputs \( x_1 \) and \( x_2 \) and outputs \( y \):
 
    The AND and XOR Gates 
    
 
 
    
-The AND gate is defined as
+The AND gate is defined as
 
 
    
 
    
@@ -1527,7 +1523,7 @@ The AND gate is defined as
 
    
 
    
 
    
-And finally we have the XOR gate
+And finally we have the XOR gate
 
 
    
 
@@ -1572,30 +1568,13 @@ We define first our design matrix and the various output vectors for the differe
 
    """
 Simple code that tests XOR, OR and AND gates with linear regression
 """
+
 # import necessary packages
 import numpy as np
 import matplotlib.pyplot as plt
 from sklearn import datasets
 
-# Design matrix
-X = np.array([ [1, 0, 0], [1, 0, 1], [1, 1, 0],[1, 1, 1]],dtype=np.float64)
-
-# The XOR gate 
-yXOR = np.array( [ 0, 1 ,1, 0])
-# The OR gate 
-yOR = np.array( [ 0, 1 ,1, 1])
-# The AND gate 
-yAND = np.array( [ 0, 0 ,0, 1])
-
    
-
    
-









    
-
-
    Then the first Feed Forward pass 
    
-
-
    
-
-
-
    def sigmoid(x):
+def sigmoid(x):
     return 1/(1 + np.exp(-x))
 
 def feed_forward(X):
@@ -1616,11 +1595,18 @@ yAND = np.array( [ 0, return np.argmax(probabilities, axis=1)
 
-
-
 # ensure the same random numbers appear every time
 np.random.seed(0)
 
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
 
 # Defining the neural network
 n_inputs, n_features = X.shape
diff --git a/doc/pub/week41/html/week41.html b/doc/pub/week41/html/week41.html
index 235fa407b..d5f5402c0 100644
--- a/doc/pub/week41/html/week41.html
+++ b/doc/pub/week41/html/week41.html
@@ -145,10 +145,6 @@ div { text-align: justify; text-justify: inter-word; }
                2,
                None,
                'setting-up-the-neural-network'),
-              ('Then the first Feed Forward pass',
-               2,
-               None,
-               'then-the-first-feed-forward-pass'),
               ('The Code using Scikit-Learn',
                2,
                None,
@@ -331,9 +327,9 @@ The four equations  derived last week provide us with a way of computing the gra
 
    
 
 
    
-First, we set up the input data \( \hat{x} \) and the activations
-\( \hat{z}_1 \) of the input layer and compute the activation function and
-the pertinent outputs \( \hat{a}^1 \).
+First, we set up the input data \( \boldsymbol{x} \) and the activations
+\( \boldsymbol{z}_1 \) of the input layer and compute the activation function and
+the pertinent outputs \( \boldsymbol{a}^1 \).
 
    
 
 
@@ -342,8 +338,8 @@ the pertinent outputs \( \hat{a}^1 \).
 
 
    
 Secondly, we perform then the feed forward till we reach the output
-layer and compute all \( \hat{z}_l \) of the input layer and compute the
-activation function and the pertinent outputs \( \hat{a}^l \) for
+layer and compute all \( \boldsymbol{z}_l \) of the input layer and compute the
+activation function and the pertinent outputs \( \boldsymbol{a}^l \) for
 \( l=2,3,\dots,L \).
 
    
 
@@ -352,7 +348,7 @@ activation function and the pertinent outputs \( \hat{a}^l \) for
 
    
 
 
    
-Thereafter we compute the ouput error \( \hat{\delta}^L \) by computing all
+Thereafter we compute the ouput error \( \boldsymbol{\delta}^L \) by computing all
 $$
 \delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}.
 $$
@@ -416,16 +412,16 @@ For an input \( \boldsymbol{a} \) from the hidden layer, the probability that th
 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 \( x \)
 represents our activation values \( z \). We have
 $$
-P(y = 0 \mid \hat{x}, \hat{\theta}) = \frac{1}{1 + \exp{(- \hat{x}})} ,
+P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) = \frac{1}{1 + \exp{(- \boldsymbol{x}})} ,
 $$
 
 and
 $$
-P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) ,
+P(y = 1 \mid \boldsymbol{x}, \boldsymbol{\theta}) = 1 - P(y = 0 \mid \boldsymbol{x}, \boldsymbol{\theta}) ,
 $$
 
 
    
-where \( y \in \{0, 1\} \)  and \( \hat{\theta} \) represents the weights and biases
+where \( y \in \{0, 1\} \)  and \( \boldsymbol{\theta} \) represents the weights and biases
 of our network.
 
 
    
@@ -436,13 +432,13 @@ of our network.
 
    
 Our cost function is given as (see the Logistic regression lectures)
 $$
-\mathcal{C}(\hat{\theta}) = - \ln P(\mathcal{D} \mid \hat{\theta}) = - \sum_{i=1}^n
-y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\hat{\theta}) .
+\mathcal{C}(\boldsymbol{\theta}) = - \ln P(\mathcal{D} \mid \boldsymbol{\theta}) = - \sum_{i=1}^n
+y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\boldsymbol{\theta}) .
 $$
 
 
    
 This last equality means that we can interpret our cost function as a sum over the loss function
-for each point in the dataset \( \mathcal{L}_i(\hat{\theta}) \).  
+for each point in the dataset \( \mathcal{L}_i(\boldsymbol{\theta}) \).  
 The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather
 than maximizing a negative number.
 
@@ -450,22 +446,22 @@ than maximizing a negative number.
 In multiclass classification it is common to treat each integer label as a so called one-hot vector:
 
 
    
-\( y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and
+\( y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) , \) and
 
 
    
-\( y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)
+\( y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) , \)
 
 
    
 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 \( 9 \))..
 
