From e8b71b60123e44864fc4a7e1624908e535bfb5db Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 30 Sep 2024 13:11:27 +0200
Subject: [PATCH] added video

---
 .../_build/.doctrees/environment.pickle       |  Bin 415266 -> 415723 bytes
 .../_build/.doctrees/week40.doctree           |  Bin 632744 -> 631326 bytes
 .../_build/html/_images/week40_100_1.png      |  Bin 22124 -> 22123 bytes
 .../_build/html/_images/week40_104_1.png      |  Bin 22750 -> 22220 bytes
 .../_build/html/_images/week40_34_1.png       |  Bin 21806 -> 20750 bytes
 .../_build/html/_sources/week40.ipynb         | 1527 +++++++++--------
 doc/LectureNotes/_build/html/searchindex.js   |    2 +-
 doc/LectureNotes/_build/html/week40.html      |  237 +--
 .../_build/jupyter_execute/week40.ipynb       | 1341 +++++++++------
 .../_build/jupyter_execute/week40.py          |    6 +-
 .../_build/jupyter_execute/week40_100_1.png   |  Bin 22124 -> 22123 bytes
 .../_build/jupyter_execute/week40_104_1.png   |  Bin 22750 -> 22220 bytes
 .../_build/jupyter_execute/week40_34_1.png    |  Bin 21806 -> 20750 bytes
 doc/LectureNotes/week40.ipynb                 | 1527 +++++++++--------
 14 files changed, 2561 insertions(+), 2079 deletions(-)

diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index bfdb1008624fc5a073ebe715ef0fc5b4431617c2..9a98d1a0a3e78478b0739bc4a010d19cc088d2e5 100644
GIT binary patch
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diff --git a/doc/LectureNotes/_build/html/_sources/week40.ipynb b/doc/LectureNotes/_build/html/_sources/week40.ipynb
index cfe6bdd0b..c316b1d31 100644
--- a/doc/LectureNotes/_build/html/_sources/week40.ipynb
+++ b/doc/LectureNotes/_build/html/_sources/week40.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "54c44098",
-   "metadata": {},
+   "id": "71c0e62a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week40.do.txt --no_mako -->\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f64073c9",
-   "metadata": {},
+   "id": "4e0afae4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 40: Gradient descent methods (continued) and start Neural networks\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway and Department of Physics and Astronomy and Facility for Rare Ion Beams, Michigan State University, USA\n",
@@ -23,29 +27,37 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2d0f844",
-   "metadata": {},
+   "id": "e6b378ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 40"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c9630d37",
-   "metadata": {},
+   "id": "1ba91689",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lecture Monday September 30, 2024\n",
     "1. Stochastic Gradient descent with examples and automatic differentiation\n",
     "\n",
     "2. If we get time, we start with the basics of Neural Networks, setting up the basic steps, from the simple perceptron model to the multi-layer perceptron model\n",
-    "<!-- * [Video of lecture](https://youtu.be/75pr3hKY20U) -->\n",
-    "<!-- * \"Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesOct5.pdf> -->"
+    "\n",
+    "3. [Video of lecture](https://youtu.be/jdJoOrCIdII)\n",
+    "\n",
+    "4. Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember30.pdf>"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4b447216",
-   "metadata": {},
+   "id": "fb1da492",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Suggested readings and videos\n",
     "**Readings and Videos:**\n",
@@ -67,8 +79,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fb799c1",
-   "metadata": {},
+   "id": "5e18b164",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lab sessions Tuesday and Wednesday\n",
     "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
@@ -84,8 +98,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a202eb3",
-   "metadata": {},
+   "id": "ca1eb3e1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Summary from last week, using gradient descent methods, limitations\n",
     "\n",
@@ -104,8 +120,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0b36267",
-   "metadata": {},
+   "id": "d1832283",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Simple implementation of GD for OLS, Ridge and Lasso\n",
     "\n",
@@ -115,29 +133,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
-   "id": "2d9d73e5",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Parameters for OLS using gradient descent\n",
-      "[[4.04553909]\n",
-      " [2.85718534]\n",
-      " [5.07124072]]\n",
-      "Parameters for Ridge using gradient descent\n",
-      "[[3.8048267 ]\n",
-      " [3.33344121]\n",
-      " [4.85905287]]\n",
-      "Parameters for Lasso using gradient descent\n",
-      "[[3.87867385]\n",
-      " [3.192587  ]\n",
-      " [4.93045409]]\n"
-     ]
-    }
-   ],
+   "execution_count": 1,
+   "id": "0dee3b51",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "from random import random, seed\n",
     "import numpy as np\n",
@@ -186,8 +188,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcf0f686",
-   "metadata": {},
+   "id": "cda18663",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## But none of these can compete with Newton's method\n",
     "\n",
@@ -196,30 +200,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
-   "id": "1550b223",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.]\n",
-      " [3.]\n",
-      " [5.]]\n",
-      "0 [-26.91927647] [-35.76071889]\n",
-      "1 [-6.07158768e-14] [-1.55935271e-13]\n",
-      "2 [-6.03961325e-16] [-9.79527859e-16]\n",
-      "3 [-1.54543045e-15] [-2.38042396e-15]\n",
-      "4 [1.27897692e-15] [1.94409177e-15]\n",
-      "beta from own Newton code\n",
-      "[[4.]\n",
-      " [3.]\n",
-      " [5.]]\n"
-     ]
-    }
-   ],
+   "execution_count": 2,
+   "id": "e1e51c75",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Newton's method\n",
     "from random import random, seed\n",
@@ -258,8 +245,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1777d437",
-   "metadata": {},
+   "id": "8de3d7c1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Gradient descent and Logistic regression\n",
     "\n",
@@ -270,18 +259,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
-   "id": "94a3c22b",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Predictions: [1, 1, 1, 1]\n"
-     ]
-    }
-   ],
+   "execution_count": 3,
+   "id": "4f87ae26",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "class LogisticRegression:\n",
@@ -318,8 +302,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d9bd47b",
-   "metadata": {},
+   "id": "c2781943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Overview video on Stochastic Gradient Descent\n",
     "\n",
@@ -335,8 +321,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0107149a",
-   "metadata": {},
+   "id": "1e37491a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Batches and mini-batches\n",
     "\n",
@@ -354,8 +342,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "acb322f8",
-   "metadata": {},
+   "id": "6feab258",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Stochastic Gradient Descent (SGD)\n",
     "\n",
@@ -384,8 +374,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9073ab44",
-   "metadata": {},
+   "id": "204c15af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Stochastic Gradient Descent\n",
     "\n",
@@ -399,8 +391,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a457a90",
-   "metadata": {},
+   "id": "c9453416",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n",
@@ -410,8 +404,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be758e1d",
-   "metadata": {},
+   "id": "19b0403c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Computation of gradients\n",
     "\n",
@@ -421,8 +417,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "411db876",
-   "metadata": {},
+   "id": "37025507",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
@@ -432,8 +430,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c23bb658",
-   "metadata": {},
+   "id": "cc7aaec1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Stochasticity/randomness is introduced by only taking the\n",
     "gradient on a subset of the data called minibatches.  If there are $n$\n",
@@ -444,8 +444,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adea87fe",
-   "metadata": {},
+   "id": "3a3a0d11",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## SGD example\n",
     "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n",
@@ -464,8 +466,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e5dee91",
-   "metadata": {},
+   "id": "0acfc986",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\nabla_{\\beta}\n",
@@ -477,8 +481,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97047a5f",
-   "metadata": {},
+   "id": "8d3f995d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The gradient step\n",
     "\n",
@@ -487,8 +493,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9a59d5c",
-   "metadata": {},
+   "id": "8c73ac82",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
@@ -498,8 +506,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9b20c1c",
-   "metadata": {},
+   "id": "f88656c1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $k$ is picked at random with equal\n",
     "probability from $[1,n/M]$. An iteration over the number of\n",
@@ -510,17 +520,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3867a529",
-   "metadata": {},
+   "id": "e80a498f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Simple example code"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
-   "id": "e5f4f9a8",
-   "metadata": {},
+   "execution_count": 4,
+   "id": "626ac884",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import numpy as np \n",
@@ -541,8 +556,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "786c5900",
-   "metadata": {},
+   "id": "3c9a754d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Taking the gradient only on a subset of the data has two important\n",
     "benefits. First, it introduces randomness which decreases the chance\n",
@@ -555,8 +572,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f510fcf",
-   "metadata": {},
+   "id": "2790ab60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## When do we stop?\n",
     "\n",
@@ -574,8 +593,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f0043c6",
-   "metadata": {},
+   "id": "3ea3ee12",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Slightly different approach\n",
     "\n",
@@ -592,8 +613,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbc5d941",
-   "metadata": {},
+   "id": "3c39cc08",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Time decay rate\n",
     "\n",
@@ -608,18 +631,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
-   "id": "f96c423d",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "gamma_j after 500 epochs: 9.97108e-05\n"
-     ]
-    }
-   ],
+   "execution_count": 5,
+   "id": "294edbef",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import numpy as np \n",
     "\n",
@@ -649,8 +667,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdf1efeb",
-   "metadata": {},
+   "id": "f60f930b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Code with a Number of Minibatches which varies\n",
     "\n",
@@ -659,37 +679,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
-   "id": "e221b4f3",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[3.8913351 ]\n",
-      " [2.83275949]]\n",
-      "Eigenvalues of Hessian Matrix:[0.33918672 3.94965845]\n",
-      "theta from own gd\n",
-      "[[3.8913351 ]\n",
-      " [2.83275949]]\n",
-      "theta from own sdg\n",
-      "[[3.9644494 ]\n",
-      " [2.80907715]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": 6,
+   "id": "41a929b5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "%matplotlib inline\n",
     "\n",
@@ -763,8 +759,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e858f37",
-   "metadata": {},
+   "id": "af8f3db9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Replace or not\n",
     "\n",
@@ -776,8 +774,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7dace8c0",
-   "metadata": {},
+   "id": "ce1d1147",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Momentum based GD\n",
     "\n",
@@ -789,8 +789,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd079d0",
-   "metadata": {},
+   "id": "b8750f09",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
@@ -799,8 +801,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "305a75c3",
-   "metadata": {},
+   "id": "6b18d51a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -815,8 +819,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "026d8598",
-   "metadata": {},
+   "id": "efa3113f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have introduced a momentum parameter $\\gamma$, with\n",
     "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
@@ -832,8 +838,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80e73593",
-   "metadata": {},
+   "id": "2007f72c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
@@ -842,16 +850,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a5b87d4",
-   "metadata": {},
+   "id": "149a0faa",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f9bbf0cd",
-   "metadata": {},
+   "id": "3930d988",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More on momentum based approaches\n",
     "\n",
@@ -864,8 +876,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e7986cc",
-   "metadata": {},
+   "id": "8560c22c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
@@ -874,16 +888,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50d69000",
-   "metadata": {},
+   "id": "6f4563fe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We can discretize this equation in the usual way to get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e7d9df0a",
-   "metadata": {},
+   "id": "8fe2b7ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
@@ -892,16 +910,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6f67ad8",
-   "metadata": {},
+   "id": "207eae67",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Rearranging this equation, we can rewrite this as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "443f0b02",
-   "metadata": {},
+   "id": "9770730e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
@@ -910,8 +932,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d89ab74d",
-   "metadata": {},
+   "id": "c233679d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Momentum parameter\n",
     "\n",
@@ -924,8 +948,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3401047f",
-   "metadata": {},
+   "id": "cf54be10",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
@@ -934,8 +960,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7c24040",
-   "metadata": {},
+   "id": "35f187e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Thus, as the name suggests, the momentum parameter is proportional to\n",
     "the mass of the particle and effectively provides inertia.\n",
@@ -965,8 +993,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22e04f6c",
-   "metadata": {},
+   "id": "476338d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
@@ -975,8 +1005,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65b1fa09",
-   "metadata": {},
+   "id": "c23f6df7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -991,16 +1023,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7acccb8b",
-   "metadata": {},
+   "id": "e36c0680",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "795e6ab5",
-   "metadata": {},
+   "id": "484048bb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Second moment of the gradient\n",
     "\n",
@@ -1028,8 +1064,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dec5061d",
-   "metadata": {},
+   "id": "ed915ab1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMS prop\n",
     "\n",
@@ -1041,8 +1079,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3dfb0934",
-   "metadata": {},
+   "id": "c4d8b1a8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto3\"></div>\n",
@@ -1057,8 +1097,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf4b7a89",
-   "metadata": {},
+   "id": "6819d54f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
@@ -1067,8 +1109,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "510c8591",
-   "metadata": {},
+   "id": "c38fa00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
@@ -1077,8 +1121,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a0e569f",
-   "metadata": {},
+   "id": "7ff83ef0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\beta$ controls the averaging time of the second moment and is\n",
     "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n",
@@ -1093,8 +1139,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "977c9c79",
-   "metadata": {},
+   "id": "ba98f789",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n",
     "\n",
@@ -1120,8 +1168,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d188330b",
-   "metadata": {},
+   "id": "03428756",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto4\"></div>\n",
@@ -1136,8 +1186,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "776b649a",
-   "metadata": {},
+   "id": "ef5b461b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
@@ -1146,8 +1198,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f8a0d72",
-   "metadata": {},
+   "id": "0149850a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
@@ -1156,8 +1210,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53f1a2ce",
-   "metadata": {},
+   "id": "4ae41be8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
@@ -1166,8 +1222,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc7cd55a",
-   "metadata": {},
+   "id": "5d36d54a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
@@ -1176,8 +1234,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6bd6e651",
-   "metadata": {},
+   "id": "08eb5528",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
@@ -1186,8 +1246,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "677f1aef",
-   "metadata": {},
+   "id": "4a5e4b7b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto5\"></div>\n",
@@ -1201,8 +1263,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bb1d86d",
-   "metadata": {},
+   "id": "b71679d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n",
     "second moment and are typically taken to be $0.9$ and $0.99$\n",
@@ -1218,8 +1282,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "812cca90",
-   "metadata": {},
+   "id": "a9910c4b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 +  m_t^2 }+\\epsilon}.\n",
@@ -1228,8 +1294,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51ddf251",
-   "metadata": {},
+   "id": "85d963d2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
     "\n",
@@ -1240,8 +1308,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "676bc1af",
-   "metadata": {},
+   "id": "bc9de56d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## AdaGrad algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1254,8 +1324,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e0a4bd5",
-   "metadata": {},
+   "id": "e6293208",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMSProp algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1268,8 +1340,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9eccc07",
-   "metadata": {},
+   "id": "40fde17d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## ADAM algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1282,8 +1356,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b81a38cf",
-   "metadata": {},
+   "id": "f9066e5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Practical tips\n",
     "\n",
@@ -1300,8 +1376,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2be4b8ad",
-   "metadata": {},
+   "id": "cfac43d8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Automatic differentiation\n",
     "\n",
@@ -1336,8 +1414,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78ce59cc",
-   "metadata": {},
+   "id": "6c1afa20",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
@@ -1346,16 +1426,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1de3aaf",
-   "metadata": {},
+   "id": "4c038cf3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which has the following derivative"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "99aa41ec",
-   "metadata": {},
+   "id": "eed0ca87",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n",
@@ -1364,36 +1448,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76989f22",
-   "metadata": {},
+   "id": "3f493ed1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Using **autograd** we have"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
-   "id": "b9cd37f2",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The max absolute difference is: 1.77636e-15\n"
-     ]
-    }
-   ],
+   "execution_count": 7,
+   "id": "f42e9964",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "\n",
@@ -1433,8 +1504,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f495197",
-   "metadata": {},
+   "id": "9a9dd7cb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using autograd\n",
     "\n",
@@ -1447,19 +1520,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
-   "id": "3e79535c",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The gradient of f1 evaluated at a = 1 using autograd is: 3\n",
-      "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n"
-     ]
-    }
-   ],
+   "execution_count": 8,
+   "id": "f5d99737",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -1482,8 +1549,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d764d7c",
-   "metadata": {},
+   "id": "1a033f2a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Autograd with more complicated functions\n",