 
    
-If \( \hat{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th
-output vector \( \hat{y}_i \).  
-The probability of \( \hat{x}_i \) being in class \( c \) will be given by the softmax function:  
+If \( \boldsymbol{x}_i \) is the \( i \)-th input (image), \( y_{ic} \) refers to the \( c \)-th component of the \( i \)-th
+output vector \( \boldsymbol{y}_i \).  
+The probability of \( \boldsymbol{x}_i \) being in class \( c \) will be given by the softmax function:  
 
 $$
-P(y_{ic} = 1 \mid \hat{x}_i, \hat{\theta}) = \frac{\exp{((\hat{a}_i^{hidden})^T \hat{w}_c)}}
-{\sum_{c'=0}^{C-1} \exp{((\hat{a}_i^{hidden})^T \hat{w}_{c'})}} ,
+P(y_{ic} = 1 \mid \boldsymbol{x}_i, \boldsymbol{\theta}) = \frac{\exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_c)}}
+{\sum_{c'=0}^{C-1} \exp{((\boldsymbol{a}_i^{hidden})^T \boldsymbol{w}_{c'})}} ,
 $$
 
 
    
@@ -474,13 +470,13 @@ The likelihood of this \( C \)-class classifier
 is now given as:  
 
 $$
-P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
+P(\mathcal{D} \mid \boldsymbol{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
 $$
 
 Again we take the negative log-likelihood to define our cost function:  
 
 $$
-\mathcal{C}(\hat{\theta}) = - \log{P(\mathcal{D} \mid \hat{\theta})}.
+\mathcal{C}(\boldsymbol{\theta}) = - \log{P(\mathcal{D} \mid \boldsymbol{\theta})}.
 $$
 
 See the logistic regression lectures for a full definition of the cost function.
@@ -496,20 +492,20 @@ The back propagation equations need now only a small change, namely the definiti
 
    
 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
 $$
-\mathcal{C}(\hat{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\hat{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\hat{\beta})}\right),
+\mathcal{C}(\boldsymbol{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\boldsymbol{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\boldsymbol{\beta})}\right),
 $$
 
 where we had defined the logistic (sigmoid) function
 $$
-p(y_i =1\vert x_i,\hat{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
+p(y_i =1\vert x_i,\boldsymbol{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
 $$
 
 and
 $$
-p(y_i =0\vert x_i,\hat{\beta})=1-p(y_i =1\vert x_i,\hat{\beta}).
+p(y_i =0\vert x_i,\boldsymbol{\beta})=1-p(y_i =1\vert x_i,\boldsymbol{\beta}).
 $$
 
-The parameters \( \hat{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.
+The parameters \( \boldsymbol{\beta} \) were defined using a minimization method like gradient descent or Newton-Raphson's method.
 
 
    
 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 \( b_i^l \). 
@@ -526,12 +522,12 @@ $$
 where the superscript \( l-1 \) indicates that these are the outputs from layer \( l-1 \).
 Our cost function at the final layer \( l=L \) is now
 $$
-\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
+\mathcal{C}(\boldsymbol{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
 $$
 
 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
 $$
-\frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
+\frac{\partial \mathcal{C}(\boldsymbol{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
 $$
 
 In case we use another activation function than the logistic one, we need to evaluate other derivatives.
@@ -795,11 +791,11 @@ For a soft binary classifier, we could use a single neuron and interpret the out
 
    
 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:  
 
-$$ P(\text{class \( j \)} \mid \text{input \( \hat{a} \)}) = \frac{\exp{(\hat{a}^T \hat{w}_j)}}
-{\sum_{c=0}^{9} \exp{(\hat{a}^T \hat{w}_c)}} ,$$
+$$ P(\text{class \( j \)} \mid \text{input \( \boldsymbol{a} \)}) = \frac{\exp{(\boldsymbol{a}^T \boldsymbol{w}_j)}}
+{\sum_{c=0}^{9} \exp{(\boldsymbol{a}^T \boldsymbol{w}_c)}} ,$$
 
 
    
-i.e. each neuron \( j \) outputs the probability of being in class \( j \) given an input from the hidden layer \( \hat{a} \), with \( \hat{w}_j \) the weights of neuron \( j \) to the inputs.  
+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.  
 The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  
 The exponent is just the weighted sum of inputs as before:  
 
@@ -825,7 +821,7 @@ of values. Without it, any input with the value 0 will be mapped to zero (before
 $$ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.$$
 
 
    
-The bias weights \( \hat{b} \) 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.
+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.
 
    
 
 
@@ -890,23 +886,23 @@ and obtain a matrix that holds the weighted sum of inputs to the hidden layer
 for each input image and each hidden neuron.    
 We also add the bias to obtain a matrix of weighted sums to the hidden layer \( Z^{h} \):  
 
-$$ \hat{z}^{l} = \hat{X} \hat{W}^{l} + \hat{b}^{l} ,$$
+$$ \boldsymbol{z}^{l} = \boldsymbol{X} \boldsymbol{W}^{l} + \boldsymbol{b}^{l} ,$$
 
 
    
 meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.  
 This is then passed through the activation:  
 
-$$ \hat{a}^{l} = f(\hat{z}^l) .$$
+$$ \boldsymbol{a}^{l} = f(\boldsymbol{z}^l) .$$
 
 
    
 This is fed to the output layer:  
 
-$$ \hat{z}^{L} = \hat{a}^{L} \hat{W}^{L} + \hat{b}^{L} .$$
+$$ \boldsymbol{z}^{L} = \boldsymbol{a}^{L} \boldsymbol{W}^{L} + \boldsymbol{b}^{L} .$$
 
 
    
 Finally we receive our output values for each image and each category by passing it through the softmax function:  
 
-$$ output = softmax (\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$
+$$ output = softmax (\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$
 
 
    
 
@@ -961,22 +957,22 @@ A typical choice for multiclass classification is the cross-entropy los
 
    
 In multiclass classification it is common to treat each integer label as a so called one-hot vector:  
 
-$$ y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
+$$ y = 5 \quad \rightarrow \quad \boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
 
-$$ y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$
+$$ y = 1 \quad \rightarrow \quad \boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$
 
 
    
 i.e. a binary bit string of length \( C \), where \( C = 10 \) is the number of classes in the MNIST dataset.
 
 
    
 Let \( y_{ic} \) denote the \( c \)-th component of the \( i \)-th one-hot vector.  
-We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \hat{x}_i \) in the dataset.
+We define the cost function \( \mathcal{C} \) as a sum over the cross-entropy loss for each point \( \boldsymbol{x}_i \) in the dataset.
 
 
    
 In the one-hot representation only one of the terms in the loss function is non-zero, namely the
 probability of the correct category \( c' \)  
 (i.e. the category \( c' \) such that \( y_{ic'} = 1 \)). This means that the cross entropy loss only punishes you for how wrong
-you got the correct label. The probability of category \( c \) is given by the softmax function. The vector \( \hat{\theta} \) represents the parameters of our network, i.e. all the weights and biases.
+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.
 
 
    
 









    
@@ -1035,7 +1031,7 @@ reduces overfitting.
 We will measure the size of the weights using the so called L2-norm, meaning our cost function becomes:  
 
 $$  \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad
-\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \hat{w} \rvert \rvert_2^2 
+\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \boldsymbol{w} \rvert \rvert_2^2 
 = \frac{1}{N} \sum_{i=1}^N  \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,$$
 
 
    
@@ -1058,23 +1054,23 @@ calculate the gradient efficently.
 
 
    
 To more efficently train our network these equations are implemented using matrix operations.  
-The error in the output layer is calculated simply as, with \( \hat{t} \) being our targets,  
+The error in the output layer is calculated simply as, with \( \boldsymbol{t} \) being our targets,  
 
-$$ \delta_L = \hat{t} - \hat{y} = (n_{inputs}, n_{categories}) .$$
+$$ \delta_L = \boldsymbol{t} - \boldsymbol{y} = (n_{inputs}, n_{categories}) .$$
 
 
    
 The gradient for the output weights is calculated as  
 
-$$ \nabla W_{L} = \hat{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
+$$ \nabla W_{L} = \boldsymbol{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
 
 
    
-where \( \hat{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input.  
+where \( \boldsymbol{a} = (n_{inputs}, n_{hidden}) \). This simply means that we are summing up the gradients for each input.  
 Since we are going backwards we have to transpose the activation matrix.
 
 
    
 The gradient with respect to the output bias is then  
 
-$$ \nabla \hat{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$
+$$ \nabla \boldsymbol{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$
 
 
    
 The error in the hidden layer is  
@@ -1307,10 +1303,10 @@ To measure the performance of our network we evaluate how well it does it data i
 We measure the performance of the network using the accuracy score.  
 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 \( 1 \).  
 
-$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\hat{y}_i = y_i)}{n} ,$$
+$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,$$
 
 
    
-where \( I \) is the indicator function, \( 1 \) if \( \hat{y}_i = y_i \) and \( 0 \) otherwise.
+where \( I \) is the indicator function, \( 1 \) if \( \tilde{y}_i = y_i \) and \( 0 \) otherwise.
 
 
    
 
@@ -1517,7 +1513,7 @@ inputs \( x_1 \) and \( x_2 \) and outputs \( y \):
 
    The AND and XOR Gates 
    
 
 
    
-The AND gate is defined as
+The AND gate is defined as
 
 
    
 
    
@@ -1532,7 +1528,7 @@ The AND gate is defined as
 
    
 
    
 
    
-And finally we have the XOR gate
+And finally we have the XOR gate
 
 
    
 
@@ -1577,30 +1573,13 @@ We define first our design matrix and the various output vectors for the differe
 
    """
 Simple code that tests XOR, OR and AND gates with linear regression
 """
+
 # import necessary packages
 import numpy as np
 import matplotlib.pyplot as plt
 from sklearn import datasets
 
-# Design matrix
-X = np.array([ [1, 0, 0], [1, 0, 1], [1, 1, 0],[1, 1, 1]],dtype=np.float64)
-
-# The XOR gate 
-yXOR = np.array( [ 0, 1 ,1, 0])
-# The OR gate 
-yOR = np.array( [ 0, 1 ,1, 1])
-# The AND gate 
-yAND = np.array( [ 0, 0 ,0, 1])
-
    
-
    
-









    
-
-
    Then the first Feed Forward pass 
    
-
-
    
-
-
-
    def sigmoid(x):
+def sigmoid(x):
     return 1/(1 + np.exp(-x))
 
 def feed_forward(X):
@@ -1621,11 +1600,18 @@ yAND = np.= feed_forward(X)
     return np.argmax(probabilities, axis=1)
 
-
-
 # ensure the same random numbers appear every time
 np.random.seed(0)
 