     "\n",
@@ -1494,24 +1563,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
-   "id": "b171c0bc",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Evaluating at x1 = 1, x2 = 3\n",
-      "------------------------------\n",
-      "The derivative of f2 w.r.t x1: 12\n",
-      "The analytical derivative of f2 w.r.t x1: 12\n",
-      "\n",
-      "The derivative of f2 w.r.t x2: -4\n",
-      "The analytical derivative of f2 w.r.t x2: -4\n"
-     ]
-    }
-   ],
+   "execution_count": 9,
+   "id": "36ba3883",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -1550,25 +1608,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65098808",
-   "metadata": {},
+   "id": "98a7ad40",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5d60df18",
-   "metadata": {},
+   "id": "a840a46c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More complicated functions using the elements of their arguments directly"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
-   "id": "cc4cc7eb",
-   "metadata": {},
+   "execution_count": 10,
+   "id": "0ce16fc4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1592,8 +1657,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d71a9a54",
-   "metadata": {},
+   "id": "470f7e16",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that in this case, when sending an array as input argument, the\n",
     "output from Autograd is another array. This is the true gradient of\n",
@@ -1605,17 +1672,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "290988a2",
-   "metadata": {},
+   "id": "4d7c7e61",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Functions using mathematical functions from Numpy"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
-   "id": "4afa9fe3",
-   "metadata": {},
+   "execution_count": 11,
+   "id": "69eceec6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1639,17 +1711,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec23dce0",
-   "metadata": {},
+   "id": "02192e06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More autograd"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
-   "id": "be794060",
-   "metadata": {},
+   "execution_count": 12,
+   "id": "6f5d7fa7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1670,17 +1747,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d8e15c2",
-   "metadata": {},
+   "id": "25b7c609",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And  with loops"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
-   "id": "d696c96c",
-   "metadata": {},
+   "execution_count": 13,
+   "id": "043eb7de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1711,9 +1793,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
-   "id": "5cdbff7d",
-   "metadata": {},
+   "execution_count": 14,
+   "id": "880bc7f0",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1729,17 +1814,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec95c41c",
-   "metadata": {},
+   "id": "322163dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using recursion"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "id": "06c8423e",
-   "metadata": {},
+   "execution_count": 15,
+   "id": "09f1a79b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1773,16 +1863,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4675445a",
-   "metadata": {},
+   "id": "33d9596d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3ea2267f",
-   "metadata": {},
+   "id": "2b87a3af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Autograd with OLS\n",
     "\n",
@@ -1793,34 +1887,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
-   "id": "49c5a124",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[3.98094809]\n",
-      " [3.10504501]]\n",
-      "Eigenvalues of Hessian Matrix:[0.27678028 4.83090115]\n",
-      "theta from own gd\n",
-      "[[3.98094809]\n",
-      " [3.10504501]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": 16,
+   "id": "4674f449",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients for OLS\n",
     "from random import random, seed\n",
@@ -1875,95 +1948,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f952160a",
-   "metadata": {},
+   "id": "7c4e2d90",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Same code but now with momentum gradient descent"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
-   "id": "b0595e43",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.]\n",
-      " [3.]]\n",
-      "Eigenvalues of Hessian Matrix:[0.25823312 3.94225609]\n",
-      "0 [-12.96884773] [-13.21205258]\n",
-      "1 [-0.22528633] [0.21334212]\n",
-      "2 [-0.21052919] [0.19936738]\n",
-      "3 [-0.19673871] [0.18630804]\n",
-      "4 [-0.18385156] [0.17410414]\n",
-      "5 [-0.17180857] [0.16269964]\n",
-      "6 [-0.16055444] [0.15204218]\n",
-      "7 [-0.1500375] [0.14208282]\n",
-      "8 [-0.14020946] [0.13277585]\n",
-      "9 [-0.13102519] [0.12407851]\n",
-      "10 [-0.12244253] [0.11595089]\n",
-      "11 [-0.11442207] [0.10835565]\n",
-      "12 [-0.10692698] [0.10125793]\n",
-      "13 [-0.09992285] [0.09462515]\n",
-      "14 [-0.09337751] [0.08842683]\n",
-      "15 [-0.08726092] [0.08263453]\n",
-      "16 [-0.08154499] [0.07722165]\n",
-      "17 [-0.07620348] [0.07216333]\n",
-      "18 [-0.07121185] [0.06743635]\n",
-      "19 [-0.0665472] [0.063019]\n",
-      "20 [-0.0621881] [0.05889101]\n",
-      "21 [-0.05811453] [0.05503342]\n",
-      "22 [-0.05430781] [0.05142852]\n",
-      "23 [-0.05075043] [0.04805975]\n",
-      "24 [-0.04742608] [0.04491165]\n",
-      "25 [-0.04431949] [0.04196976]\n",
-      "26 [-0.04141639] [0.03922058]\n",
-      "27 [-0.03870346] [0.03665148]\n",
-      "28 [-0.03616823] [0.03425066]\n",
-      "29 [-0.03379907] [0.03200711]\n",
-      "theta from own gd\n",
-      "[[3.87768766]\n",
-      " [3.1158276 ]]\n",
-      "0 [-0.0315851] [0.02991052]\n",
-      "1 [-0.02951615] [0.02795127]\n",
-      "2 [-0.02696204] [0.02553257]\n",
-      "3 [-0.02442969] [0.02313448]\n",
-      "4 [-0.02206975] [0.02089966]\n",
-      "5 [-0.01991611] [0.0188602]\n",
-      "6 [-0.01796544] [0.01701295]\n",
-      "7 [-0.01620343] [0.01534436]\n",
-      "8 [-0.01461344] [0.01383866]\n",
-      "9 [-0.0131792] [0.01248047]\n",
-      "10 [-0.01188564] [0.01125549]\n",
-      "11 [-0.01071902] [0.01015072]\n",
-      "12 [-0.0096669] [0.00915438]\n",
-      "13 [-0.00871804] [0.00825583]\n",
-      "14 [-0.00786232] [0.00744547]\n",
-      "15 [-0.00709059] [0.00671466]\n",
-      "16 [-0.00639461] [0.00605558]\n",
-      "17 [-0.00576694] [0.00546119]\n",
-      "18 [-0.00520089] [0.00492515]\n",
-      "19 [-0.00469039] [0.00444172]\n",
-      "20 [-0.00423] [0.00400574]\n",
-      "21 [-0.0038148] [0.00361255]\n",
-      "22 [-0.00344036] [0.00325796]\n",
-      "23 [-0.00310267] [0.00293817]\n",
-      "24 [-0.00279813] [0.00264978]\n",
-      "25 [-0.00252348] [0.00238969]\n",
-      "26 [-0.00227578] [0.00215513]\n",
-      "27 [-0.0020524] [0.00194359]\n",
-      "28 [-0.00185095] [0.00175281]\n",
-      "29 [-0.00166927] [0.00158077]\n",
-      "theta from own gd wth momentum\n",
-      "[[3.99417031]\n",
-      " [3.00552061]]\n"
-     ]
-    }
-   ],
+   "execution_count": 17,
+   "id": "be5e6b23",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients for OLS\n",
     "from random import random, seed\n",
@@ -2022,8 +2023,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43200e36",
-   "metadata": {},
+   "id": "0002f816",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Including Stochastic Gradient Descent with Autograd\n",
     "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
@@ -2031,43 +2034,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
-   "id": "b369d846",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.23287562]\n",
-      " [2.86347636]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31306035 4.34432759]\n",
-      "theta from own gd\n",
-      "[[4.23287562]\n",
-      " [2.86347636]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "theta from own sdg\n",
-      "[[4.25869167]\n",
-      " [2.84271642]]\n"
-     ]
-    }
-   ],
+   "execution_count": 18,
+   "id": "ccb60a39",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using SGD\n",
     "# OLS example\n",
@@ -2146,35 +2119,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1caa8279",
-   "metadata": {},
+   "id": "502d537b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Same code but now with momentum gradient descent"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
-   "id": "a9695688",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[3.96584049]\n",
-      " [3.04808331]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31564325 4.60725403]\n",
-      "theta from own gd\n",
-      "[[3.96536405]\n",
-      " [3.04846625]]\n",
-      "theta from own sdg with momentum\n",
-      "[[4.01326831]\n",
-      " [3.04081676]]\n"
-     ]
-    }
-   ],
+   "execution_count": 19,
+   "id": "d62b1fd8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using SGD\n",
     "# OLS example\n",
@@ -2247,33 +2208,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e8ab93f",
-   "metadata": {},
+   "id": "ab2dfdcf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Similar (second order function now) problem but now with AdaGrad"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
-   "id": "be9894c6",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[2.]\n",
-      " [3.]\n",
-      " [4.]]\n",
-      "theta from own AdaGrad\n",
-      "[[1.99993955]\n",
-      " [3.00039584]\n",
-      " [3.99962062]]\n"
-     ]
-    }
-   ],
+   "execution_count": 20,
+   "id": "24784ec8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
     "# OLS example\n",
@@ -2327,41 +2278,33 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c181ef",
-   "metadata": {},
+   "id": "b525a878",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Running this code we note an almost perfect agreement with the results from matrix inversion."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3f40101d",
-   "metadata": {},
+   "id": "f3de5529",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
-   "id": "da9f2895",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[2.]\n",
-      " [3.]\n",
-      " [4.]]\n",
-      "theta from own RMSprop\n",
-      "[[1.99943878]\n",
-      " [2.99892878]\n",
-      " [3.99871777]]\n"
-     ]
-    }
-   ],
+   "execution_count": 21,
+   "id": "770a0f44",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
     "# OLS example\n",
@@ -2421,33 +2364,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2075df0a",
-   "metadata": {},
+   "id": "2cf458d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
-   "id": "b9e0fd59",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[2.]\n",
-      " [3.]\n",
-      " [4.]]\n",
-      "theta from own ADAM\n",
-      "[[1.99994314]\n",
-      " [3.00031228]\n",
-      " [3.99972037]]\n"
-     ]
-    }
-   ],
+   "execution_count": 22,
+   "id": "ebe031fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
     "# OLS example\n",
@@ -2512,17 +2445,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3186664b",
-   "metadata": {},
+   "id": "df82f58c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And Logistic Regression"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
-   "id": "c4119a68",
-   "metadata": {},
+   "execution_count": 23,
+   "id": "23a3aae7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2562,8 +2500,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e182eb",
-   "metadata": {},
+   "id": "04692c2e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
     "\n",
@@ -2576,17 +2516,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae059fd0",
-   "metadata": {},
+   "id": "c9531ff9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Getting started with Jax, note the way we import numpy"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
-   "id": "1ad5b0d3",
-   "metadata": {},
+   "execution_count": 24,
+   "id": "1082677a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import jax\n",
@@ -2599,17 +2544,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc8fd16c",
-   "metadata": {},
+   "id": "ddab1050",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### A warm-up example"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
-   "id": "443386ca",
-   "metadata": {},
+   "execution_count": 25,
+   "id": "9a64315e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "def function(x):\n",
@@ -2650,17 +2600,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b313e4d6",
-   "metadata": {},
+   "id": "fbaa615b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### A more advanced example"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
-   "id": "7ff7b64d",
-   "metadata": {},
+   "execution_count": 26,
+   "id": "6400dac8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "backend = np\n",
@@ -2687,8 +2642,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b913d744",
-   "metadata": {},
+   "id": "b7cd2078",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Introduction to Neural networks\n",
     "\n",
@@ -2703,8 +2660,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04b70882",
-   "metadata": {},
+   "id": "4b41d4a3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Artificial neurons\n",
     "\n",
@@ -2725,8 +2684,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44405ff2",
-   "metadata": {},
+   "id": "05bbca92",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"artificialNeuron\"></div>\n",
@@ -2741,8 +2702,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b39653f7",
-   "metadata": {},
+   "id": "63e4ecd2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here, the output $y$ of the neuron is the value of its activation function, which have as input\n",
     "a weighted sum of signals $x_i, \\dots ,x_n$ received by $n$ other neurons.\n",
@@ -2779,8 +2742,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4db5fb89",
-   "metadata": {},
+   "id": "16405c0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Neural network types\n",
     "\n",
@@ -2806,8 +2771,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "400c590f",
-   "metadata": {},
+   "id": "49a77aeb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Feed-forward neural networks\n",
     "\n",
@@ -2825,8 +2792,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1536d443",
-   "metadata": {},
+   "id": "4408658f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Convolutional Neural Network\n",
     "\n",
@@ -2852,8 +2821,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ce4aacc",
-   "metadata": {},
+   "id": "cf8d97ad",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Recurrent neural networks\n",
     "\n",
@@ -2871,8 +2842,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c187a3e9",
-   "metadata": {},
+   "id": "3cc3819b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Other types of networks\n",
     "\n",
@@ -2890,8 +2863,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a5d9c4f",
-   "metadata": {},
+   "id": "920fd548",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Multilayer perceptrons\n",
     "\n",
@@ -2905,8 +2880,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2abe1a3e",
-   "metadata": {},
+   "id": "d08f461e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why multilayer perceptrons?\n",
     "\n",
@@ -2924,8 +2901,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "187cb30d",
-   "metadata": {},
+   "id": "dc59c40b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Illustration of a single perceptron model and a multi-perceptron model\n",
     "\n",
@@ -2938,8 +2917,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6269f804",
-   "metadata": {},
+   "id": "89c1b368",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Examples of XOR, OR and AND gates\n",
     "\n",
@@ -2952,9 +2933,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
-   "id": "1ad6269c",
-   "metadata": {},
+   "execution_count": 27,
+   "id": "f2a213fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"\n",
@@ -2991,25 +2975,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4ac557d",
-   "metadata": {},
+   "id": "046c878f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "What is happening here?"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6c5b5b78",
-   "metadata": {},
+   "id": "8dbddf81",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Does Logistic Regression do a better Job?"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
-   "id": "78d9fe1b",
-   "metadata": {},
+   "execution_count": 28,
+   "id": "3032a2c1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"\n",
@@ -3065,25 +3056,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "522ea0b9",
-   "metadata": {},
+   "id": "ea8b4e4b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not exactly impressive, but somewhat better."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "633277bf",
-   "metadata": {},
+   "id": "ef2b283b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Adding Neural Networks"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
-   "id": "55106a0e",
-   "metadata": {},
+   "execution_count": 29,
+   "id": "7415b824",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -3099,8 +3097,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6933a546",
-   "metadata": {},
+   "id": "bbfc7004",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3109,8 +3109,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a392cc52",
-   "metadata": {},
+   "id": "973905d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "y = f\\left(\\sum_{i=1}^n w_ix_i + b_i\\right) = f(z),\n",
@@ -3119,8 +3121,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc1e3563",
-   "metadata": {},
+   "id": "9343ae60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This function receives $x_i$ as inputs.\n",
     "Here the activation $z=(\\sum_{i=1}^n w_ix_i+b_i)$. \n",
@@ -3132,8 +3136,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "947e6060",
-   "metadata": {},
+   "id": "0fcd0bdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3142,8 +3148,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "190e7764",
-   "metadata": {},
+   "id": "98e91440",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto6\"></div>\n",
@@ -3157,8 +3165,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d4df41f",
-   "metadata": {},
+   "id": "944ccc68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here $b_i$ is the so-called bias which is normally needed in\n",
     "case of zero activation weights or inputs. How to fix the biases and\n",
@@ -3170,8 +3180,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8c69c2e",
-   "metadata": {},
+   "id": "17edaee3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"outputLayer1\"></div>\n",
@@ -3186,8 +3198,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80a632b1",
-   "metadata": {},
+   "id": "dbe292f0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we assume that all nodes in the same layer have identical\n",
     "activation functions, hence the notation $f$. In general, we could assume in the more general case that different layers have different activation functions.\n",
@@ -3196,8 +3210,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20de39bb",
-   "metadata": {},
+   "id": "ab06ec71",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"generalLayer\"></div>\n",
@@ -3212,8 +3228,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01031b37",
-   "metadata": {},
+   "id": "0f069e07",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $N_l$ is the number of nodes in layer $l$. When the output of\n",
     "all the nodes in the first hidden layer are computed, the values of\n",
@@ -3223,8 +3241,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9560b5e1",
-   "metadata": {},
+   "id": "3ee71e06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3233,8 +3253,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "baaac514",
-   "metadata": {},
+   "id": "cecfe50e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto7\"></div>\n",
@@ -3249,8 +3271,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2a439d9",
-   "metadata": {},
+   "id": "dc2a6523",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"outputLayer2\"></div>\n",
@@ -3265,16 +3289,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ba7b5ad",
-   "metadata": {},
+   "id": "3f73c82a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have substituted $y_k^1$ with the inputs $x_k$. Finally, the ANN output reads"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bed342fd",
-   "metadata": {},
+   "id": "8b1a1945",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto8\"></div>\n",
@@ -3289,8 +3317,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1beb8c9",
-   "metadata": {},
+   "id": "ecd88770",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto9\"></div>\n",
@@ -3306,8 +3336,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a71895ad",
-   "metadata": {},
+   "id": "6b6ce470",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3317,8 +3349,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9bd25ff",
-   "metadata": {},
+   "id": "6e018962",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"completeNN\"></div>\n",
@@ -3333,8 +3367,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7737a5b",
-   "metadata": {},
+   "id": "bf0b66e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which illustrates a basic property of MLPs: The only independent\n",
     "variables are the input values $x_n$."