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
 
 # Defining the neural network
 n_inputs, n_features = X.shape
diff --git a/doc/pub/week41/ipynb/ipynb-week41-src.tar.gz b/doc/pub/week41/ipynb/ipynb-week41-src.tar.gz
index ad3fdbd7991799b9a51c39e3f837afcb5438662e..b7245f60f8c270e512b08a01ac9a34325dd52144 100644
GIT binary patch
delta 41
vcmcb2M&aHW1vdF^4u;Mzjcl!KjIC@;t!&J#Y%Hy8tgUQ75%#TY91&^&BohmJ

delta 41
vcmcb2M&aHW1vdF^4hFpsjcl!KjIC@;t!&J#Y%Hy8tgUQ75%#TY91&^&81)Mr

diff --git a/doc/pub/week41/ipynb/week41.ipynb b/doc/pub/week41/ipynb/week41.ipynb
index dbc02bf4e..2112445d8 100644
--- a/doc/pub/week41/ipynb/week41.ipynb
+++ b/doc/pub/week41/ipynb/week41.ipynb
@@ -39,20 +39,20 @@
     "\n",
     "The four equations  derived last week provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.\n",
     "\n",
-    "First, we set up the input data $\\hat{x}$ and the activations\n",
-    "$\\hat{z}_1$ of the input layer and compute the activation function and\n",
-    "the pertinent outputs $\\hat{a}^1$.\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",
     "\n",
     "\n",
     "Secondly, we perform then the feed forward till we reach the output\n",
-    "layer and compute all $\\hat{z}_l$ of the input layer and compute the\n",
-    "activation function and the pertinent outputs $\\hat{a}^l$ for\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",
     "$l=2,3,\\dots,L$.\n",
     "\n",
     "\n",
     "\n",
-    "Thereafter we compute the ouput error $\\hat{\\delta}^L$ by computing all"
+    "Thereafter we compute the ouput error $\\boldsymbol{\\delta}^L$ by computing all"
    ]
   },
   {
@@ -142,7 +142,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "P(y = 0 \\mid \\hat{x}, \\hat{\\theta}) = \\frac{1}{1 + \\exp{(- \\hat{x}})} ,\n",
+    "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n",
     "$$"
    ]
   },
@@ -158,7 +158,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "P(y = 1 \\mid \\hat{x}, \\hat{\\theta}) = 1 - P(y = 0 \\mid \\hat{x}, \\hat{\\theta}) ,\n",
+    "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
     "$$"
    ]
   },
@@ -166,7 +166,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "where $y \\in \\{0, 1\\}$  and $\\hat{\\theta}$ represents the weights and biases\n",
+    "where $y \\in \\{0, 1\\}$  and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
     "of our network.\n",
     "\n",
     "\n",
@@ -180,8 +180,8 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\mathcal{C}(\\hat{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\hat{\\theta}) = - \\sum_{i=1}^n\n",
-    "y_i \\ln[P(y_i = 0)] + (1 - y_i) \\ln [1 - P(y_i = 0)] = \\sum_{i=1}^n \\mathcal{L}_i(\\hat{\\theta}) .\n",
+    "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
+    "y_i \\ln[P(y_i = 0)] + (1 - y_i) \\ln [1 - P(y_i = 0)] = \\sum_{i=1}^n \\mathcal{L}_i(\\boldsymbol{\\theta}) .\n",
     "$$"
    ]
   },
@@ -190,23 +190,23 @@
    "metadata": {},
    "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 $\\mathcal{L}_i(\\hat{\\theta})$.  \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",
-    "$y = 5 \\quad \\rightarrow \\quad \\hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n",
+    "$y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n",
     "\n",
     "\n",
-    "$y = 1 \\quad \\rightarrow \\quad \\hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n",
+    "$y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n",
     "\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 $\\hat{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n",
-    "output vector $\\hat{y}_i$.  \n",
-    "The probability of $\\hat{x}_i$ being in class $c$ will be given by the softmax function:"
+    "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:"
    ]
   },
   {
@@ -214,8 +214,8 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "P(y_{ic} = 1 \\mid \\hat{x}_i, \\hat{\\theta}) = \\frac{\\exp{((\\hat{a}_i^{hidden})^T \\hat{w}_c)}}\n",
-    "{\\sum_{c'=0}^{C-1} \\exp{((\\hat{a}_i^{hidden})^T \\hat{w}_{c'})}} ,\n",
+    "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
+    "{\\sum_{c'=0}^{C-1} \\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_{c'})}} ,\n",
     "$$"
    ]
   },
@@ -233,7 +233,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "P(\\mathcal{D} \\mid \\hat{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
+    "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
     "$$"
    ]
   },
@@ -249,7 +249,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\mathcal{C}(\\hat{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\hat{\\theta})}.\n",
+    "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n",
     "$$"
    ]
   },
@@ -271,7 +271,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\mathcal{C}(\\hat{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\hat{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\hat{\\beta})}\\right),\n",
+    "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n",
     "$$"
    ]
   },
@@ -287,7 +287,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "p(y_i =1\\vert x_i,\\hat{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
+    "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
     "$$"
    ]
   },
@@ -303,7 +303,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "p(y_i =0\\vert x_i,\\hat{\\beta})=1-p(y_i =1\\vert x_i,\\hat{\\beta}).\n",
+    "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n",
     "$$"
    ]
   },
@@ -311,7 +311,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The parameters $\\hat{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n",
+    "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"
@@ -355,7 +355,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\mathcal{C}(\\hat{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
+    "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
     "$$"
    ]
   },
@@ -371,7 +371,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\frac{\\partial \\mathcal{C}(\\hat{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
+    "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
     "$$"
    ]
   },
@@ -665,10 +665,10 @@
     "\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",
-    "$$ P(\\text{class $j$} \\mid \\text{input $\\hat{a}$}) = \\frac{\\exp{(\\hat{a}^T \\hat{w}_j)}}\n",