@@ -3342,8 +3378,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "384040ce",
-   "metadata": {},
+   "id": "4827bb05",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3359,8 +3397,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a27ed92",
-   "metadata": {},
+   "id": "6fc6eadd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto10\"></div>\n",
@@ -3375,8 +3415,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c71650e0",
-   "metadata": {},
+   "id": "f7c37a39",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the parameters $c_i$ are weights and biases. By adjusting these\n",
     "parameters, the activation functions can be shifted up and down or\n",
@@ -3386,8 +3428,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6291c8a",
-   "metadata": {},
+   "id": "09472aa3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Matrix-vector notation\n",
     "\n",
@@ -3404,8 +3448,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da4b43f7",
-   "metadata": {},
+   "id": "1824564d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto11\"></div>\n",
@@ -3435,8 +3481,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fe1f511",
-   "metadata": {},
+   "id": "eafbe02e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Matrix-vector notation  and activation\n",
     "\n",
@@ -3445,8 +3493,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d53241ba",
-   "metadata": {},
+   "id": "f52242e3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto12\"></div>\n",
@@ -3462,8 +3512,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "962e06e9",
-   "metadata": {},
+   "id": "72371715",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This is not just a convenient and compact notation, but also a useful\n",
     "and intuitive way to think about MLPs: The output is calculated by a\n",
@@ -3474,8 +3526,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6446fdc6",
-   "metadata": {},
+   "id": "b455d9ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -3495,8 +3549,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69aff123",
-   "metadata": {},
+   "id": "7de531f8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions, Logistic and Hyperbolic ones\n",
     "\n",
@@ -3512,8 +3568,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbb74732",
-   "metadata": {},
+   "id": "dedb08ff",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\frac{1}{1 + e^{-x}},\n",
@@ -3522,16 +3580,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "216973d6",
-   "metadata": {},
+   "id": "ed7c69c9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the *hyperbolic tangent* function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a8643aed",
-   "metadata": {},
+   "id": "37be8225",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\tanh(x)\n",
@@ -3540,8 +3602,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6450655",
-   "metadata": {},
+   "id": "a8176533",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Relevance\n",
     "\n",
@@ -3554,9 +3618,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
-   "id": "0565ead1",
-   "metadata": {},
+   "execution_count": 30,
+   "id": "1b3252bc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"The sigmoid function (or the logistic curve) is a \n",
@@ -3633,25 +3700,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
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-    "name": "ipython",
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-   "mimetype": "text/x-python",
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-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.18"
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+ "metadata": {},
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 }
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index f8b8c58a4..d40c99bc5 100644
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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural 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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks"],titleterms:{"1":[0,15,16,17,18,23,28,29],"16":32,"2":[0,15,16,17,18,28,29,30],"2023":26,"2024":[23,33,34],"21":[],"23":33,"26":29,"27":33,"3":[0,15,16,28,29],"30":34,"34":[15,28],"35":[16,29],"36":[17,30],"37":[18,31],"38":[19,32],"39":[20,33],"4":[0,29],"40":34,"5":0,"7":23,"9":31,"case":[8,10,25,29,30,32,33],"class":32,"do":[1,30,31,33,34],"final":[12,29,30,33,34],"function":[0,1,6,7,8,10,11,12,13,23,25,28,29,30,31,32,33,34],"import":[5,22,28,29,30,34],"new":[4,30,31],A:[0,1,4,8,9,28,30,31,32,34],AND:34,And:[28,29,30,32,33,34],But:[33,34],For:29,In:26,Ising:6,OR:34,The:[0,1,2,3,5,6,7,8,9,11,12,17,21,28,29,30,31,32,33,34],To:[28,29],With:[4,30],about:[28,29],abov:30,activ:[1,12,30,34],ad:[0,6,17,23,28,29,34],adaboost:10,adagrad:[13,33,34],adam:[13,33,34],adapt:[10,33,34],adjust:1,advanc:34,adversari:4,again:[3,9,32],ai:[23,28],aim:[8,9,17,18,19,20,28],aka:[28,29],al:34,algebra:[22,28],algorithm:[9,10,11,12,29,33,34],algortithm:[13,32,33],all:8,an:[0,4,10,28],analys:[5,29],analysi:[0,5,6,11,21,23,25,28,29,30,31],analyt:[0,16,17],ani:[13,32,33],anoth:[9,30,31],appli:21,approach:[0,8,14,28,31,33,34],approxim:12,architectur:1,argument:[33,34],arrai:[22,28],artifici:34,assist:26,assumpt:[30,31],august:29,autocorrel:25,autograd:[2,13,33,34],automat:[13,33,34],avoid:[],b:[17,23,33],back:[1,11,12],background:[21,23,31],bag:10,base:[13,31,33,34],basic:[0,5,7,9,10,11,22,29,30,31,32],batch:[1,33,34],bay:[5,30,31],befor:11,beta:[30,31],better:[8,34],bia:[6,23,31],binari:1,bind:28,bird:10,boldsymbol:[29,30,31],boost:10,bootstrap:[6,10,31],boston:0,breast:1,brief:[28,31,32,33],bring:12,build:[1,3,9],c:[23,28],calcul:29,can:[28,31,33,34],cancer:[1,7,9,11,32],cart:9,center:29,central:[13,21,25,31,32,33],chain:12,challeng:32,chang:10,channel:28,chi:[0,28],choos:1,cifar01:3,classic:11,classif:[1,9,10,32],classifi:[8,32],clip:1,cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,28,29,30,31,32,33,34],collect:[1,3],come:32,commun:28,compact:32,compar:[2,10],comparison:30,compet:[33,34],complet:29,complex:[0,6,23,29],complic:[6,33,34],compon:11,comput:[9,33,34],computation:31,computerlab:28,con:9,concept:25,condit:[30,31,32,33],confid:31,conjug:[13,33],continu:34,contn:28,convex:[8,13,32,33],convolut:[3,12,34],correctli:[30,31],correl:[11,29,32],correspond:[32,33],cost:[1,10,29,30,31,32,33],cours:[21,27,28],covari:[5,11,25,29],cover:28,cross:[6,23,31,32],cython:28,d:23,data:[0,1,3,6,7,9,11,15,16,21,23,25,28,29,30,32],dataset:[1,3],deadlin:[23,28],decai:[2,33,34],decis:[9,10],decomposit:[5,11,17,22,29],deep:[1,2,28,32],defin:[1,28],degre:[0,29],deliveri:23,delta:31,dens:[0,28],deriv:[5,12,29,30,31,32,33],descent:[2,10,13,32,33,34],descript:23,design:29,detail:[3,28],develop:1,diagon:11,differ:[8,33,34],differenti:[2,13,33,34],diffus:2,dimension:[2,3,8,23,29],directli:[33,34],disadvantag:9,discret:25,discuss:32,distribut:[5,25,30,31],distrubut:31,doe:[29,30,34],domain:25,dot:33,down:1,dropout:1,e:23,each:32,economi:29,electron:23,element:[0,25,28,33,34],elimin:22,energi:28,ensembl:10,entropi:[9,32],environ:[0,15,28],equat:[0,2,12,28,29,30,32,33],error:[0,10,28,29,31],essenti:28,estim:[30,31],et:34,etc:28,euler:2,evalu:1,exampl:[0,1,2,3,4,6,7,8,9,10,28,29,30,31,32,33,34],exercis:[0,6,15,16,17,18,19,20,28,29],expect:[18,25,30,31],expens:31,experi:25,explor:[0,15,16,28],exponenti:2,express:[17,18,29,32,33],extend:[32,33],extrapol:4,extrem:[10,28],ey:10,f:23,fall:26,famili:[1,28,29],famou:22,fantast:29,featur:[9,22,29],feed:[1,12,34],find:[31,33],fine:1,first:[4,12,28,29,30,32,33],fit:[0,10,28,30],fix:29,fold:[31,32],forc:3,forest:10,format:[23,28],forward:[1,2,12,34],fourier:3,frank:[6,23,29],freedom:[0,29],frequent:29,frequentist:[0,28],fridai:[],from:[5,10,12,29,30,31,32,33,34],full:2,further:[3,5,29],g:23,gan:4,gate:34,gaussian:22,gd:[13,33,34],gener:[4,9,28],geometr:[11,32,33],get:34,gini:9,good:[0,28],goodfellow:34,grade:[26,28],gradient:[1,2,10,13,32,33,34],grid:32,group:32,growth:2,ha:21,handl:[22,28,29],happen:[30,31],hessian:[29,32,33],hidden:2,histogram:31,homework:[32,33],hous:0,how:32,hyperbol:34,hyperparamet:1,hyperplan:8,i:1,id3:9,idea:11,ideal:[32,33],ident:[30,31],identifi:31,ii:28,iid:[30,31],illustr:[30,34],implement:[1,34],implic:[5,29],improv:[1,33],includ:[13,32,33,34],increment:11,independ:[30,31],index:9,inform:26,input:2,instal:[21,23,28],instructor:26,intercept:29,interpret:[5,11,28,29,30,31,32,33],interv:31,introduc:[11,13,29,33,34],introduct:[0,6,21,22,23,28,34],invers:[5,22,30],invert:29,iter:[10,33],its:29,jacobian:29,jax:[13,33,34],job:34,julia:28,jungl:10,k:[31,32],kera:[1,3],kernel:[8,11],lab:[31,32,33,34],lagrangian:8,lambda:32,lasso:[5,6,23,29,30,31,32,34],last:[29,32,34],later:[5,29],layer:[1,2,3,12],learn:[0,1,2,11,13,14,15,16,21,23,28,29,30,31,32,33,34],least:[5,6,18,23,28,29,30],lectur:[28,29,30,31,32,33,34],level:10,librari:[21,28],likelihood:[7,30,31,32],limit:[1,13,25,31,32,33,34],linear:[0,8,13,22,28,29,30,32],link:[5,11,24,27,29,30,31],literatur:23,logist:[7,28,32,33,34],loop:[33,34],loss:[29,32,33],lu:22,machin:[0,8,13,21,23,28,32,33],made:[30,31],main:[25,28],make:[0,9,10,15,16,28,29],mani:[10,12],manipul:29,margin:[30,31],mass:28,materi:[23,24,28,29,30,31,32],math:[5,29],mathemat:[3,5,8,29,33,34],matric:[5,22,28,30],matrix:[1,5,11,12,22,28,29,30,32,33,34],matter:[0,28],max:29,maximum:[30,31,32],mean:[0,29,30,32],measur:32,meet:[5,10,25,28,29],mercer:8,method:[6,9,10,13,23,28,31,32,33,34],midnight:23,min:29,mini:[33,34],minibatch:[33,34],minim:[28,32],ml:28,mle:[30,31],mlp:12,mnist:[3,4],model:[0,1,4,6,12,28,34],moment:[33,34],momentum:[13,33,34],mondai:[29,30,31,32,33,34],moon:[8,9],more:[3,6,22,23,28,29,30,31,32,33,34],multi:34,multilay:[12,34],multipl:[1,3],multipli:8,need:[23,28],network:[1,2,3,4,7,12,28,32,34],neural:[1,2,3,4,7,12,28,34],neuron:34,newton:[32,33,34],noen:[],non:8,none:[33,34],normal:[0,1,31],notat:[12,34],note:[23,29,30,34],now:[1,9,13,30,31,33,34],nuclear:[0,28],nueral:32,numba:28,number:[0,2,25,29,33,34],numer:[2,23,25],numpi:[22,28,33,34],object:3,obtain:11,octob:23,od:2,off:[6,23],ol:[5,6,23,30,31,33,34],one:[2,12,32,33],ones:34,oper:22,optim:[1,8,13,21,28,29,32,33,34],order:[13,33,34],ordinari:[5,6,18,23,28,29,30],organ:[0,28],oslo:27,other:[4,9,11,12,22,23,28,29,32,34],our:[0,4,5,11,13,28,29,32,33],outcom:[21,28],output:2,overarch:[0,4,8,9,17,18,19,20,28,29],overview:[10,28,33,34],own:[0,10,11,15,16,28,29],packag:[22,28],panda:[28,29],paper:23,paramet:[28,29,32,33,34],part:[13,21,23,29,32,33],partial:2,pass:1,pca:11,pdf:25,pencil:23,perceptron:[12,34],perform:[1,9],period:3,perspect:1,plan:[29,30,31,32,33,34],plot:[31,32],point:4,poisson:2,polynomi:[3,30],popul:2,popular:28,practic:[13,26,28,33,34],pre:[1,3],preambl:23,predict:4,predictor:32,preprocess:29,prerequisit:[3,21,28],princip:11,principl:3,pro:9,probabl:[5,25,30,31],problem:[1,2,13,28,29,30,32,33,34],procedur:[9,28],process:[1,3],product:33,program:[2,13,23,32,33],project:[6,23,28,32],prop:[13,33,34],propag:[1,12],properti:[5,25,29,32],python:[0,9,15,21,22,28],quick:8,r:28,random:[10,11,25,32],raphson:[32,33],rate:[33,34],read:[9,28,29,31,32,34],real:[6,23,28],recommend:[28,29],rectangular:30,recurr:[4,12,34],recurs:[33,34],reduc:[0,29],reduct:3,refer:23,reformul:2,regress:[0,5,6,7,9,10,13,17,18,23,28,29,30,31,32,33,34],regular:[1,32],relat:29,relev:[27,29,32,34],relu:1,remark:3,remind:[6,8,28,32,33],repeat:29,replac:[13,33,34],report:23,repositori:31,requir:[2,21],resampl:[6,23,31],rescal:[6,30],residu:29,resourc:2,result:[29,30],revisit:[13,32,33],rewrit:[28,29,31],rewritten:32,ridg:[0,5,6,17,18,23,29,30,31,32,33,34],rm:[13,33,34],rmsprop:[33,34],rule:12,s:[8,10,31,32,33,34],same:[13,31,33,34],sampl:11,scale:29,schedul:[24,28],schemat:9,scheme:2,scienc:28,scikit:[0,1,11,15,16,28,29,30,31,32,33],search:32,second:[13,33,34],select:32,semest:26,sensit:[32,33],septemb:[30,31,32,33,34],session:[29,30,31,32,33,34],set:[0,2,3,9,12,15,28,29,32],sgd:[13,33,34],should:1,similar:[13,33,34],simpl:[0,4,9,13,28,29,30,32,33,34],singl:[10,34],singular:[5,11,17,29],size:29,slightli:[33,34],soft:8,softmax:1,softwar:[23,28],solv:[2,30,32,33],solver:13,some:[13,22,29,32,33],specifi:2,split:[0,15,16,28,29],squar:[0,5,6,10,18,23,28,29,30],standard:[13,29,31,33],start:34,state:[0,28],statist:[5,6,21,25,28,30,31],steepest:[10,13,32,33],step:[31,32,33,34],still:29,stochast:[13,25,33,34],stop:[33,34],strongli:28,studi:32,subtract:29,suggest:[28,32,34],sum:31,summari:[26,28,34],superposit:3,supervis:1,support:8,svd:[5,29,30],syntax:33,systemat:3,t:[29,30],taken:34,teach:[24,26],teacher:[26,28],technic:30,techniqu:[6,11,23],technolog:21,tensorflow:[1,3],tent:28,term:31,test:[0,1,15,16,28,29,30],text:28,textbook:[27,28],than:[32,33],theorem:[5,8,11,12,25,30,31],theori:25,thi:[17,18,19,20,28],think:29,thursdai:[],time:[33,34],tip:[13,33,34],togeth:12,tool:[23,28],top:1,topic:28,toward:11,trade:[6,23],tradeoff:[6,31],train:[0,1,4,15,16,28,29],transform:3,tree:[9,10],tuesdai:[30,34],tune:1,two:[3,8,21,23,29,32],type:[2,4,12,28,34],uio:28,understand:31,univers:[12,27],unsupervis:14,unsupport:33,up:[0,2,9,12,15,28,29,31,32,34],us:[0,1,2,3,7,13,21,23,28,29,32,33,34],usag:[30,31],valid:[6,23,31,32],valu:[5,11,17,18,25,29,30,31,32],vari:[33,34],variabl:[25,32,33],varianc:[6,23,30,31],variou:[0,15,28,31,32],vector:[8,12,22,28,29,34],video:[32,33,34],view:[0,4,10,29],visual:[1,9],vs:3,wai:[9,31,34],warm:34,wave:2,we:[28,33,34],wednesdai:[30,34],week:[15,16,17,18,19,20,28,29,30,31,32,33,34],weekend:32,weekli:24,what:[0,28,29,30,31],when:[33,34],which:[1,33,34],why:[28,29,31,34],wisconsin:[7,32],wrap:[29,31],write:[4,11,23,30],x:[29,30],xgboost:10,xor:34,yet:30,your:[0,10,15,16,28,29],yourself:32}})
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/week40.html b/doc/LectureNotes/_build/html/week40.html
index 5387fc4e3..46b7cf5fc 100644
--- a/doc/LectureNotes/_build/html/week40.html
+++ b/doc/LectureNotes/_build/html/week40.html
@@ -1197,9 +1197,10 @@ doconce format html week40.do.txt --no_mako -->
 <ol class="simple">
 <li><p>Stochastic Gradient descent with examples and automatic differentiation</p></li>
 <li><p>If we get time, we start with the basics of Neural Networks, setting up the basic steps, from the simple perceptron model to the multi-layer perceptron model</p></li>
+<li><p><a class="reference external" href="https://youtu.be/jdJoOrCIdII">Video of lecture</a></p></li>
+<li><p>Whiteboard notes at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember30.pdf">https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember30.pdf</a></p></li>
 </ol>
-<!-- * [Video of lecture](https://youtu.be/75pr3hKY20U) -->
-<!-- * "Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesOct5.pdf> --></div>
+</div>
 <div class="section" id="suggested-readings-and-videos">
 <h2>Suggested readings and videos<a class="headerlink" href="#suggested-readings-and-videos" title="Permalink to this headline">¶</a></h2>
 <p><strong>Readings and Videos:</strong></p>
@@ -1288,17 +1289,17 @@ We summarize some of these here for the methods we hvae studied in project one,
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Parameters for OLS using gradient descent
-[[3.870337  ]
- [3.34871778]
- [4.83363025]]
+[[3.53732988]
+ [4.06277313]
+ [4.51728978]]
 Parameters for Ridge using gradient descent
-[[3.66951679]
- [3.76942272]
- [4.63546236]]
+[[3.62671667]
+ [3.79849321]
+ [4.63207408]]
 Parameters for Lasso using gradient descent
-[[3.65759901]
- [3.87732748]
- [4.58735893]]
+[[4.1547556 ]
+ [2.58013829]
+ [5.20288581]]
 </pre></div>
 </div>
 </div>
@@ -1350,11 +1351,11 @@ Parameters for Lasso using gradient descent
 [[4.]
  [3.]
  [5.]]
-0 [-23.78254537] [-30.51512235]
-1 [1.30917499e-14] [-1.01327148e-14]
-2 [9.76996262e-16] [1.28164443e-15]
-3 [-7.28306304e-16] [-8.17359583e-16]
-4 [-7.63833441e-16] [-1.32422234e-15]
+0 [-27.10587277] [-37.81035098]
+1 [1.16209264e-13] [2.08824304e-13]
+2 [8.8817842e-17] [2.62242138e-16]
+3 [-1.77635684e-17] [-1.50600514e-16]
+4 [-3.37507799e-16] [-2.280464e-16]
 beta from own Newton code
 [[4.]
  [3.]
@@ -1696,15 +1697,15 @@ function.</p>
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[4.12220276]
- [2.95115528]]
-Eigenvalues of Hessian Matrix:[0.31601423 3.93074023]
+[[4.30637636]
+ [2.56947078]]
+Eigenvalues of Hessian Matrix:[0.30000613 4.12600095]
 theta from own gd
-[[4.12220276]
- [2.95115528]]
+[[4.30637636]
+ [2.56947078]]
 theta from own sdg
-[[4.12206013]
- [2.92370959]]
+[[4.34759233]
+ [2.63142731]]
 </pre></div>
 </div>
 <img alt="_images/week40_34_1.png" src="_images/week40_34_1.png" />
@@ -2418,12 +2419,12 @@ first example shows results with ordinary leats squares.</p>
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[3.62286539]
- [3.36754671]]
-Eigenvalues of Hessian Matrix:[0.30134885 4.08702578]
+[[3.88064505]
+ [2.99072374]]
+Eigenvalues of Hessian Matrix:[0.30141906 4.73853838]
 theta from own gd
-[[3.62286539]
- [3.36754671]]
+[[3.88064505]
+ [2.99072374]]
 </pre></div>
 </div>
 <img alt="_images/week40_100_1.png" src="_images/week40_100_1.png" />
@@ -2494,73 +2495,73 @@ theta from own gd
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
 [[4.]
  [3.]]
-Eigenvalues of Hessian Matrix:[0.27124938 4.56804783]
-0 [-8.64009263] [-10.94092702]
-1 [0.18925625] [-0.15527976]
-2 [0.17801827] [-0.14605929]
-3 [0.16744759] [-0.13738633]
-4 [0.1575046] [-0.12922837]
-5 [0.14815202] [-0.12155483]
-6 [0.1393548] [-0.11433693]
-7 [0.13107995] [-0.10754764]
-8 [0.12329646] [-0.10116149]
-9 [0.11597515] [-0.09515455]
-10 [0.10908858] [-0.0895043]
-11 [0.10261093] [-0.08418956]
-12 [0.09651792] [-0.07919041]
-13 [0.09078672] [-0.0744881]
-14 [0.08539583] [-0.07006502]
-15 [0.08032505] [-0.06590458]
-16 [0.07555537] [-0.06199119]
-17 [0.07106891] [-0.05831017]
-18 [0.06684886] [-0.05484773]
-19 [0.06287939] [-0.05159088]
-20 [0.05914563] [-0.04852743]
-21 [0.05563358] [-0.04564589]
-22 [0.05233008] [-0.04293545]
-23 [0.04922273] [-0.04038595]
-24 [0.0462999] [-0.03798785]
-25 [0.04355062] [-0.03573214]
-26 [0.0409646] [-0.03361037]
-27 [0.03853213] [-0.0316146]
-28 [0.03624411] [-0.02973733]
-29 [0.03409194] [-0.02797154]
+Eigenvalues of Hessian Matrix:[0.31702609 3.84351715]
+0 [-13.26083712] [-12.67834752]
+1 [-0.55020405] [0.5257011]
+2 [-0.50482139] [0.48233952]
+3 [-0.46318204] [0.44255455]
+4 [-0.42497724] [0.40605118]
+5 [-0.38992371] [0.37255873]
+6 [-0.3577615] [0.34182884]
+7 [-0.32825214] [0.31363366]
+8 [-0.30117681] [0.28776411]
+9 [-0.27633474] [0.26402837]
+10 [-0.25354173] [0.24225043]
+11 [-0.23262877] [0.22226881]
+12 [-0.21344077] [0.20393534]
+13 [-0.19583547] [0.18711407]
+14 [-0.17968231] [0.17168028]
+15 [-0.16486151] [0.15751952]
+16 [-0.15126318] [0.14452678]
+17 [-0.13878649] [0.13260573]
+18 [-0.12733892] [0.12166797]
+19 [-0.11683558] [0.11163239]
+20 [-0.10719859] [0.10242458]
+21 [-0.0983565] [0.09397626]
+22 [-0.09024373] [0.08622478]
+23 [-0.08280012] [0.07911268]
+24 [-0.07597049] [0.0725872]
+25 [-0.06970419] [0.06659997]
+26 [-0.06395476] [0.06110658]
+27 [-0.05867956] [0.0560663]
+28 [-0.05383947] [0.05144177]
+29 [-0.04939861] [0.04719868]
 theta from own gd
-[[4.11822173]
- [2.90300219]]
-0 [0.03206757] [-0.0263106]
-1 [0.03016341] [-0.02474828]
-2 [0.02780107] [-0.02281004]
-3 [0.02544154] [-0.02087411]
-4 [0.02322297] [-0.01905384]
-5 [0.02117843] [-0.01737634]
-6 [0.0193075] [-0.01584129]
-7 [0.01759974] [-0.01444013]
-8 [0.01604235] [-0.01316233]
-9 [0.01462254] [-0.01199741]
-10 [0.01332832] [-0.01093553]
-11 [0.01214862] [-0.00996762]
-12 [0.01107333] [-0.00908537]
-13 [0.01009321] [-0.00828121]
-14 [0.00919984] [-0.00754823]
-15 [0.00838555] [-0.00688012]
-16 [0.00764333] [-0.00627115]
-17 [0.0069668] [-0.00571608]
-18 [0.00635016] [-0.00521014]
-19 [0.00578809] [-0.00474898]
-20 [0.00527578] [-0.00432864]
-21 [0.00480881] [-0.0039455]
-22 [0.00438318] [-0.00359628]
-23 [0.00399521] [-0.00327797]
-24 [0.00364159] [-0.00298783]
-25 [0.00331927] [-0.00272337]
-26 [0.00302547] [-0.00248232]
-27 [0.00275768] [-0.0022626]
-28 [0.00251359] [-0.00206234]
-29 [0.00229111] [-0.0018798]
+[[3.85703369]
+ [3.13659941]]
+0 [-0.04532405] [0.04330558]
+1 [-0.04158557] [0.03973359]
+2 [-0.03703391] [0.03538463]
+3 [-0.03261373] [0.0311613]
+4 [-0.02859759] [0.02732402]
+5 [-0.02503392] [0.02391906]
+6 [-0.02189994] [0.02092464]
+7 [-0.01915337] [0.01830039]
+8 [-0.01674956] [0.01600363]
+9 [-0.01464686] [0.01399457]
+10 [-0.01280793] [0.01223754]
+11 [-0.01119981] [0.01070103]
+12 [-0.00979357] [0.00935742]
+13 [-0.0085639] [0.00818251]
+14 [-0.00748862] [0.00715512]
+15 [-0.00654835] [0.00625672]
+16 [-0.00572613] [0.00547113]
+17 [-0.00500716] [0.00478417]
+18 [-0.00437846] [0.00418347]
+19 [-0.0038287] [0.00365819]
+20 [-0.00334797] [0.00319887]
+21 [-0.0029276] [0.00279722]
+22 [-0.00256001] [0.002446]
+23 [-0.00223857] [0.00213888]
+24 [-0.0019575] [0.00187032]
+25 [-0.00171171] [0.00163548]
+26 [-0.00149679] [0.00143013]
+27 [-0.00130885] [0.00125057]
+28 [-0.00114451] [0.00109354]
+29 [-0.00100081] [0.00095624]
 theta from own gd wth momentum
-[[4.0076989 ]
- [2.99368326]]
+[[3.99723951]
+ [3.00263755]]
 </pre></div>
 </div>
 </div>
@@ -2649,18 +2650,18 @@ theta from own gd wth momentum
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[3.4870934 ]
- [3.55042779]]
-Eigenvalues of Hessian Matrix:[0.28793787 4.56453869]
+[[3.95935439]
+ [3.09360113]]
+Eigenvalues of Hessian Matrix:[0.32606139 4.1033455 ]
 theta from own gd
-[[3.4870934 ]
- [3.55042779]]
+[[3.95935439]
+ [3.09360113]]
 </pre></div>
 </div>
 <img alt="_images/week40_104_1.png" src="_images/week40_104_1.png" />
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
-[[3.48900413]
- [3.56763673]]
+[[3.96916206]
+ [3.10276112]]
 </pre></div>
 </div>
 </div>
@@ -2742,15 +2743,15 @@ theta from own gd
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[4.11571507]
- [2.86067818]]
-Eigenvalues of Hessian Matrix:[0.25849623 4.84605507]
+[[4.16532977]
+ [2.86943859]]
+Eigenvalues of Hessian Matrix:[0.29633608 4.22128142]
 theta from own gd
-[[4.10888197]
- [2.86602331]]
+[[4.16445858]
+ [2.87020155]]
 theta from own sdg with momentum
-[[4.15361856]
- [2.92376655]]
+[[4.149433  ]
+ [2.89654756]]
 </pre></div>
 </div>
 </div>
@@ -2819,9 +2820,9 @@ theta from own sdg with momentum
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
-[[1.99968451]
- [3.001795  ]
- [3.99848215]]
+[[1.99415296]
+ [3.03274273]
+ [3.96850191]]
 </pre></div>
 </div>
 </div>
@@ -2897,9 +2898,9 @@ theta from own sdg with momentum
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
-[[1.99887767]
- [3.01261048]
- [3.99294056]]
+[[2.00022969]
+ [2.99954278]
+ [4.00046631]]
 </pre></div>
 </div>
 </div>
@@ -2979,9 +2980,9 @@ theta from own sdg with momentum
 </pre></div>
 </div>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
-[[1.99996755]
- [3.00016535]
- [3.99977375]]
+[[1.99991245]
+ [3.00042721]
+ [3.99954434]]
 </pre></div>
 </div>
 </div>
@@ -3102,7 +3103,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
   return asarray(x, dtype=self.dtype)
 </pre></div>
 </div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x117c17be0&gt;]
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x11975e550&gt;]
 </pre></div>
 </div>
 <img alt="_images/week40_120_2.png" src="_images/week40_120_2.png" />
@@ -3137,7 +3138,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x117893340&gt;
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.collections.PathCollection at 0x11b160a60&gt;
 </pre></div>
 </div>
 <img alt="_images/week40_122_1.png" src="_images/week40_122_1.png" />
diff --git a/doc/LectureNotes/_build/jupyter_execute/week40.ipynb b/doc/LectureNotes/_build/jupyter_execute/week40.ipynb
index da3495a20..12f7f93f4 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week40.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week40.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "54c44098",
-   "metadata": {},
+   "id": "71c0e62a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week40.do.txt --no_mako -->\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f64073c9",
-   "metadata": {},
+   "id": "4e0afae4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 40: Gradient descent methods (continued) and start Neural networks\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway and Department of Physics and Astronomy and Facility for Rare Ion Beams, Michigan State University, USA\n",
@@ -23,29 +27,37 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2d0f844",
-   "metadata": {},
+   "id": "e6b378ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 40"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c9630d37",
-   "metadata": {},
+   "id": "1ba91689",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lecture Monday September 30, 2024\n",
     "1. Stochastic Gradient descent with examples and automatic differentiation\n",
     "\n",
     "2. If we get time, we start with the basics of Neural Networks, setting up the basic steps, from the simple perceptron model to the multi-layer perceptron model\n",
-    "<!-- * [Video of lecture](https://youtu.be/75pr3hKY20U) -->\n",
-    "<!-- * \"Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesOct5.pdf> -->"
+    "\n",
+    "3. [Video of lecture](https://youtu.be/jdJoOrCIdII)\n",
+    "\n",
+    "4. Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember30.pdf>"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4b447216",
-   "metadata": {},
+   "id": "fb1da492",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Suggested readings and videos\n",
     "**Readings and Videos:**\n",
@@ -67,8 +79,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fb799c1",
-   "metadata": {},
+   "id": "5e18b164",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lab sessions Tuesday and Wednesday\n",
     "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
@@ -84,8 +98,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a202eb3",
-   "metadata": {},
+   "id": "ca1eb3e1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Summary from last week, using gradient descent methods, limitations\n",
     "\n",
@@ -104,8 +120,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0b36267",
-   "metadata": {},
+   "id": "d1832283",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Simple implementation of GD for OLS, Ridge and Lasso\n",
     "\n",
@@ -116,25 +134,28 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "2d9d73e5",
-   "metadata": {},
+   "id": "0dee3b51",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Parameters for OLS using gradient descent\n",
-      "[[3.870337  ]\n",
-      " [3.34871778]\n",
-      " [4.83363025]]\n",
+      "[[3.53732988]\n",
+      " [4.06277313]\n",
+      " [4.51728978]]\n",
       "Parameters for Ridge using gradient descent\n",
-      "[[3.66951679]\n",
-      " [3.76942272]\n",
-      " [4.63546236]]\n",
+      "[[3.62671667]\n",
+      " [3.79849321]\n",
+      " [4.63207408]]\n",
       "Parameters for Lasso using gradient descent\n",
-      "[[3.65759901]\n",
-      " [3.87732748]\n",
-      " [4.58735893]]\n"
+      "[[4.1547556 ]\n",
+      " [2.58013829]\n",
+      " [5.20288581]]\n"
      ]
     }
    ],
@@ -186,8 +207,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcf0f686",
-   "metadata": {},
+   "id": "cda18663",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## But none of these can compete with Newton's method\n",
     "\n",
@@ -197,8 +220,11 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "1550b223",
-   "metadata": {},
+   "id": "e1e51c75",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -208,11 +234,11 @@
       "[[4.]\n",
       " [3.]\n",
       " [5.]]\n",
-      "0 [-23.78254537] [-30.51512235]\n",
-      "1 [1.30917499e-14] [-1.01327148e-14]\n",
-      "2 [9.76996262e-16] [1.28164443e-15]\n",
-      "3 [-7.28306304e-16] [-8.17359583e-16]\n",
-      "4 [-7.63833441e-16] [-1.32422234e-15]\n",
+      "0 [-27.10587277] [-37.81035098]\n",
+      "1 [1.16209264e-13] [2.08824304e-13]\n",
+      "2 [8.8817842e-17] [2.62242138e-16]\n",
+      "3 [-1.77635684e-17] [-1.50600514e-16]\n",
+      "4 [-3.37507799e-16] [-2.280464e-16]\n",
       "beta from own Newton code\n",
       "[[4.]\n",
       " [3.]\n",
@@ -258,8 +284,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1777d437",
-   "metadata": {},
+   "id": "8de3d7c1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Gradient descent and Logistic regression\n",
     "\n",
@@ -271,8 +299,11 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "94a3c22b",
-   "metadata": {},
+   "id": "4f87ae26",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -318,8 +349,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d9bd47b",
-   "metadata": {},
+   "id": "c2781943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Overview video on Stochastic Gradient Descent\n",
     "\n",
@@ -335,8 +368,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0107149a",
-   "metadata": {},
+   "id": "1e37491a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Batches and mini-batches\n",
     "\n",
@@ -354,8 +389,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "acb322f8",
-   "metadata": {},
+   "id": "6feab258",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Stochastic Gradient Descent (SGD)\n",
     "\n",
@@ -384,8 +421,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9073ab44",
-   "metadata": {},
+   "id": "204c15af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Stochastic Gradient Descent\n",
     "\n",
@@ -399,8 +438,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a457a90",
-   "metadata": {},
+   "id": "c9453416",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n",
@@ -410,8 +451,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be758e1d",
-   "metadata": {},
+   "id": "19b0403c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Computation of gradients\n",
     "\n",
@@ -421,8 +464,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "411db876",
-   "metadata": {},
+   "id": "37025507",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
@@ -432,8 +477,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c23bb658",
-   "metadata": {},
+   "id": "cc7aaec1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Stochasticity/randomness is introduced by only taking the\n",
     "gradient on a subset of the data called minibatches.  If there are $n$\n",
@@ -444,8 +491,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adea87fe",
-   "metadata": {},
+   "id": "3a3a0d11",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## SGD example\n",
     "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n",
@@ -464,8 +513,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e5dee91",
-   "metadata": {},
+   "id": "0acfc986",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\nabla_{\\beta}\n",
@@ -477,8 +528,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97047a5f",
-   "metadata": {},
+   "id": "8d3f995d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The gradient step\n",
     "\n",
@@ -487,8 +540,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9a59d5c",
-   "metadata": {},
+   "id": "8c73ac82",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
@@ -498,8 +553,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9b20c1c",
-   "metadata": {},
+   "id": "f88656c1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $k$ is picked at random with equal\n",
     "probability from $[1,n/M]$. An iteration over the number of\n",
@@ -510,8 +567,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3867a529",
-   "metadata": {},
+   "id": "e80a498f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Simple example code"
    ]
@@ -519,8 +578,11 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "e5f4f9a8",
-   "metadata": {},
+   "id": "626ac884",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import numpy as np \n",
@@ -541,8 +603,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "786c5900",
-   "metadata": {},
+   "id": "3c9a754d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Taking the gradient only on a subset of the data has two important\n",
     "benefits. First, it introduces randomness which decreases the chance\n",
@@ -555,8 +619,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f510fcf",
-   "metadata": {},
+   "id": "2790ab60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## When do we stop?\n",
     "\n",
@@ -574,8 +640,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f0043c6",
-   "metadata": {},
+   "id": "3ea3ee12",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Slightly different approach\n",
     "\n",
@@ -592,8 +660,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbc5d941",
-   "metadata": {},
+   "id": "3c39cc08",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Time decay rate\n",
     "\n",
@@ -609,8 +679,11 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "f96c423d",
-   "metadata": {},
+   "id": "294edbef",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -649,8 +722,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdf1efeb",
-   "metadata": {},