-    "{\\sum_{c=0}^{9} \\exp{(\\hat{a}^T \\hat{w}_c)}} ,$$  \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 $\\hat{a}$, with $\\hat{w}_j$ the weights of neuron $j$ to the inputs.  \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",
@@ -688,7 +688,7 @@
     "\n",
     "$$ z_j = \\sum_{i=1}^n w_ {ij} a_i + b_j.$$  \n",
     "\n",
-    "The bias weights $\\hat{b}$ 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."
+    "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."
    ]
   },
   {
@@ -755,20 +755,20 @@
     "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",
-    "$$ \\hat{z}^{l} = \\hat{X} \\hat{W}^{l} + \\hat{b}^{l} ,$$\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",
-    "$$ \\hat{a}^{l} = f(\\hat{z}^l) .$$  \n",
+    "$$ \\boldsymbol{a}^{l} = f(\\boldsymbol{z}^l) .$$  \n",
     "\n",
     "This is fed to the output layer:  \n",
     "\n",
-    "$$ \\hat{z}^{L} = \\hat{a}^{L} \\hat{W}^{L} + \\hat{b}^{L} .$$\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",
-    "$$ output = softmax (\\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$"
+    "$$ output = softmax (\\boldsymbol{z}^{L}) = (n_{inputs}, n_{categories}) .$$"
    ]
   },
   {
@@ -830,21 +830,21 @@
     "\n",
     "In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  \n",
     "\n",
-    "$$ y = 5 \\quad \\rightarrow \\quad \\hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  \n",
+    "$$ y = 5 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  \n",
     "\n",
     "\n",
-    "$$ y = 1 \\quad \\rightarrow \\quad \\hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  \n",
+    "$$ y = 1 \\quad \\rightarrow \\quad \\boldsymbol{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  \n",
     "\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 $\\hat{x}_i$ in the dataset.\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 $\\hat{\\theta}$ represents the parameters of our network, i.e. all the weights and biases.  \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.  \n",
     "\n",
     "\n",
     "## Optimizing the cost function\n",
@@ -890,7 +890,7 @@
     "We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes:  \n",
     "\n",
     "$$  \\mathcal{C}(\\theta) = \\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}_i(\\theta) \\quad \\rightarrow \\quad\n",
-    "\\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}_i(\\theta) + \\lambda \\lvert \\lvert \\hat{w} \\rvert \\rvert_2^2 \n",
+    "\\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}_i(\\theta) + \\lambda \\lvert \\lvert \\boldsymbol{w} \\rvert \\rvert_2^2 \n",
     "= \\frac{1}{N} \\sum_{i=1}^N  \\mathcal{L}(\\theta) + \\lambda \\sum_{ij} w_{ij}^2,$$  \n",
     "\n",
     "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n",
@@ -909,20 +909,20 @@
     "## 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 $\\hat{t}$ being our targets,  \n",
+    "The error in the output layer is calculated simply as, with $\\boldsymbol{t}$ being our targets,  \n",
     "\n",
-    "$$ \\delta_L = \\hat{t} - \\hat{y} = (n_{inputs}, n_{categories}) .$$  \n",
+    "$$ \\delta_L = \\boldsymbol{t} - \\boldsymbol{y} = (n_{inputs}, n_{categories}) .$$  \n",
     "\n",
     "The gradient for the output weights is calculated as  \n",
     "\n",
-    "$$ \\nabla W_{L} = \\hat{a}^T \\delta_L   = (n_{hidden}, n_{categories}) ,$$\n",
+    "$$ \\nabla W_{L} = \\boldsymbol{a}^T \\delta_L   = (n_{hidden}, n_{categories}) ,$$\n",
     "\n",
-    "where $\\hat{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input.  \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",
-    "$$ \\nabla \\hat{b}_{L} = \\sum_{i=1}^{n_{inputs}} \\delta_L = (n_{categories}) .$$  \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",
@@ -1161,9 +1161,9 @@
     "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",
-    "$$ \\text{Accuracy} = \\frac{\\sum_{i=1}^n I(\\hat{y}_i = y_i)}{n} ,$$  \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 $\\hat{y}_i = y_i$ and $0$ otherwise."
+    "where $I$ is the indicator function, $1$ if $\\tilde{y}_i = y_i$ and $0$ otherwise."
    ]
   },
   {
@@ -1407,7 +1407,7 @@
     "
    \n",
     "## The AND and XOR Gates\n",
     "\n",
-    "The **AND** gate is defined as\n",
+    "The AND gate is defined as\n",
     "\n",
     "\n",
     "\n",
@@ -1420,7 +1420,7 @@
     "\n",
     "\n",
     "
       1            1            1       
    \n",
-    "And finally we have the **XOR** gate\n",
+    "And finally we have the XOR gate\n",
     "\n",
     "\n",
     "\n",
@@ -1473,40 +1473,12 @@
     "\"\"\"\n",
     "Simple code that tests XOR, OR and AND gates with linear regression\n",
     "\"\"\"\n",
+    "\n",
     "# import necessary packages\n",
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "from sklearn import datasets\n",
     "\n",
-    "# Design matrix\n",
-    "X = np.array([ [1, 0, 0], [1, 0, 1], [1, 1, 0],[1, 1, 1]],dtype=np.float64)\n",
-    "\n",
-    "# The XOR gate \n",
-    "yXOR = np.array( [ 0, 1 ,1, 0])\n",
-    "# The OR gate \n",
-    "yOR = np.array( [ 0, 1 ,1, 1])\n",
-    "# The AND gate \n",
-    "yAND = np.array( [ 0, 0 ,0, 1])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Then the first Feed Forward pass"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "\n",
-    "\n",
     "def sigmoid(x):\n",
     "    return 1/(1 + np.exp(-x))\n",
     "\n",
@@ -1528,11 +1500,18 @@
     "    probabilities = feed_forward(X)\n",
     "    return np.argmax(probabilities, axis=1)\n",
     "\n",
-    "\n",
-    "\n",
     "# ensure the same random numbers appear every time\n",
     "np.random.seed(0)\n",
     "\n",
+    "# Design matrix\n",
+    "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",
+    "# The OR gate\n",
+    "yOR = np.array( [ 0, 1 ,1, 1])\n",
+    "# The AND gate\n",
+    "yAND = np.array( [ 0, 0 ,0, 1])\n",
     "\n",
     "# Defining the neural network\n",
     "n_inputs, n_features = X.shape\n",
diff --git a/doc/src/week41/week41.do.txt b/doc/src/week41/week41.do.txt
index 637c5b33a..6d143cefd 100644
--- a/doc/src/week41/week41.do.txt
+++ b/doc/src/week41/week41.do.txt
@@ -29,20 +29,20 @@ For a more in depth discussion on  neural networks we recommend Goodfellow et al
 The four equations  derived last week provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.
 