+   "id": "f60f930b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Code with a Number of Minibatches which varies\n",
     "\n",
@@ -660,28 +735,31 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "e221b4f3",
-   "metadata": {},
+   "id": "41a929b5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[4.12220276]\n",
-      " [2.95115528]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31601423 3.93074023]\n",
+      "[[4.30637636]\n",
+      " [2.56947078]]\n",
+      "Eigenvalues of Hessian Matrix:[0.30000613 4.12600095]\n",
       "theta from own gd\n",
-      "[[4.12220276]\n",
-      " [2.95115528]]\n",
+      "[[4.30637636]\n",
+      " [2.56947078]]\n",
       "theta from own sdg\n",
-      "[[4.12206013]\n",
-      " [2.92370959]]\n"
+      "[[4.34759233]\n",
+      " [2.63142731]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -767,8 +845,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e858f37",
-   "metadata": {},
+   "id": "af8f3db9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Replace or not\n",
     "\n",
@@ -780,8 +860,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7dace8c0",
-   "metadata": {},
+   "id": "ce1d1147",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Momentum based GD\n",
     "\n",
@@ -793,8 +875,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd079d0",
-   "metadata": {},
+   "id": "b8750f09",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
@@ -803,8 +887,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "305a75c3",
-   "metadata": {},
+   "id": "6b18d51a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -819,8 +905,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "026d8598",
-   "metadata": {},
+   "id": "efa3113f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have introduced a momentum parameter $\\gamma$, with\n",
     "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
@@ -836,8 +924,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80e73593",
-   "metadata": {},
+   "id": "2007f72c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
@@ -846,16 +936,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a5b87d4",
-   "metadata": {},
+   "id": "149a0faa",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f9bbf0cd",
-   "metadata": {},
+   "id": "3930d988",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More on momentum based approaches\n",
     "\n",
@@ -868,8 +962,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e7986cc",
-   "metadata": {},
+   "id": "8560c22c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
@@ -878,16 +974,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50d69000",
-   "metadata": {},
+   "id": "6f4563fe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We can discretize this equation in the usual way to get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e7d9df0a",
-   "metadata": {},
+   "id": "8fe2b7ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
@@ -896,16 +996,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6f67ad8",
-   "metadata": {},
+   "id": "207eae67",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Rearranging this equation, we can rewrite this as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "443f0b02",
-   "metadata": {},
+   "id": "9770730e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
@@ -914,8 +1018,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d89ab74d",
-   "metadata": {},
+   "id": "c233679d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Momentum parameter\n",
     "\n",
@@ -928,8 +1034,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3401047f",
-   "metadata": {},
+   "id": "cf54be10",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
@@ -938,8 +1046,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7c24040",
-   "metadata": {},
+   "id": "35f187e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Thus, as the name suggests, the momentum parameter is proportional to\n",
     "the mass of the particle and effectively provides inertia.\n",
@@ -969,8 +1079,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22e04f6c",
-   "metadata": {},
+   "id": "476338d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
@@ -979,8 +1091,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65b1fa09",
-   "metadata": {},
+   "id": "c23f6df7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -995,16 +1109,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7acccb8b",
-   "metadata": {},
+   "id": "e36c0680",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "795e6ab5",
-   "metadata": {},
+   "id": "484048bb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Second moment of the gradient\n",
     "\n",
@@ -1032,8 +1150,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dec5061d",
-   "metadata": {},
+   "id": "ed915ab1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMS prop\n",
     "\n",
@@ -1045,8 +1165,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3dfb0934",
-   "metadata": {},
+   "id": "c4d8b1a8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto3\"></div>\n",
@@ -1061,8 +1183,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf4b7a89",
-   "metadata": {},
+   "id": "6819d54f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
@@ -1071,8 +1195,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "510c8591",
-   "metadata": {},
+   "id": "c38fa00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
@@ -1081,8 +1207,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a0e569f",
-   "metadata": {},
+   "id": "7ff83ef0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\beta$ controls the averaging time of the second moment and is\n",
     "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n",
@@ -1097,8 +1225,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "977c9c79",
-   "metadata": {},
+   "id": "ba98f789",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n",
     "\n",
@@ -1124,8 +1254,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d188330b",
-   "metadata": {},
+   "id": "03428756",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto4\"></div>\n",
@@ -1140,8 +1272,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "776b649a",
-   "metadata": {},
+   "id": "ef5b461b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
@@ -1150,8 +1284,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f8a0d72",
-   "metadata": {},
+   "id": "0149850a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
@@ -1160,8 +1296,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53f1a2ce",
-   "metadata": {},
+   "id": "4ae41be8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
@@ -1170,8 +1308,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc7cd55a",
-   "metadata": {},
+   "id": "5d36d54a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
@@ -1180,8 +1320,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6bd6e651",
-   "metadata": {},
+   "id": "08eb5528",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
@@ -1190,8 +1332,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "677f1aef",
-   "metadata": {},
+   "id": "4a5e4b7b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto5\"></div>\n",
@@ -1205,8 +1349,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bb1d86d",
-   "metadata": {},
+   "id": "b71679d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n",
     "second moment and are typically taken to be $0.9$ and $0.99$\n",
@@ -1222,8 +1368,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "812cca90",
-   "metadata": {},
+   "id": "a9910c4b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 +  m_t^2 }+\\epsilon}.\n",
@@ -1232,8 +1380,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51ddf251",
-   "metadata": {},
+   "id": "85d963d2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
     "\n",
@@ -1244,8 +1394,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "676bc1af",
-   "metadata": {},
+   "id": "bc9de56d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## AdaGrad algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1258,8 +1410,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e0a4bd5",
-   "metadata": {},
+   "id": "e6293208",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMSProp algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1272,8 +1426,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9eccc07",
-   "metadata": {},
+   "id": "40fde17d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## ADAM algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1286,8 +1442,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b81a38cf",
-   "metadata": {},
+   "id": "f9066e5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Practical tips\n",
     "\n",
@@ -1304,8 +1462,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2be4b8ad",
-   "metadata": {},
+   "id": "cfac43d8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Automatic differentiation\n",
     "\n",
@@ -1340,8 +1500,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78ce59cc",
-   "metadata": {},
+   "id": "6c1afa20",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
@@ -1350,16 +1512,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1de3aaf",
-   "metadata": {},
+   "id": "4c038cf3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which has the following derivative"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "99aa41ec",
-   "metadata": {},
+   "id": "eed0ca87",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n",
@@ -1368,8 +1534,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76989f22",
-   "metadata": {},
+   "id": "3f493ed1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Using **autograd** we have"
    ]
@@ -1377,8 +1545,11 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "b9cd37f2",
-   "metadata": {},
+   "id": "f42e9964",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "data": {
@@ -1441,8 +1612,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f495197",
-   "metadata": {},
+   "id": "9a9dd7cb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using autograd\n",
     "\n",
@@ -1456,8 +1629,11 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "3e79535c",
-   "metadata": {},
+   "id": "f5d99737",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1490,8 +1666,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d764d7c",
-   "metadata": {},
+   "id": "1a033f2a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Autograd with more complicated functions\n",
     "\n",
@@ -1503,8 +1681,11 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "b171c0bc",
-   "metadata": {},
+   "id": "36ba3883",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1558,16 +1739,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65098808",
-   "metadata": {},
+   "id": "98a7ad40",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5d60df18",
-   "metadata": {},
+   "id": "a840a46c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More complicated functions using the elements of their arguments directly"
    ]
@@ -1575,8 +1760,11 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "cc4cc7eb",
-   "metadata": {},
+   "id": "0ce16fc4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1609,8 +1797,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d71a9a54",
-   "metadata": {},
+   "id": "470f7e16",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that in this case, when sending an array as input argument, the\n",
     "output from Autograd is another array. This is the true gradient of\n",
@@ -1622,8 +1812,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "290988a2",
-   "metadata": {},
+   "id": "4d7c7e61",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Functions using mathematical functions from Numpy"
    ]
@@ -1631,8 +1823,11 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "4afa9fe3",
-   "metadata": {},
+   "id": "69eceec6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1665,8 +1860,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec23dce0",
-   "metadata": {},
+   "id": "02192e06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More autograd"
    ]
@@ -1674,8 +1871,11 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "be794060",
-   "metadata": {},
+   "id": "6f5d7fa7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1704,8 +1904,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d8e15c2",
-   "metadata": {},
+   "id": "25b7c609",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And  with loops"
    ]
@@ -1713,8 +1915,11 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "d696c96c",
-   "metadata": {},
+   "id": "043eb7de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1755,8 +1960,11 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "5cdbff7d",
-   "metadata": {},
+   "id": "880bc7f0",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1780,8 +1988,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec95c41c",
-   "metadata": {},
+   "id": "322163dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using recursion"
    ]
@@ -1789,8 +1999,11 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "06c8423e",
-   "metadata": {},
+   "id": "09f1a79b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1833,16 +2046,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4675445a",
-   "metadata": {},
+   "id": "33d9596d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3ea2267f",
-   "metadata": {},
+   "id": "2b87a3af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Autograd with OLS\n",
     "\n",
@@ -1854,25 +2071,28 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "49c5a124",
-   "metadata": {},
+   "id": "4674f449",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.62286539]\n",
-      " [3.36754671]]\n",
-      "Eigenvalues of Hessian Matrix:[0.30134885 4.08702578]\n",
+      "[[3.88064505]\n",
+      " [2.99072374]]\n",
+      "Eigenvalues of Hessian Matrix:[0.30141906 4.73853838]\n",
       "theta from own gd\n",
-      "[[3.62286539]\n",
-      " [3.36754671]]\n"
+      "[[3.88064505]\n",
+      " [2.99072374]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -1939,8 +2159,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f952160a",
-   "metadata": {},
+   "id": "7c4e2d90",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Same code but now with momentum gradient descent"
    ]
@@ -1948,8 +2170,11 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "b0595e43",
-   "metadata": {},
+   "id": "be5e6b23",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1958,73 +2183,73 @@
       "Own inversion\n",
       "[[4.]\n",
       " [3.]]\n",
-      "Eigenvalues of Hessian Matrix:[0.27124938 4.56804783]\n",
-      "0 [-8.64009263] [-10.94092702]\n",
-      "1 [0.18925625] [-0.15527976]\n",
-      "2 [0.17801827] [-0.14605929]\n",
-      "3 [0.16744759] [-0.13738633]\n",
-      "4 [0.1575046] [-0.12922837]\n",
-      "5 [0.14815202] [-0.12155483]\n",
-      "6 [0.1393548] [-0.11433693]\n",
-      "7 [0.13107995] [-0.10754764]\n",
-      "8 [0.12329646] [-0.10116149]\n",
-      "9 [0.11597515] [-0.09515455]\n",
-      "10 [0.10908858] [-0.0895043]\n",
-      "11 [0.10261093] [-0.08418956]\n",
-      "12 [0.09651792] [-0.07919041]\n",
-      "13 [0.09078672] [-0.0744881]\n",
-      "14 [0.08539583] [-0.07006502]\n",
-      "15 [0.08032505] [-0.06590458]\n",
-      "16 [0.07555537] [-0.06199119]\n",
-      "17 [0.07106891] [-0.05831017]\n",
-      "18 [0.06684886] [-0.05484773]\n",
-      "19 [0.06287939] [-0.05159088]\n",
-      "20 [0.05914563] [-0.04852743]\n",
-      "21 [0.05563358] [-0.04564589]\n",
-      "22 [0.05233008] [-0.04293545]\n",
-      "23 [0.04922273] [-0.04038595]\n",
-      "24 [0.0462999] [-0.03798785]\n",
-      "25 [0.04355062] [-0.03573214]\n",
-      "26 [0.0409646] [-0.03361037]\n",
-      "27 [0.03853213] [-0.0316146]\n",
-      "28 [0.03624411] [-0.02973733]\n",
-      "29 [0.03409194] [-0.02797154]\n",
+      "Eigenvalues of Hessian Matrix:[0.31702609 3.84351715]\n",
+      "0 [-13.26083712] [-12.67834752]\n",
+      "1 [-0.55020405] [0.5257011]\n",
+      "2 [-0.50482139] [0.48233952]\n",
+      "3 [-0.46318204] [0.44255455]\n",
+      "4 [-0.42497724] [0.40605118]\n",
+      "5 [-0.38992371] [0.37255873]\n",
+      "6 [-0.3577615] [0.34182884]\n",
+      "7 [-0.32825214] [0.31363366]\n",
+      "8 [-0.30117681] [0.28776411]\n",
+      "9 [-0.27633474] [0.26402837]\n",
+      "10 [-0.25354173] [0.24225043]\n",
+      "11 [-0.23262877] [0.22226881]\n",
+      "12 [-0.21344077] [0.20393534]\n",
+      "13 [-0.19583547] [0.18711407]\n",
+      "14 [-0.17968231] [0.17168028]\n",
+      "15 [-0.16486151] [0.15751952]\n",
+      "16 [-0.15126318] [0.14452678]\n",
+      "17 [-0.13878649] [0.13260573]\n",
+      "18 [-0.12733892] [0.12166797]\n",
+      "19 [-0.11683558] [0.11163239]\n",
+      "20 [-0.10719859] [0.10242458]\n",
+      "21 [-0.0983565] [0.09397626]\n",
+      "22 [-0.09024373] [0.08622478]\n",
+      "23 [-0.08280012] [0.07911268]\n",
+      "24 [-0.07597049] [0.0725872]\n",
+      "25 [-0.06970419] [0.06659997]\n",
+      "26 [-0.06395476] [0.06110658]\n",
+      "27 [-0.05867956] [0.0560663]\n",
+      "28 [-0.05383947] [0.05144177]\n",
+      "29 [-0.04939861] [0.04719868]\n",
       "theta from own gd\n",
-      "[[4.11822173]\n",
-      " [2.90300219]]\n",
-      "0 [0.03206757] [-0.0263106]\n",
-      "1 [0.03016341] [-0.02474828]\n",
-      "2 [0.02780107] [-0.02281004]\n",
-      "3 [0.02544154] [-0.02087411]\n",
-      "4 [0.02322297] [-0.01905384]\n",
-      "5 [0.02117843] [-0.01737634]\n",