 !bblock
-First, we set up the input data $\hat{x}$ and the activations
-$\hat{z}_1$ of the input layer and compute the activation function and
-the pertinent outputs $\hat{a}^1$.
+First, we set up the input data $\bm{x}$ and the activations
+$\bm{z}_1$ of the input layer and compute the activation function and
+the pertinent outputs $\bm{a}^1$.
 !eblock
 
 !bblock
 Secondly, we perform then the feed forward till we reach the output
-layer and compute all $\hat{z}_l$ of the input layer and compute the
-activation function and the pertinent outputs $\hat{a}^l$ for
+layer and compute all $\bm{z}_l$ of the input layer and compute the
+activation function and the pertinent outputs $\bm{a}^l$ for
 $l=2,3,\dots,L$.
 !eblock
 
 !bblock
-Thereafter we compute the ouput error $\hat{\delta}^L$ by computing all
+Thereafter we compute the ouput error $\bm{\delta}^L$ by computing all
 !bt
 \[
 \delta_j^L = f'(z_j^L)\frac{\partial {\cal C}}{\partial (a_j^L)}.
@@ -102,17 +102,17 @@ is in class 0 or 1 is just. We let $\theta$ represent the unknown weights and bi
 represents our activation values $z$. We have
 !bt
 \[
-P(y = 0 \mid \hat{x}, \hat{\theta}) = \frac{1}{1 + \exp{(- \hat{x}})} ,
+P(y = 0 \mid \bm{x}, \bm{\theta}) = \frac{1}{1 + \exp{(- \bm{x}})} ,
 \]
 !et
 and
 !bt
 \[
-P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) ,
+P(y = 1 \mid \bm{x}, \bm{\theta}) = 1 - P(y = 0 \mid \bm{x}, \bm{\theta}) ,
 \]
 !et
   
-where $y \in \{0, 1\}$  and $\hat{\theta}$ represents the weights and biases
+where $y \in \{0, 1\}$  and $\bm{\theta}$ represents the weights and biases
 of our network.
   
 
@@ -122,34 +122,34 @@ of our network.
 Our cost function is given as (see the Logistic regression lectures)
 !bt
 \[
-\mathcal{C}(\hat{\theta}) = - \ln P(\mathcal{D} \mid \hat{\theta}) = - \sum_{i=1}^n
-y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\hat{\theta}) .
+\mathcal{C}(\bm{\theta}) = - \ln P(\mathcal{D} \mid \bm{\theta}) = - \sum_{i=1}^n
+y_i \ln[P(y_i = 0)] + (1 - y_i) \ln [1 - P(y_i = 0)] = \sum_{i=1}^n \mathcal{L}_i(\bm{\theta}) .
 \]
 !et
   
 This last equality means that we can interpret our *cost* function as a sum over the *loss* function
-for each point in the dataset $\mathcal{L}_i(\hat{\theta})$.  
+for each point in the dataset $\mathcal{L}_i(\bm{\theta})$.  
 The negative sign is just so that we can think about our algorithm as minimizing a positive number, rather
 than maximizing a negative number.  
   
 In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  
   
-$y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and
+$y = 5 \quad \rightarrow \quad \bm{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and
 
   
-$y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ 
+$y = 1 \quad \rightarrow \quad \bm{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ 
   
   
 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 $9$)..  
   
-If $\hat{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th
-output vector $\hat{y}_i$.  
-The probability of $\hat{x}_i$ being in class $c$ will be given by the softmax function:  
+If $\bm{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th
+output vector $\bm{y}_i$.  
+The probability of $\bm{x}_i$ being in class $c$ will be given by the softmax function:  
   
 !bt
 \[
-P(y_{ic} = 1 \mid \hat{x}_i, \hat{\theta}) = \frac{\exp{((\hat{a}_i^{hidden})^T \hat{w}_c)}}
-{\sum_{c'=0}^{C-1} \exp{((\hat{a}_i^{hidden})^T \hat{w}_{c'})}} ,
+P(y_{ic} = 1 \mid \bm{x}_i, \bm{\theta}) = \frac{\exp{((\bm{a}_i^{hidden})^T \bm{w}_c)}}
+{\sum_{c'=0}^{C-1} \exp{((\bm{a}_i^{hidden})^T \bm{w}_{c'})}} ,
 \]
 !et
   
@@ -159,14 +159,14 @@ is now given as:
   
 !bt
 \[
-P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
+P(\mathcal{D} \mid \bm{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .
 \]
 !et
 Again we take the negative log-likelihood to define our cost function:  
   