-      "6 [0.0193075] [-0.01584129]\n",
-      "7 [0.01759974] [-0.01444013]\n",
-      "8 [0.01604235] [-0.01316233]\n",
-      "9 [0.01462254] [-0.01199741]\n",
-      "10 [0.01332832] [-0.01093553]\n",
-      "11 [0.01214862] [-0.00996762]\n",
-      "12 [0.01107333] [-0.00908537]\n",
-      "13 [0.01009321] [-0.00828121]\n",
-      "14 [0.00919984] [-0.00754823]\n",
-      "15 [0.00838555] [-0.00688012]\n",
-      "16 [0.00764333] [-0.00627115]\n",
-      "17 [0.0069668] [-0.00571608]\n",
-      "18 [0.00635016] [-0.00521014]\n",
-      "19 [0.00578809] [-0.00474898]\n",
-      "20 [0.00527578] [-0.00432864]\n",
-      "21 [0.00480881] [-0.0039455]\n",
-      "22 [0.00438318] [-0.00359628]\n",
-      "23 [0.00399521] [-0.00327797]\n",
-      "24 [0.00364159] [-0.00298783]\n",
-      "25 [0.00331927] [-0.00272337]\n",
-      "26 [0.00302547] [-0.00248232]\n",
-      "27 [0.00275768] [-0.0022626]\n",
-      "28 [0.00251359] [-0.00206234]\n",
-      "29 [0.00229111] [-0.0018798]\n",
+      "[[3.85703369]\n",
+      " [3.13659941]]\n",
+      "0 [-0.04532405] [0.04330558]\n",
+      "1 [-0.04158557] [0.03973359]\n",
+      "2 [-0.03703391] [0.03538463]\n",
+      "3 [-0.03261373] [0.0311613]\n",
+      "4 [-0.02859759] [0.02732402]\n",
+      "5 [-0.02503392] [0.02391906]\n",
+      "6 [-0.02189994] [0.02092464]\n",
+      "7 [-0.01915337] [0.01830039]\n",
+      "8 [-0.01674956] [0.01600363]\n",
+      "9 [-0.01464686] [0.01399457]\n",
+      "10 [-0.01280793] [0.01223754]\n",
+      "11 [-0.01119981] [0.01070103]\n",
+      "12 [-0.00979357] [0.00935742]\n",
+      "13 [-0.0085639] [0.00818251]\n",
+      "14 [-0.00748862] [0.00715512]\n",
+      "15 [-0.00654835] [0.00625672]\n",
+      "16 [-0.00572613] [0.00547113]\n",
+      "17 [-0.00500716] [0.00478417]\n",
+      "18 [-0.00437846] [0.00418347]\n",
+      "19 [-0.0038287] [0.00365819]\n",
+      "20 [-0.00334797] [0.00319887]\n",
+      "21 [-0.0029276] [0.00279722]\n",
+      "22 [-0.00256001] [0.002446]\n",
+      "23 [-0.00223857] [0.00213888]\n",
+      "24 [-0.0019575] [0.00187032]\n",
+      "25 [-0.00171171] [0.00163548]\n",
+      "26 [-0.00149679] [0.00143013]\n",
+      "27 [-0.00130885] [0.00125057]\n",
+      "28 [-0.00114451] [0.00109354]\n",
+      "29 [-0.00100081] [0.00095624]\n",
       "theta from own gd wth momentum\n",
-      "[[4.0076989 ]\n",
-      " [2.99368326]]\n"
+      "[[3.99723951]\n",
+      " [3.00263755]]\n"
      ]
     }
    ],
@@ -2086,8 +2311,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43200e36",
-   "metadata": {},
+   "id": "0002f816",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Including Stochastic Gradient Descent with Autograd\n",
     "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
@@ -2096,25 +2323,28 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "b369d846",
-   "metadata": {},
+   "id": "ccb60a39",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[3.4870934 ]\n",
-      " [3.55042779]]\n",
-      "Eigenvalues of Hessian Matrix:[0.28793787 4.56453869]\n",
+      "[[3.95935439]\n",
+      " [3.09360113]]\n",
+      "Eigenvalues of Hessian Matrix:[0.32606139 4.1033455 ]\n",
       "theta from own gd\n",
-      "[[3.4870934 ]\n",
-      " [3.55042779]]\n"
+      "[[3.95935439]\n",
+      " [3.09360113]]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -2131,8 +2361,8 @@
      "output_type": "stream",
      "text": [
       "theta from own sdg\n",
-      "[[3.48900413]\n",
-      " [3.56763673]]\n"
+      "[[3.96916206]\n",
+      " [3.10276112]]\n"
      ]
     }
    ],
@@ -2214,8 +2444,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1caa8279",
-   "metadata": {},
+   "id": "502d537b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Same code but now with momentum gradient descent"
    ]
@@ -2223,23 +2455,26 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "a9695688",
-   "metadata": {},
+   "id": "d62b1fd8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Own inversion\n",
-      "[[4.11571507]\n",
-      " [2.86067818]]\n",
-      "Eigenvalues of Hessian Matrix:[0.25849623 4.84605507]\n",
+      "[[4.16532977]\n",
+      " [2.86943859]]\n",
+      "Eigenvalues of Hessian Matrix:[0.29633608 4.22128142]\n",
       "theta from own gd\n",
-      "[[4.10888197]\n",
-      " [2.86602331]]\n",
+      "[[4.16445858]\n",
+      " [2.87020155]]\n",
       "theta from own sdg with momentum\n",
-      "[[4.15361856]\n",
-      " [2.92376655]]\n"
+      "[[4.149433  ]\n",
+      " [2.89654756]]\n"
      ]
     }
    ],
@@ -2315,8 +2550,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e8ab93f",
-   "metadata": {},
+   "id": "ab2dfdcf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Similar (second order function now) problem but now with AdaGrad"
    ]
@@ -2324,8 +2561,11 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "be9894c6",
-   "metadata": {},
+   "id": "24784ec8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -2342,9 +2582,9 @@
      "output_type": "stream",
      "text": [
       "theta from own AdaGrad\n",
-      "[[1.99968451]\n",
-      " [3.001795  ]\n",
-      " [3.99848215]]\n"
+      "[[1.99415296]\n",
+      " [3.03274273]\n",
+      " [3.96850191]]\n"
      ]
     }
    ],
@@ -2401,16 +2641,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c181ef",
-   "metadata": {},
+   "id": "b525a878",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Running this code we note an almost perfect agreement with the results from matrix inversion."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3f40101d",
-   "metadata": {},
+   "id": "f3de5529",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
    ]
@@ -2418,8 +2662,11 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "da9f2895",
-   "metadata": {},
+   "id": "770a0f44",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -2436,9 +2683,9 @@
      "output_type": "stream",
      "text": [
       "theta from own RMSprop\n",
-      "[[1.99887767]\n",
-      " [3.01261048]\n",
-      " [3.99294056]]\n"
+      "[[2.00022969]\n",
+      " [2.99954278]\n",
+      " [4.00046631]]\n"
      ]
     }
    ],
@@ -2501,8 +2748,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2075df0a",
-   "metadata": {},
+   "id": "2cf458d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
    ]
@@ -2510,8 +2759,11 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "b9e0fd59",
-   "metadata": {},
+   "id": "ebe031fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -2528,9 +2780,9 @@
      "output_type": "stream",
      "text": [
       "theta from own ADAM\n",
-      "[[1.99996755]\n",
-      " [3.00016535]\n",
-      " [3.99977375]]\n"
+      "[[1.99991245]\n",
+      " [3.00042721]\n",
+      " [3.99954434]]\n"
      ]
     }
    ],
@@ -2598,8 +2850,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3186664b",
-   "metadata": {},
+   "id": "df82f58c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And Logistic Regression"
    ]
@@ -2607,8 +2861,11 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "c4119a68",
-   "metadata": {},
+   "id": "23a3aae7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -2657,8 +2914,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e182eb",
-   "metadata": {},
+   "id": "04692c2e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
     "\n",
@@ -2671,8 +2930,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae059fd0",
-   "metadata": {},
+   "id": "c9531ff9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Getting started with Jax, note the way we import numpy"
    ]
@@ -2680,8 +2941,11 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "1ad5b0d3",
-   "metadata": {},
+   "id": "1082677a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import jax\n",
@@ -2694,8 +2958,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc8fd16c",
-   "metadata": {},
+   "id": "ddab1050",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### A warm-up example"
    ]
@@ -2703,8 +2969,11 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "443386ca",
-   "metadata": {},
+   "id": "9a64315e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stderr",
@@ -2717,7 +2986,7 @@
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x117c17be0>]"
+       "[<matplotlib.lines.Line2D at 0x11975e550>]"
       ]
      },
      "execution_count": 25,
@@ -2778,8 +3047,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b313e4d6",
-   "metadata": {},
+   "id": "fbaa615b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### A more advanced example"
    ]
@@ -2787,13 +3058,16 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "7ff7b64d",
-   "metadata": {},
+   "id": "6400dac8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<matplotlib.collections.PathCollection at 0x117893340>"
+       "<matplotlib.collections.PathCollection at 0x11b160a60>"
       ]
      },
      "execution_count": 26,
@@ -2840,8 +3114,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b913d744",
-   "metadata": {},
+   "id": "b7cd2078",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Introduction to Neural networks\n",
     "\n",
@@ -2856,8 +3132,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04b70882",
-   "metadata": {},
+   "id": "4b41d4a3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Artificial neurons\n",
     "\n",
@@ -2878,8 +3156,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44405ff2",
-   "metadata": {},
+   "id": "05bbca92",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"artificialNeuron\"></div>\n",
@@ -2894,8 +3174,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b39653f7",
-   "metadata": {},
+   "id": "63e4ecd2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here, the output $y$ of the neuron is the value of its activation function, which have as input\n",
     "a weighted sum of signals $x_i, \\dots ,x_n$ received by $n$ other neurons.\n",
@@ -2932,8 +3214,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4db5fb89",
-   "metadata": {},
+   "id": "16405c0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Neural network types\n",
     "\n",
@@ -2959,8 +3243,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "400c590f",
-   "metadata": {},
+   "id": "49a77aeb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Feed-forward neural networks\n",
     "\n",
@@ -2978,8 +3264,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1536d443",
-   "metadata": {},
+   "id": "4408658f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Convolutional Neural Network\n",
     "\n",
@@ -3005,8 +3293,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ce4aacc",
-   "metadata": {},
+   "id": "cf8d97ad",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Recurrent neural networks\n",
     "\n",
@@ -3024,8 +3314,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c187a3e9",
-   "metadata": {},
+   "id": "3cc3819b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Other types of networks\n",
     "\n",
@@ -3043,8 +3335,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a5d9c4f",
-   "metadata": {},
+   "id": "920fd548",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Multilayer perceptrons\n",
     "\n",
@@ -3058,8 +3352,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2abe1a3e",
-   "metadata": {},
+   "id": "d08f461e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why multilayer perceptrons?\n",
     "\n",
@@ -3077,8 +3373,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "187cb30d",
-   "metadata": {},
+   "id": "dc59c40b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Illustration of a single perceptron model and a multi-perceptron model\n",
     "\n",
@@ -3091,8 +3389,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6269f804",
-   "metadata": {},
+   "id": "89c1b368",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Examples of XOR, OR and AND gates\n",
     "\n",
@@ -3106,8 +3406,11 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "1ad6269c",
-   "metadata": {},
+   "id": "f2a213fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -3163,16 +3466,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4ac557d",
-   "metadata": {},
+   "id": "046c878f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "What is happening here?"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6c5b5b78",
-   "metadata": {},
+   "id": "8dbddf81",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Does Logistic Regression do a better Job?"
    ]
@@ -3180,8 +3487,11 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "78d9fe1b",
-   "metadata": {},
+   "id": "3032a2c1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -3259,16 +3569,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "522ea0b9",
-   "metadata": {},
+   "id": "ea8b4e4b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not exactly impressive, but somewhat better."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "633277bf",
-   "metadata": {},
+   "id": "ef2b283b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Adding Neural Networks"
    ]
@@ -3276,8 +3590,11 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "55106a0e",
-   "metadata": {},
+   "id": "7415b824",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -3301,8 +3618,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6933a546",
-   "metadata": {},
+   "id": "bbfc7004",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3311,8 +3630,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a392cc52",
-   "metadata": {},
+   "id": "973905d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "y = f\\left(\\sum_{i=1}^n w_ix_i + b_i\\right) = f(z),\n",
@@ -3321,8 +3642,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc1e3563",
-   "metadata": {},
+   "id": "9343ae60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This function receives $x_i$ as inputs.\n",
     "Here the activation $z=(\\sum_{i=1}^n w_ix_i+b_i)$. \n",
@@ -3334,8 +3657,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "947e6060",
-   "metadata": {},
+   "id": "0fcd0bdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3344,8 +3669,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "190e7764",
-   "metadata": {},
+   "id": "98e91440",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto6\"></div>\n",
@@ -3359,8 +3686,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d4df41f",
-   "metadata": {},
+   "id": "944ccc68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here $b_i$ is the so-called bias which is normally needed in\n",
     "case of zero activation weights or inputs. How to fix the biases and\n",
@@ -3372,8 +3701,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8c69c2e",
-   "metadata": {},
+   "id": "17edaee3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"outputLayer1\"></div>\n",
@@ -3388,8 +3719,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80a632b1",
-   "metadata": {},
+   "id": "dbe292f0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we assume that all nodes in the same layer have identical\n",
     "activation functions, hence the notation $f$. In general, we could assume in the more general case that different layers have different activation functions.\n",
@@ -3398,8 +3731,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20de39bb",
-   "metadata": {},
+   "id": "ab06ec71",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"generalLayer\"></div>\n",
@@ -3414,8 +3749,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01031b37",
-   "metadata": {},
+   "id": "0f069e07",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $N_l$ is the number of nodes in layer $l$. When the output of\n",
     "all the nodes in the first hidden layer are computed, the values of\n",
@@ -3425,8 +3762,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9560b5e1",
-   "metadata": {},
+   "id": "3ee71e06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3435,8 +3774,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "baaac514",
-   "metadata": {},
+   "id": "cecfe50e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto7\"></div>\n",
@@ -3451,8 +3792,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2a439d9",
-   "metadata": {},
+   "id": "dc2a6523",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"outputLayer2\"></div>\n",
@@ -3467,16 +3810,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ba7b5ad",
-   "metadata": {},
+   "id": "3f73c82a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have substituted $y_k^1$ with the inputs $x_k$. Finally, the ANN output reads"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bed342fd",
-   "metadata": {},
+   "id": "8b1a1945",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto8\"></div>\n",
@@ -3491,8 +3838,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1beb8c9",
-   "metadata": {},
+   "id": "ecd88770",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto9\"></div>\n",
@@ -3508,8 +3857,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a71895ad",
-   "metadata": {},
+   "id": "6b6ce470",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3519,8 +3870,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9bd25ff",
-   "metadata": {},
+   "id": "6e018962",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"completeNN\"></div>\n",
@@ -3535,8 +3888,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7737a5b",
-   "metadata": {},
+   "id": "bf0b66e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which illustrates a basic property of MLPs: The only independent\n",
     "variables are the input values $x_n$."