 !bt
 \[
-\mathcal{C}(\hat{\theta}) = - \log{P(\mathcal{D} \mid \hat{\theta})}.
+\mathcal{C}(\bm{\theta}) = - \log{P(\mathcal{D} \mid \bm{\theta})}.
 \]
 !et
 See the logistic regression lectures for a full definition of the cost function.
@@ -179,22 +179,22 @@ The back propagation equations need now only a small change, namely the definiti
 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
 !bt
 \[
-\mathcal{C}(\hat{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\hat{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\hat{\beta})}\right),
+\mathcal{C}(\bm{\beta}) = - \sum_{i=1}^n \left(y_i\log{p(y_i \vert x_i,\bm{\beta})}+(1-y_i)\log{1-p(y_i \vert x_i,\bm{\beta})}\right),
 \]
 !et
 where we had defined the logistic (sigmoid) function
 !bt
 \[
-p(y_i =1\vert x_i,\hat{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
+p(y_i =1\vert x_i,\bm{\beta})=\frac{\exp{(\beta_0+\beta_1 x_i)}}{1+\exp{(\beta_0+\beta_1 x_i)}},
 \]
 !et
 and
 !bt
 \[
-p(y_i =0\vert x_i,\hat{\beta})=1-p(y_i =1\vert x_i,\hat{\beta}).
+p(y_i =0\vert x_i,\bm{\beta})=1-p(y_i =1\vert x_i,\bm{\beta}).
 \]
 !et
-The parameters $\hat{\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. 
+The parameters $\bm{\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. 
 
 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 $b_i^l$. 
 We have then
@@ -213,13 +213,13 @@ where the superscript $l-1$ indicates that these are the outputs from layer $l-1
 Our cost function at the final layer $l=L$ is now
 !bt
 \[
-\mathcal{C}(\hat{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
+\mathcal{C}(\bm{W}) = - \sum_{i=1}^n \left(t_i\log{a_i^L}+(1-t_i)\log{(1-a_i^L)}\right),
 \]
 !et
 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
 !bt
 \[
-\frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
+\frac{\partial \mathcal{C}(\bm{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. 
 \]
 !et
 In case we use another activation function than the logistic one, we need to evaluate other derivatives. 
@@ -448,10 +448,10 @@ For a soft binary classifier, we could use a single neuron and interpret the out
   
 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:  
   
-$$ P(\text{class $j$} \mid \text{input $\hat{a}$}) = \frac{\exp{(\hat{a}^T \hat{w}_j)}}
-{\sum_{c=0}^{9} \exp{(\hat{a}^T \hat{w}_c)}} ,$$  
+$$ P(\text{class $j$} \mid \text{input $\bm{a}$}) = \frac{\exp{(\bm{a}^T \bm{w}_j)}}
+{\sum_{c=0}^{9} \exp{(\bm{a}^T \bm{w}_c)}} ,$$  
   
-i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\hat{a}$, with $\hat{w}_j$ the weights of neuron $j$ to the inputs.  
+i.e. each neuron $j$ outputs the probability of being in class $j$ given an input from the hidden layer $\bm{a}$, with $\bm{w}_j$ the weights of neuron $j$ to the inputs.  
 The denominator is a normalization factor to ensure the outputs (probabilities) sum up to 1.  
 The exponent is just the weighted sum of inputs as before:  
   
@@ -471,7 +471,7 @@ of values. Without it, any input with the value 0 will be mapped to zero (before
   
 $$ z_j = \sum_{i=1}^n w_ {ij} a_i + b_j.$$  
   
-The bias weights $\hat{b}$ 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.
+The bias weights $\bm{b}$ 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.
 !bc pycod
 # building our neural network
 
@@ -525,20 +525,20 @@ and obtain a matrix that holds the weighted sum of inputs to the hidden layer
 for each input image and each hidden neuron.    
 We also add the bias to obtain a matrix of weighted sums to the hidden layer $Z^{h}$:  
   
-$$ \hat{z}^{l} = \hat{X} \hat{W}^{l} + \hat{b}^{l} ,$$
+$$ \bm{z}^{l} = \bm{X} \bm{W}^{l} + \bm{b}^{l} ,$$
   
 meaning the same bias (1D array with size equal number of hidden neurons) is added to each input image.  
 This is then passed through the activation:  
   
-$$ \hat{a}^{l} = f(\hat{z}^l) .$$  
+$$ \bm{a}^{l} = f(\bm{z}^l) .$$  
   
 This is fed to the output layer:  
   
-$$ \hat{z}^{L} = \hat{a}^{L} \hat{W}^{L} + \hat{b}^{L} .$$
+$$ \bm{z}^{L} = \bm{a}^{L} \bm{W}^{L} + \bm{b}^{L} .$$
   
 Finally we receive our output values for each image and each category by passing it through the softmax function:  
   
-$$ output = softmax (\hat{z}^{L}) = (n_{inputs}, n_{categories}) .$$
+$$ output = softmax (\bm{z}^{L}) = (n_{inputs}, n_{categories}) .$$
 
 
 !bc pycod
@@ -589,21 +589,21 @@ A typical choice for multiclass classification is the *cross-entropy* loss, also
   
 In *multiclass* classification it is common to treat each integer label as a so called *one-hot* vector:  
   
-$$ y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
+$$ y = 5 \quad \rightarrow \quad \bm{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$  
 
   
-$$ y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  
+$$ y = 1 \quad \rightarrow \quad \bm{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$  
   
   
 i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset.  
   
 Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector.  
-We define the cost function $\mathcal{C}$ as a sum over the cross-entropy loss for each point $\hat{x}_i$ in the dataset.
+We define the cost function $\mathcal{C}$ as a sum over the cross-entropy loss for each point $\bm{x}_i$ in the dataset.
   
 In the one-hot representation only one of the terms in the loss function is non-zero, namely the
 probability of the correct category $c'$  
 (i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong
-you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\hat{\theta}$ represents the parameters of our network, i.e. all the weights and biases.  
+you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\bm{\theta}$ represents the parameters of our network, i.e. all the weights and biases.  
   
   
 !split
@@ -649,7 +649,7 @@ reduces *overfitting*.
 We will measure the size of the weights using the so called *L2-norm*, meaning our cost function becomes:  
   
 $$  \mathcal{C}(\theta) = \frac{1}{N} \sum_{i=1}^N \mathcal{L}_i(\theta) \quad \rightarrow \quad
-\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \hat{w} \rvert \rvert_2^2 
+\frac{1}{N} \sum_{i=1}^N  \mathcal{L}_i(\theta) + \lambda \lvert \lvert \bm{w} \rvert \rvert_2^2 
 = \frac{1}{N} \sum_{i=1}^N  \mathcal{L}(\theta) + \lambda \sum_{ij} w_{ij}^2,$$  
   
 i.e. we sum up all the weights squared. The factor $\lambda$ is known as a regularization parameter.
@@ -669,20 +669,20 @@ calculate the gradient efficently.
 ===== Matrix  multiplication =====
   
 To more efficently train our network these equations are implemented using matrix operations.  
-The error in the output layer is calculated simply as, with $\hat{t}$ being our targets,  
+The error in the output layer is calculated simply as, with $\bm{t}$ being our targets,  
   
-$$ \delta_L = \hat{t} - \hat{y} = (n_{inputs}, n_{categories}) .$$  
+$$ \delta_L = \bm{t} - \bm{y} = (n_{inputs}, n_{categories}) .$$  
   
 The gradient for the output weights is calculated as  
   
-$$ \nabla W_{L} = \hat{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
+$$ \nabla W_{L} = \bm{a}^T \delta_L   = (n_{hidden}, n_{categories}) ,$$
   
-where $\hat{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input.  
+where $\bm{a} = (n_{inputs}, n_{hidden})$. This simply means that we are summing up the gradients for each input.  
 Since we are going backwards we have to transpose the activation matrix.  
   
 The gradient with respect to the output bias is then  
   
-$$ \nabla \hat{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$  
+$$ \nabla \bm{b}_{L} = \sum_{i=1}^{n_{inputs}} \delta_L = (n_{categories}) .$$  
   
 The error in the hidden layer is  
   
@@ -900,9 +900,9 @@ To measure the performance of our network we evaluate how well it does it data i
 We measure the performance of the network using the *accuracy* score.  
 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 $1$.  
   
-$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\hat{y}_i = y_i)}{n} ,$$  
+$$ \text{Accuracy} = \frac{\sum_{i=1}^n I(\tilde{y}_i = y_i)}{n} ,$$  
   
-where $I$ is the indicator function, $1$ if $\hat{y}_i = y_i$ and $0$ otherwise.
+where $I$ is the indicator function, $1$ if $\tilde{y}_i = y_i$ and $0$ otherwise.
 
 
 !bc pycod
@@ -1087,7 +1087,7 @@ inputs $x_1$ and $x_2$ and outputs $y$:
 !split
 ===== The AND and XOR Gates =====
 
-The _AND_ gate is defined as
+The AND gate is defined as
 
 |---------------------|
 | $x_1$ | $x_2$ | $y$ |
@@ -1098,7 +1098,7 @@ The _AND_ gate is defined as
 | 1    | 1  | 1 |
 |---------------------|
 
-And finally we have the _XOR_ gate
+And finally we have the XOR gate
 
 |---------------------|
 | $x_1$ | $x_2$ | $y$ |
@@ -1131,29 +1131,12 @@ We define first our design matrix and the various output vectors for the differe
 """
 Simple code that tests XOR, OR and AND gates with linear regression
 """
+
 # import necessary packages
 import numpy as np
 import matplotlib.pyplot as plt
 from sklearn import datasets
 
-# Design matrix
-X = np.array([ [1, 0, 0], [1, 0, 1], [1, 1, 0],[1, 1, 1]],dtype=np.float64)
-
-# The XOR gate 
-yXOR = np.array( [ 0, 1 ,1, 0])
-# The OR gate 
-yOR = np.array( [ 0, 1 ,1, 1])
-# The AND gate 
-yAND = np.array( [ 0, 0 ,0, 1])
-!ec
-
-
-!split
-=====  Then the first Feed Forward pass =====
-
-!bc pycod
-
-
 def sigmoid(x):
     return 1/(1 + np.exp(-x))
 
@@ -1175,11 +1158,18 @@ def predict(X):
     probabilities = feed_forward(X)
     return np.argmax(probabilities, axis=1)
 
-
-
 # ensure the same random numbers appear every time
 np.random.seed(0)
 
+# Design matrix
+X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)
+
+# The XOR gate
+yXOR = np.array( [ 0, 1 ,1, 0])
+# The OR gate
+yOR = np.array( [ 0, 1 ,1, 1])
+# The AND gate
+yAND = np.array( [ 0, 0 ,0, 1])
 
 # Defining the neural network
 n_inputs, n_features = X.shape
@@ -1203,6 +1193,7 @@ print(probabilities)
 
 predictions = predict(X)
 print(predictions)
+
 !ec
 Not an impressive result, but this was our first forward pass with randomly assigned weights. Let us now add the full network with the back-propagation algorithm discussed above.