@@ -3544,8 +3899,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "384040ce",
-   "metadata": {},
+   "id": "4827bb05",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3561,8 +3918,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a27ed92",
-   "metadata": {},
+   "id": "6fc6eadd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto10\"></div>\n",
@@ -3577,8 +3936,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c71650e0",
-   "metadata": {},
+   "id": "f7c37a39",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the parameters $c_i$ are weights and biases. By adjusting these\n",
     "parameters, the activation functions can be shifted up and down or\n",
@@ -3588,8 +3949,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6291c8a",
-   "metadata": {},
+   "id": "09472aa3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Matrix-vector notation\n",
     "\n",
@@ -3606,8 +3969,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da4b43f7",
-   "metadata": {},
+   "id": "1824564d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto11\"></div>\n",
@@ -3637,8 +4002,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fe1f511",
-   "metadata": {},
+   "id": "eafbe02e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Matrix-vector notation  and activation\n",
     "\n",
@@ -3647,8 +4014,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d53241ba",
-   "metadata": {},
+   "id": "f52242e3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto12\"></div>\n",
@@ -3664,8 +4033,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "962e06e9",
-   "metadata": {},
+   "id": "72371715",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This is not just a convenient and compact notation, but also a useful\n",
     "and intuitive way to think about MLPs: The output is calculated by a\n",
@@ -3676,8 +4047,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6446fdc6",
-   "metadata": {},
+   "id": "b455d9ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -3697,8 +4070,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69aff123",
-   "metadata": {},
+   "id": "7de531f8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions, Logistic and Hyperbolic ones\n",
     "\n",
@@ -3714,8 +4089,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbb74732",
-   "metadata": {},
+   "id": "dedb08ff",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\frac{1}{1 + e^{-x}},\n",
@@ -3724,16 +4101,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "216973d6",
-   "metadata": {},
+   "id": "ed7c69c9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the *hyperbolic tangent* function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a8643aed",
-   "metadata": {},
+   "id": "37be8225",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\tanh(x)\n",
@@ -3742,8 +4123,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6450655",
-   "metadata": {},
+   "id": "a8176533",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Relevance\n",
     "\n",
@@ -3757,8 +4140,11 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "0565ead1",
-   "metadata": {},
+   "id": "1b3252bc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "data": {
@@ -3893,11 +4279,6 @@
   }
  ],
  "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
diff --git a/doc/LectureNotes/_build/jupyter_execute/week40.py b/doc/LectureNotes/_build/jupyter_execute/week40.py
index 9563fbb25..92a2065bd 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week40.py
+++ b/doc/LectureNotes/_build/jupyter_execute/week40.py
@@ -16,8 +16,10 @@
 # 1. Stochastic Gradient descent with examples and automatic differentiation
 # 
 # 2. If we get time, we start with the basics of Neural Networks, setting up the basic steps, from the simple perceptron model to the multi-layer perceptron model
-# <!-- * [Video of lecture](https://youtu.be/75pr3hKY20U) -->
-# <!-- * "Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesOct5.pdf> -->
+# 
+# 3. [Video of lecture](https://youtu.be/jdJoOrCIdII)
+# 
+# 4. Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember30.pdf>
 
 # ## Suggested readings and videos
 # **Readings and Videos:**
diff --git a/doc/LectureNotes/_build/jupyter_execute/week40_100_1.png b/doc/LectureNotes/_build/jupyter_execute/week40_100_1.png
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diff --git a/doc/LectureNotes/week40.ipynb b/doc/LectureNotes/week40.ipynb
index cfe6bdd0b..c316b1d31 100644
--- a/doc/LectureNotes/week40.ipynb
+++ b/doc/LectureNotes/week40.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "54c44098",
-   "metadata": {},
+   "id": "71c0e62a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week40.do.txt --no_mako -->\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f64073c9",
-   "metadata": {},
+   "id": "4e0afae4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 40: Gradient descent methods (continued) and start Neural networks\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway and Department of Physics and Astronomy and Facility for Rare Ion Beams, Michigan State University, USA\n",
@@ -23,29 +27,37 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2d0f844",
-   "metadata": {},
+   "id": "e6b378ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 40"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c9630d37",
-   "metadata": {},
+   "id": "1ba91689",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lecture Monday September 30, 2024\n",
     "1. Stochastic Gradient descent with examples and automatic differentiation\n",
     "\n",
     "2. If we get time, we start with the basics of Neural Networks, setting up the basic steps, from the simple perceptron model to the multi-layer perceptron model\n",
-    "<!-- * [Video of lecture](https://youtu.be/75pr3hKY20U) -->\n",
-    "<!-- * \"Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesOct5.pdf> -->"
+    "\n",
+    "3. [Video of lecture](https://youtu.be/jdJoOrCIdII)\n",
+    "\n",
+    "4. Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesSeptember30.pdf>"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4b447216",
-   "metadata": {},
+   "id": "fb1da492",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Suggested readings and videos\n",
     "**Readings and Videos:**\n",
@@ -67,8 +79,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fb799c1",
-   "metadata": {},
+   "id": "5e18b164",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lab sessions Tuesday and Wednesday\n",
     "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
@@ -84,8 +98,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a202eb3",
-   "metadata": {},
+   "id": "ca1eb3e1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Summary from last week, using gradient descent methods, limitations\n",
     "\n",
@@ -104,8 +120,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0b36267",
-   "metadata": {},
+   "id": "d1832283",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Simple implementation of GD for OLS, Ridge and Lasso\n",
     "\n",
@@ -115,29 +133,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
-   "id": "2d9d73e5",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Parameters for OLS using gradient descent\n",
-      "[[4.04553909]\n",
-      " [2.85718534]\n",
-      " [5.07124072]]\n",
-      "Parameters for Ridge using gradient descent\n",
-      "[[3.8048267 ]\n",
-      " [3.33344121]\n",
-      " [4.85905287]]\n",
-      "Parameters for Lasso using gradient descent\n",
-      "[[3.87867385]\n",
-      " [3.192587  ]\n",
-      " [4.93045409]]\n"
-     ]
-    }
-   ],
+   "execution_count": 1,
+   "id": "0dee3b51",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "from random import random, seed\n",
     "import numpy as np\n",
@@ -186,8 +188,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fcf0f686",
-   "metadata": {},
+   "id": "cda18663",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## But none of these can compete with Newton's method\n",
     "\n",
@@ -196,30 +200,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
-   "id": "1550b223",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.]\n",
-      " [3.]\n",
-      " [5.]]\n",
-      "0 [-26.91927647] [-35.76071889]\n",
-      "1 [-6.07158768e-14] [-1.55935271e-13]\n",
-      "2 [-6.03961325e-16] [-9.79527859e-16]\n",
-      "3 [-1.54543045e-15] [-2.38042396e-15]\n",
-      "4 [1.27897692e-15] [1.94409177e-15]\n",
-      "beta from own Newton code\n",
-      "[[4.]\n",
-      " [3.]\n",
-      " [5.]]\n"
-     ]
-    }
-   ],
+   "execution_count": 2,
+   "id": "e1e51c75",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Newton's method\n",
     "from random import random, seed\n",
@@ -258,8 +245,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1777d437",
-   "metadata": {},
+   "id": "8de3d7c1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Gradient descent and Logistic regression\n",
     "\n",
@@ -270,18 +259,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
-   "id": "94a3c22b",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Predictions: [1, 1, 1, 1]\n"
-     ]
-    }
-   ],
+   "execution_count": 3,
+   "id": "4f87ae26",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "class LogisticRegression:\n",
@@ -318,8 +302,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d9bd47b",
-   "metadata": {},
+   "id": "c2781943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Overview video on Stochastic Gradient Descent\n",
     "\n",
@@ -335,8 +321,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0107149a",
-   "metadata": {},
+   "id": "1e37491a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Batches and mini-batches\n",
     "\n",
@@ -354,8 +342,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "acb322f8",
-   "metadata": {},
+   "id": "6feab258",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Stochastic Gradient Descent (SGD)\n",
     "\n",
@@ -384,8 +374,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9073ab44",
-   "metadata": {},
+   "id": "204c15af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Stochastic Gradient Descent\n",
     "\n",
@@ -399,8 +391,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a457a90",
-   "metadata": {},
+   "id": "c9453416",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n",
@@ -410,8 +404,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be758e1d",
-   "metadata": {},
+   "id": "19b0403c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Computation of gradients\n",
     "\n",
@@ -421,8 +417,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "411db876",
-   "metadata": {},
+   "id": "37025507",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
@@ -432,8 +430,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c23bb658",
-   "metadata": {},
+   "id": "cc7aaec1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Stochasticity/randomness is introduced by only taking the\n",
     "gradient on a subset of the data called minibatches.  If there are $n$\n",
@@ -444,8 +444,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adea87fe",
-   "metadata": {},
+   "id": "3a3a0d11",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## SGD example\n",
     "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n",
@@ -464,8 +466,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e5dee91",
-   "metadata": {},
+   "id": "0acfc986",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\nabla_{\\beta}\n",
@@ -477,8 +481,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97047a5f",
-   "metadata": {},
+   "id": "8d3f995d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The gradient step\n",
     "\n",
@@ -487,8 +493,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9a59d5c",
-   "metadata": {},
+   "id": "8c73ac82",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
@@ -498,8 +506,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9b20c1c",
-   "metadata": {},
+   "id": "f88656c1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $k$ is picked at random with equal\n",
     "probability from $[1,n/M]$. An iteration over the number of\n",
@@ -510,17 +520,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3867a529",
-   "metadata": {},
+   "id": "e80a498f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Simple example code"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
-   "id": "e5f4f9a8",
-   "metadata": {},
+   "execution_count": 4,
+   "id": "626ac884",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import numpy as np \n",
@@ -541,8 +556,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "786c5900",
-   "metadata": {},
+   "id": "3c9a754d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Taking the gradient only on a subset of the data has two important\n",
     "benefits. First, it introduces randomness which decreases the chance\n",
@@ -555,8 +572,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f510fcf",
-   "metadata": {},
+   "id": "2790ab60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## When do we stop?\n",
     "\n",
@@ -574,8 +593,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f0043c6",
-   "metadata": {},
+   "id": "3ea3ee12",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Slightly different approach\n",
     "\n",
@@ -592,8 +613,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbc5d941",
-   "metadata": {},
+   "id": "3c39cc08",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Time decay rate\n",
     "\n",
@@ -608,18 +631,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
-   "id": "f96c423d",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "gamma_j after 500 epochs: 9.97108e-05\n"
-     ]
-    }
-   ],
+   "execution_count": 5,
+   "id": "294edbef",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import numpy as np \n",
     "\n",
@@ -649,8 +667,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdf1efeb",
-   "metadata": {},
+   "id": "f60f930b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Code with a Number of Minibatches which varies\n",
     "\n",
@@ -659,37 +679,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
-   "id": "e221b4f3",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[3.8913351 ]\n",
-      " [2.83275949]]\n",
-      "Eigenvalues of Hessian Matrix:[0.33918672 3.94965845]\n",
-      "theta from own gd\n",
-      "[[3.8913351 ]\n",
-      " [2.83275949]]\n",
-      "theta from own sdg\n",
-      "[[3.9644494 ]\n",
-      " [2.80907715]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": 6,
+   "id": "41a929b5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "%matplotlib inline\n",
     "\n",
@@ -763,8 +759,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e858f37",
-   "metadata": {},
+   "id": "af8f3db9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Replace or not\n",
     "\n",
@@ -776,8 +774,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7dace8c0",
-   "metadata": {},
+   "id": "ce1d1147",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Momentum based GD\n",
     "\n",
@@ -789,8 +789,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd079d0",
-   "metadata": {},
+   "id": "b8750f09",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
@@ -799,8 +801,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "305a75c3",
-   "metadata": {},
+   "id": "6b18d51a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -815,8 +819,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "026d8598",
-   "metadata": {},
+   "id": "efa3113f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have introduced a momentum parameter $\\gamma$, with\n",
     "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
@@ -832,8 +838,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80e73593",
-   "metadata": {},
+   "id": "2007f72c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
@@ -842,16 +850,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a5b87d4",
-   "metadata": {},
+   "id": "149a0faa",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f9bbf0cd",
-   "metadata": {},
+   "id": "3930d988",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More on momentum based approaches\n",
     "\n",
@@ -864,8 +876,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e7986cc",
-   "metadata": {},
+   "id": "8560c22c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
@@ -874,16 +888,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50d69000",
-   "metadata": {},
+   "id": "6f4563fe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We can discretize this equation in the usual way to get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e7d9df0a",
-   "metadata": {},
+   "id": "8fe2b7ac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
@@ -892,16 +910,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6f67ad8",
-   "metadata": {},
+   "id": "207eae67",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Rearranging this equation, we can rewrite this as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "443f0b02",
-   "metadata": {},
+   "id": "9770730e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
@@ -910,8 +932,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d89ab74d",
-   "metadata": {},
+   "id": "c233679d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Momentum parameter\n",
     "\n",
@@ -924,8 +948,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3401047f",
-   "metadata": {},
+   "id": "cf54be10",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
@@ -934,8 +960,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7c24040",
-   "metadata": {},
+   "id": "35f187e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Thus, as the name suggests, the momentum parameter is proportional to\n",
     "the mass of the particle and effectively provides inertia.\n",
@@ -965,8 +993,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22e04f6c",
-   "metadata": {},
+   "id": "476338d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
@@ -975,8 +1005,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65b1fa09",
-   "metadata": {},
+   "id": "c23f6df7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -991,16 +1023,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7acccb8b",
-   "metadata": {},
+   "id": "e36c0680",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "795e6ab5",
-   "metadata": {},
+   "id": "484048bb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Second moment of the gradient\n",
     "\n",
@@ -1028,8 +1064,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dec5061d",
-   "metadata": {},
+   "id": "ed915ab1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMS prop\n",
     "\n",
@@ -1041,8 +1079,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3dfb0934",
-   "metadata": {},
+   "id": "c4d8b1a8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto3\"></div>\n",
@@ -1057,8 +1097,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf4b7a89",
-   "metadata": {},
+   "id": "6819d54f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
@@ -1067,8 +1109,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "510c8591",
-   "metadata": {},
+   "id": "c38fa00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
@@ -1077,8 +1121,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a0e569f",
-   "metadata": {},
+   "id": "7ff83ef0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\beta$ controls the averaging time of the second moment and is\n",
     "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n",
@@ -1093,8 +1139,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "977c9c79",
-   "metadata": {},
+   "id": "ba98f789",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n",
     "\n",
@@ -1120,8 +1168,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d188330b",
-   "metadata": {},
+   "id": "03428756",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto4\"></div>\n",
@@ -1136,8 +1186,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "776b649a",
-   "metadata": {},
+   "id": "ef5b461b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
@@ -1146,8 +1198,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f8a0d72",
-   "metadata": {},
+   "id": "0149850a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
@@ -1156,8 +1210,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53f1a2ce",
-   "metadata": {},
+   "id": "4ae41be8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
@@ -1166,8 +1222,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc7cd55a",
-   "metadata": {},
+   "id": "5d36d54a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
@@ -1176,8 +1234,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6bd6e651",
-   "metadata": {},
+   "id": "08eb5528",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
@@ -1186,8 +1246,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "677f1aef",
-   "metadata": {},
+   "id": "4a5e4b7b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto5\"></div>\n",
@@ -1201,8 +1263,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bb1d86d",
-   "metadata": {},
+   "id": "b71679d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n",
     "second moment and are typically taken to be $0.9$ and $0.99$\n",
@@ -1218,8 +1282,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "812cca90",
-   "metadata": {},
+   "id": "a9910c4b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 +  m_t^2 }+\\epsilon}.\n",
@@ -1228,8 +1294,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51ddf251",
-   "metadata": {},
+   "id": "85d963d2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
     "\n",
@@ -1240,8 +1308,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "676bc1af",
-   "metadata": {},
+   "id": "bc9de56d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## AdaGrad algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1254,8 +1324,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e0a4bd5",
-   "metadata": {},
+   "id": "e6293208",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMSProp algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1268,8 +1340,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9eccc07",
-   "metadata": {},
+   "id": "40fde17d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## ADAM algorithm, taken from [Goodfellow et al](https://www.deeplearningbook.org/contents/optimization.html)\n",
     "\n",
@@ -1282,8 +1356,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b81a38cf",
-   "metadata": {},
+   "id": "f9066e5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Practical tips\n",
     "\n",
@@ -1300,8 +1376,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2be4b8ad",
-   "metadata": {},
+   "id": "cfac43d8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Automatic differentiation\n",
     "\n",
@@ -1336,8 +1414,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78ce59cc",
-   "metadata": {},
+   "id": "6c1afa20",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
@@ -1346,16 +1426,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1de3aaf",
-   "metadata": {},
+   "id": "4c038cf3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which has the following derivative"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "99aa41ec",
-   "metadata": {},
+   "id": "eed0ca87",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n",
@@ -1364,36 +1448,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76989f22",
-   "metadata": {},
+   "id": "3f493ed1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Using **autograd** we have"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
-   "id": "b9cd37f2",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The max absolute difference is: 1.77636e-15\n"
-     ]
-    }
-   ],
+   "execution_count": 7,
+   "id": "f42e9964",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "\n",
@@ -1433,8 +1504,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f495197",
-   "metadata": {},
+   "id": "9a9dd7cb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using autograd\n",
     "\n",
@@ -1447,19 +1520,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
-   "id": "3e79535c",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The gradient of f1 evaluated at a = 1 using autograd is: 3\n",
-      "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n"
-     ]
-    }
-   ],
+   "execution_count": 8,
+   "id": "f5d99737",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -1482,8 +1549,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d764d7c",
-   "metadata": {},
+   "id": "1a033f2a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Autograd with more complicated functions\n",
     "\n",
@@ -1494,24 +1563,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
-   "id": "b171c0bc",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Evaluating at x1 = 1, x2 = 3\n",
-      "------------------------------\n",
-      "The derivative of f2 w.r.t x1: 12\n",
-      "The analytical derivative of f2 w.r.t x1: 12\n",
-      "\n",
-      "The derivative of f2 w.r.t x2: -4\n",
-      "The analytical derivative of f2 w.r.t x2: -4\n"
-     ]
-    }
-   ],
+   "execution_count": 9,
+   "id": "36ba3883",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -1550,25 +1608,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65098808",
-   "metadata": {},
+   "id": "98a7ad40",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5d60df18",
-   "metadata": {},
+   "id": "a840a46c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More complicated functions using the elements of their arguments directly"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
-   "id": "cc4cc7eb",
-   "metadata": {},
+   "execution_count": 10,
+   "id": "0ce16fc4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1592,8 +1657,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d71a9a54",
-   "metadata": {},
+   "id": "470f7e16",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that in this case, when sending an array as input argument, the\n",
     "output from Autograd is another array. This is the true gradient of\n",
@@ -1605,17 +1672,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "290988a2",
-   "metadata": {},
+   "id": "4d7c7e61",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Functions using mathematical functions from Numpy"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
-   "id": "4afa9fe3",
-   "metadata": {},
+   "execution_count": 11,
+   "id": "69eceec6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1639,17 +1711,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec23dce0",
-   "metadata": {},
+   "id": "02192e06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More autograd"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
-   "id": "be794060",
-   "metadata": {},
+   "execution_count": 12,
+   "id": "6f5d7fa7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1670,17 +1747,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d8e15c2",
-   "metadata": {},
+   "id": "25b7c609",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And  with loops"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
-   "id": "d696c96c",
-   "metadata": {},
+   "execution_count": 13,
+   "id": "043eb7de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1711,9 +1793,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
-   "id": "5cdbff7d",
-   "metadata": {},
+   "execution_count": 14,
+   "id": "880bc7f0",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1729,17 +1814,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec95c41c",
-   "metadata": {},
+   "id": "322163dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using recursion"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "id": "06c8423e",
-   "metadata": {},
+   "execution_count": 15,
+   "id": "09f1a79b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -1773,16 +1863,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4675445a",
-   "metadata": {},
+   "id": "33d9596d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3ea2267f",
-   "metadata": {},
+   "id": "2b87a3af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Autograd with OLS\n",
     "\n",
@@ -1793,34 +1887,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
-   "id": "49c5a124",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[3.98094809]\n",
-      " [3.10504501]]\n",
-      "Eigenvalues of Hessian Matrix:[0.27678028 4.83090115]\n",
-      "theta from own gd\n",
-      "[[3.98094809]\n",
-      " [3.10504501]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": 16,
+   "id": "4674f449",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients for OLS\n",
     "from random import random, seed\n",
@@ -1875,95 +1948,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f952160a",
-   "metadata": {},
+   "id": "7c4e2d90",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Same code but now with momentum gradient descent"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
-   "id": "b0595e43",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.]\n",
-      " [3.]]\n",
-      "Eigenvalues of Hessian Matrix:[0.25823312 3.94225609]\n",
-      "0 [-12.96884773] [-13.21205258]\n",
-      "1 [-0.22528633] [0.21334212]\n",
-      "2 [-0.21052919] [0.19936738]\n",
-      "3 [-0.19673871] [0.18630804]\n",
-      "4 [-0.18385156] [0.17410414]\n",
-      "5 [-0.17180857] [0.16269964]\n",
-      "6 [-0.16055444] [0.15204218]\n",
-      "7 [-0.1500375] [0.14208282]\n",
-      "8 [-0.14020946] [0.13277585]\n",
-      "9 [-0.13102519] [0.12407851]\n",
-      "10 [-0.12244253] [0.11595089]\n",
-      "11 [-0.11442207] [0.10835565]\n",
-      "12 [-0.10692698] [0.10125793]\n",
-      "13 [-0.09992285] [0.09462515]\n",
-      "14 [-0.09337751] [0.08842683]\n",
-      "15 [-0.08726092] [0.08263453]\n",
-      "16 [-0.08154499] [0.07722165]\n",
-      "17 [-0.07620348] [0.07216333]\n",
-      "18 [-0.07121185] [0.06743635]\n",
-      "19 [-0.0665472] [0.063019]\n",
-      "20 [-0.0621881] [0.05889101]\n",
-      "21 [-0.05811453] [0.05503342]\n",
-      "22 [-0.05430781] [0.05142852]\n",
-      "23 [-0.05075043] [0.04805975]\n",
-      "24 [-0.04742608] [0.04491165]\n",
-      "25 [-0.04431949] [0.04196976]\n",
-      "26 [-0.04141639] [0.03922058]\n",
-      "27 [-0.03870346] [0.03665148]\n",
-      "28 [-0.03616823] [0.03425066]\n",
-      "29 [-0.03379907] [0.03200711]\n",
-      "theta from own gd\n",
-      "[[3.87768766]\n",
-      " [3.1158276 ]]\n",
-      "0 [-0.0315851] [0.02991052]\n",
-      "1 [-0.02951615] [0.02795127]\n",
-      "2 [-0.02696204] [0.02553257]\n",
-      "3 [-0.02442969] [0.02313448]\n",
-      "4 [-0.02206975] [0.02089966]\n",
-      "5 [-0.01991611] [0.0188602]\n",
-      "6 [-0.01796544] [0.01701295]\n",
-      "7 [-0.01620343] [0.01534436]\n",
-      "8 [-0.01461344] [0.01383866]\n",
-      "9 [-0.0131792] [0.01248047]\n",
-      "10 [-0.01188564] [0.01125549]\n",
-      "11 [-0.01071902] [0.01015072]\n",
-      "12 [-0.0096669] [0.00915438]\n",
-      "13 [-0.00871804] [0.00825583]\n",
-      "14 [-0.00786232] [0.00744547]\n",
-      "15 [-0.00709059] [0.00671466]\n",
-      "16 [-0.00639461] [0.00605558]\n",
-      "17 [-0.00576694] [0.00546119]\n",
-      "18 [-0.00520089] [0.00492515]\n",
-      "19 [-0.00469039] [0.00444172]\n",
-      "20 [-0.00423] [0.00400574]\n",
-      "21 [-0.0038148] [0.00361255]\n",
-      "22 [-0.00344036] [0.00325796]\n",
-      "23 [-0.00310267] [0.00293817]\n",
-      "24 [-0.00279813] [0.00264978]\n",
-      "25 [-0.00252348] [0.00238969]\n",
-      "26 [-0.00227578] [0.00215513]\n",
-      "27 [-0.0020524] [0.00194359]\n",
-      "28 [-0.00185095] [0.00175281]\n",
-      "29 [-0.00166927] [0.00158077]\n",
-      "theta from own gd wth momentum\n",
-      "[[3.99417031]\n",
-      " [3.00552061]]\n"
-     ]
-    }
-   ],
+   "execution_count": 17,
+   "id": "be5e6b23",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients for OLS\n",
     "from random import random, seed\n",
@@ -2022,8 +2023,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43200e36",
-   "metadata": {},
+   "id": "0002f816",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Including Stochastic Gradient Descent with Autograd\n",
     "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
@@ -2031,43 +2034,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
-   "id": "b369d846",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.23287562]\n",
-      " [2.86347636]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31306035 4.34432759]\n",
-      "theta from own gd\n",
-      "[[4.23287562]\n",
-      " [2.86347636]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "theta from own sdg\n",
-      "[[4.25869167]\n",
-      " [2.84271642]]\n"
-     ]
-    }
-   ],
+   "execution_count": 18,
+   "id": "ccb60a39",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using SGD\n",
     "# OLS example\n",
@@ -2146,35 +2119,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1caa8279",
-   "metadata": {},
+   "id": "502d537b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Same code but now with momentum gradient descent"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
-   "id": "a9695688",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[3.96584049]\n",
-      " [3.04808331]]\n",
-      "Eigenvalues of Hessian Matrix:[0.31564325 4.60725403]\n",
-      "theta from own gd\n",
-      "[[3.96536405]\n",
-      " [3.04846625]]\n",
-      "theta from own sdg with momentum\n",
-      "[[4.01326831]\n",
-      " [3.04081676]]\n"
-     ]
-    }
-   ],
+   "execution_count": 19,
+   "id": "d62b1fd8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using SGD\n",
     "# OLS example\n",
@@ -2247,33 +2208,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e8ab93f",
-   "metadata": {},
+   "id": "ab2dfdcf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Similar (second order function now) problem but now with AdaGrad"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
-   "id": "be9894c6",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[2.]\n",
-      " [3.]\n",
-      " [4.]]\n",
-      "theta from own AdaGrad\n",
-      "[[1.99993955]\n",
-      " [3.00039584]\n",
-      " [3.99962062]]\n"
-     ]
-    }
-   ],
+   "execution_count": 20,
+   "id": "24784ec8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
     "# OLS example\n",
@@ -2327,41 +2278,33 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c181ef",
-   "metadata": {},
+   "id": "b525a878",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Running this code we note an almost perfect agreement with the results from matrix inversion."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3f40101d",
-   "metadata": {},
+   "id": "f3de5529",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
-   "id": "da9f2895",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[2.]\n",
-      " [3.]\n",
-      " [4.]]\n",
-      "theta from own RMSprop\n",
-      "[[1.99943878]\n",
-      " [2.99892878]\n",
-      " [3.99871777]]\n"
-     ]
-    }
-   ],
+   "execution_count": 21,
+   "id": "770a0f44",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
     "# OLS example\n",
@@ -2421,33 +2364,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2075df0a",
-   "metadata": {},
+   "id": "2cf458d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
-   "id": "b9e0fd59",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[2.]\n",
-      " [3.]\n",
-      " [4.]]\n",
-      "theta from own ADAM\n",
-      "[[1.99994314]\n",
-      " [3.00031228]\n",
-      " [3.99972037]]\n"
-     ]
-    }
-   ],
+   "execution_count": 22,
+   "id": "ebe031fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
     "# OLS example\n",
@@ -2512,17 +2445,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3186664b",
-   "metadata": {},
+   "id": "df82f58c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## And Logistic Regression"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
-   "id": "c4119a68",
-   "metadata": {},
+   "execution_count": 23,
+   "id": "23a3aae7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2562,8 +2500,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e182eb",
-   "metadata": {},
+   "id": "04692c2e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
     "\n",
@@ -2576,17 +2516,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae059fd0",
-   "metadata": {},
+   "id": "c9531ff9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Getting started with Jax, note the way we import numpy"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
-   "id": "1ad5b0d3",
-   "metadata": {},
+   "execution_count": 24,
+   "id": "1082677a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import jax\n",
@@ -2599,17 +2544,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc8fd16c",
-   "metadata": {},
+   "id": "ddab1050",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### A warm-up example"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
-   "id": "443386ca",
-   "metadata": {},
+   "execution_count": 25,
+   "id": "9a64315e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "def function(x):\n",
@@ -2650,17 +2600,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b313e4d6",
-   "metadata": {},
+   "id": "fbaa615b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### A more advanced example"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
-   "id": "7ff7b64d",
-   "metadata": {},
+   "execution_count": 26,
+   "id": "6400dac8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "backend = np\n",
@@ -2687,8 +2642,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b913d744",
-   "metadata": {},
+   "id": "b7cd2078",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Introduction to Neural networks\n",
     "\n",
@@ -2703,8 +2660,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04b70882",
-   "metadata": {},
+   "id": "4b41d4a3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Artificial neurons\n",
     "\n",
@@ -2725,8 +2684,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44405ff2",
-   "metadata": {},
+   "id": "05bbca92",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"artificialNeuron\"></div>\n",
@@ -2741,8 +2702,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b39653f7",
-   "metadata": {},
+   "id": "63e4ecd2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here, the output $y$ of the neuron is the value of its activation function, which have as input\n",
     "a weighted sum of signals $x_i, \\dots ,x_n$ received by $n$ other neurons.\n",
@@ -2779,8 +2742,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4db5fb89",
-   "metadata": {},
+   "id": "16405c0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Neural network types\n",
     "\n",
@@ -2806,8 +2771,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "400c590f",
-   "metadata": {},
+   "id": "49a77aeb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Feed-forward neural networks\n",
     "\n",
@@ -2825,8 +2792,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1536d443",
-   "metadata": {},
+   "id": "4408658f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Convolutional Neural Network\n",
     "\n",
@@ -2852,8 +2821,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ce4aacc",
-   "metadata": {},
+   "id": "cf8d97ad",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Recurrent neural networks\n",
     "\n",
@@ -2871,8 +2842,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c187a3e9",
-   "metadata": {},
+   "id": "3cc3819b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Other types of networks\n",
     "\n",
@@ -2890,8 +2863,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a5d9c4f",
-   "metadata": {},
+   "id": "920fd548",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Multilayer perceptrons\n",
     "\n",
@@ -2905,8 +2880,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2abe1a3e",
-   "metadata": {},
+   "id": "d08f461e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why multilayer perceptrons?\n",
     "\n",
@@ -2924,8 +2901,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "187cb30d",
-   "metadata": {},
+   "id": "dc59c40b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Illustration of a single perceptron model and a multi-perceptron model\n",
     "\n",
@@ -2938,8 +2917,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6269f804",
-   "metadata": {},
+   "id": "89c1b368",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Examples of XOR, OR and AND gates\n",
     "\n",
@@ -2952,9 +2933,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
-   "id": "1ad6269c",
-   "metadata": {},
+   "execution_count": 27,
+   "id": "f2a213fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"\n",
@@ -2991,25 +2975,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4ac557d",
-   "metadata": {},
+   "id": "046c878f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "What is happening here?"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6c5b5b78",
-   "metadata": {},
+   "id": "8dbddf81",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Does Logistic Regression do a better Job?"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
-   "id": "78d9fe1b",
-   "metadata": {},
+   "execution_count": 28,
+   "id": "3032a2c1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"\n",
@@ -3065,25 +3056,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "522ea0b9",
-   "metadata": {},
+   "id": "ea8b4e4b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not exactly impressive, but somewhat better."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "633277bf",
-   "metadata": {},
+   "id": "ef2b283b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Adding Neural Networks"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
-   "id": "55106a0e",
-   "metadata": {},
+   "execution_count": 29,
+   "id": "7415b824",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -3099,8 +3097,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6933a546",
-   "metadata": {},
+   "id": "bbfc7004",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3109,8 +3109,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a392cc52",
-   "metadata": {},
+   "id": "973905d4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "y = f\\left(\\sum_{i=1}^n w_ix_i + b_i\\right) = f(z),\n",
@@ -3119,8 +3121,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc1e3563",
-   "metadata": {},
+   "id": "9343ae60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This function receives $x_i$ as inputs.\n",
     "Here the activation $z=(\\sum_{i=1}^n w_ix_i+b_i)$. \n",
@@ -3132,8 +3136,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "947e6060",
-   "metadata": {},
+   "id": "0fcd0bdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3142,8 +3148,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "190e7764",
-   "metadata": {},
+   "id": "98e91440",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto6\"></div>\n",
@@ -3157,8 +3165,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d4df41f",
-   "metadata": {},
+   "id": "944ccc68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here $b_i$ is the so-called bias which is normally needed in\n",
     "case of zero activation weights or inputs. How to fix the biases and\n",
@@ -3170,8 +3180,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8c69c2e",
-   "metadata": {},
+   "id": "17edaee3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"outputLayer1\"></div>\n",
@@ -3186,8 +3198,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80a632b1",
-   "metadata": {},
+   "id": "dbe292f0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we assume that all nodes in the same layer have identical\n",
     "activation functions, hence the notation $f$. In general, we could assume in the more general case that different layers have different activation functions.\n",
@@ -3196,8 +3210,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20de39bb",
-   "metadata": {},
+   "id": "ab06ec71",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"generalLayer\"></div>\n",
@@ -3212,8 +3228,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01031b37",
-   "metadata": {},
+   "id": "0f069e07",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $N_l$ is the number of nodes in layer $l$. When the output of\n",
     "all the nodes in the first hidden layer are computed, the values of\n",
@@ -3223,8 +3241,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9560b5e1",
-   "metadata": {},
+   "id": "3ee71e06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3233,8 +3253,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "baaac514",
-   "metadata": {},
+   "id": "cecfe50e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto7\"></div>\n",
@@ -3249,8 +3271,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2a439d9",
-   "metadata": {},
+   "id": "dc2a6523",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"outputLayer2\"></div>\n",
@@ -3265,16 +3289,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ba7b5ad",
-   "metadata": {},
+   "id": "3f73c82a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have substituted $y_k^1$ with the inputs $x_k$. Finally, the ANN output reads"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bed342fd",
-   "metadata": {},
+   "id": "8b1a1945",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto8\"></div>\n",
@@ -3289,8 +3317,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1beb8c9",
-   "metadata": {},
+   "id": "ecd88770",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto9\"></div>\n",
@@ -3306,8 +3336,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a71895ad",
-   "metadata": {},
+   "id": "6b6ce470",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3317,8 +3349,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9bd25ff",
-   "metadata": {},
+   "id": "6e018962",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"completeNN\"></div>\n",
@@ -3333,8 +3367,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7737a5b",
-   "metadata": {},
+   "id": "bf0b66e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which illustrates a basic property of MLPs: The only independent\n",
     "variables are the input values $x_n$."
@@ -3342,8 +3378,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "384040ce",
-   "metadata": {},
+   "id": "4827bb05",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematical model\n",
     "\n",
@@ -3359,8 +3397,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a27ed92",
-   "metadata": {},
+   "id": "6fc6eadd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto10\"></div>\n",
@@ -3375,8 +3415,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c71650e0",
-   "metadata": {},
+   "id": "f7c37a39",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the parameters $c_i$ are weights and biases. By adjusting these\n",
     "parameters, the activation functions can be shifted up and down or\n",
@@ -3386,8 +3428,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6291c8a",
-   "metadata": {},
+   "id": "09472aa3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Matrix-vector notation\n",
     "\n",
@@ -3404,8 +3448,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da4b43f7",
-   "metadata": {},
+   "id": "1824564d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto11\"></div>\n",
@@ -3435,8 +3481,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fe1f511",
-   "metadata": {},
+   "id": "eafbe02e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Matrix-vector notation  and activation\n",
     "\n",
@@ -3445,8 +3493,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d53241ba",
-   "metadata": {},
+   "id": "f52242e3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto12\"></div>\n",
@@ -3462,8 +3512,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "962e06e9",
-   "metadata": {},
+   "id": "72371715",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This is not just a convenient and compact notation, but also a useful\n",
     "and intuitive way to think about MLPs: The output is calculated by a\n",
@@ -3474,8 +3526,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6446fdc6",
-   "metadata": {},
+   "id": "b455d9ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -3495,8 +3549,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69aff123",
-   "metadata": {},
+   "id": "7de531f8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions, Logistic and Hyperbolic ones\n",
     "\n",
@@ -3512,8 +3568,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbb74732",
-   "metadata": {},
+   "id": "dedb08ff",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\frac{1}{1 + e^{-x}},\n",
@@ -3522,16 +3580,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "216973d6",
-   "metadata": {},
+   "id": "ed7c69c9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the *hyperbolic tangent* function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a8643aed",
-   "metadata": {},
+   "id": "37be8225",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(x) = \\tanh(x)\n",
@@ -3540,8 +3602,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6450655",
-   "metadata": {},
+   "id": "a8176533",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Relevance\n",
     "\n",
@@ -3554,9 +3618,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
-   "id": "0565ead1",
-   "metadata": {},
+   "execution_count": 30,
+   "id": "1b3252bc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"The sigmoid function (or the logistic curve) is a \n",
@@ -3633,25 +3700,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.18"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }