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"cell_type": "markdown", "id": "bcb25e64", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "# Exercises week 42\n", "\n", - "**October 11-18, 2024**\n", + "**October 14-18, 2024**\n", "\n", "Date: **Deadline is Friday October 18 at midnight**\n" ] @@ -29,17 +25,17 @@ { "cell_type": "markdown", "id": "bb01f126", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "# Overarching aims of the exercises this week\n", "\n", - "The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.\n", + "This week, you will implement the entire feed-forward pass of a neural network! Next week you will compute the gradient of the network by implementing back-propagation manually, and by using autograd which does back-propagation for you (much easier!). Next week, you will also use the gradient to optimize the network with a gradient method! However, there is an optional exercise this week to get started on training the network and getting good results!\n", "\n", - "This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n", + "We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n", "\n", - "If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n" + "If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1zKibVQf-iAYaAn2-GlKfgRjHtLnPlBX4#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n", + "\n", + "First, here are some functions you are going to need, don't change this cell. If you are unable to import autograd, just swap in normal numpy until you want to do the final optional exercise.\n" ] }, { @@ -365,9 +361,9 @@ "metadata": {}, "outputs": [], "source": [ - "def feed_forward(input, layers, activations):\n", + "def feed_forward(input, layers, activation_funcs):\n", " a = input\n", - " for (W, b), activation in zip(layers, activations):\n", + " for (W, b), activation_func in zip(layers, activation_funcs):\n", " z = ...\n", " a = ...\n", " return a" @@ -378,9 +374,9 @@ "id": "8f7df363", "metadata": {}, "source": [ - "**b)** Make a list with three activation functions(don't call them yet! you can make a list with function names as elements, and then call these elements of the list later), two ReLU and one sigmoid. (If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n", + "**b)** You are now given a list with three activation functions, two ReLU and one sigmoid. (Don't call them yet! you can make a list with function names as elements, and then call these elements of the list later. If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n", "\n", - "Then evaluate a network with three layers and these activation functions.\n" + "Evaluate a network with three layers and these activation functions.\n" ] }, { @@ -392,11 +388,19 @@ "source": [ "network_input_size = ...\n", "layer_output_sizes = [...]\n", - "activations = [...]\n", + "activation_funcs = [ReLU, ReLU, sigmoid]\n", "layers = ...\n", "\n", "x = np.random.randn(network_input_size)\n", - "feed_forward(x, layers, activations)" + "feed_forward(x, layers, activation_funcs)" + ] + }, + { + "cell_type": "markdown", + "id": "9c914fd0", + "metadata": {}, + "source": [ + "**c)** How does the output of the network change if you use sigmoid in the hidden layers and ReLU in the output layer?\n" ] }, { @@ -463,9 +467,9 @@ "inputs = np.random.rand(1000, 4)\n", "\n", "\n", - "def feed_forward_batch(inputs, layers, activations):\n", + "def feed_forward_batch(inputs, layers, activation_funcs):\n", " a = inputs\n", - " for (W, b), activation in zip(layers, activations):\n", + " for (W, b), activation_func in zip(layers, activation_funcs):\n", " z = ...\n", " a = ...\n", " return a" @@ -488,11 +492,11 @@ "source": [ "network_input_size = ...\n", "layer_output_sizes = [...]\n", - "activations = [...]\n", + "activation_funcs = [...]\n", "layers = create_layers_batch(network_input_size, layer_output_sizes)\n", "\n", "x = np.random.randn(network_input_size)\n", - "feed_forward_batch(inputs, layers, activations)" + "feed_forward_batch(inputs, layers, activation_funcs)" ] }, { @@ -567,7 +571,7 @@ "id": "0362c4a9", "metadata": {}, "source": [ - "**a)** What should the input size for the network be with this dataset? What should the output shape of the last layer be?\n" + "**a)** What should the input size for the network be with this dataset? What should the output size of the last layer be?\n" ] }, { @@ -604,7 +608,7 @@ "metadata": {}, "outputs": [], "source": [ - "predictions = feed_forward_batch(inputs, layers, activations)" + "predictions = feed_forward_batch(inputs, layers, activation_funcs)" ] }, { @@ -630,7 +634,7 @@ "id": "334560b6", "metadata": {}, "source": [ - "# Exercise 6 - Training on real data\n", + "# Exercise 7 - Training on real data (Optional)\n", "\n", "To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.\n" ] @@ -640,31 +644,58 @@ "id": "700cabe4", "metadata": {}, "source": [ - "The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n" + "Since we are doing a classification task with multiple output classes, we use the cross-entropy loss function, which can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n" ] }, { "cell_type": "code", "execution_count": null, - "id": "56bef776", + "id": "f30e6e2c", "metadata": {}, "outputs": [], "source": [ - "from autograd import grad\n", - "\n", + "def cross_entropy(predict, target):\n", + " return np.sum(-target * np.log(predict))\n", "\n", - "def cost(input, layers, activations, target):\n", - " predict = feed_forward_batch(input, layers, activations)\n", - " return cross_entropy(predict, target)\n", "\n", + "def cost(input, layers, activation_funcs, target):\n", + " predict = feed_forward_batch(input, layers, activation_funcs)\n", + " return cross_entropy(predict, target)" + ] + }, + { + "cell_type": "markdown", + "id": "7ea9c1a4", + "metadata": {}, + "source": [ + "To improve our network on whatever prediction task we have given it, we need to use a sensible cost function, take the gradient of that cost function with respect to our network parameters, the weights and biases, and then update the weights and biases using these gradients. To clarify, we need to find and use these\n", "\n", - "def cross_entropy(predict, target):\n", - " return np.sum(-target * np.log(predict))\n", + "$$\n", + "\\frac{\\partial C}{\\partial W}, \\frac{\\partial C}{\\partial b}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "6c753e3b", + "metadata": {}, + "source": [ + "Now we need to compute these gradients. This is pretty hard to do for a neural network, we will use most of next week to do this, but we can also use autograd to just do it for us, which is what we always do in practice. With the code cell below, we create a function which takes all of these gradients for us.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "56bef776", + "metadata": {}, + "outputs": [], + "source": [ + "from autograd import grad\n", "\n", "\n", "gradient_func = grad(\n", - " cross_entropy, 1\n", - ") # Taking the gradient wrt. the second input to the cost function" + " cost, 1\n", + ") # Taking the gradient wrt. the second input to the cost function, i.e. the layers" ] }, { @@ -684,7 +715,9 @@ "metadata": {}, "outputs": [], "source": [ - "layers_grad = gradient_func(inputs, layers, activations, targets) # Don't change this" + "layers_grad = gradient_func(\n", + " inputs, layers, activation_funcs, targets\n", + ") # Don't change this" ] }, { @@ -703,10 +736,10 @@ "outputs": [], "source": [ "def train_network(\n", - " inputs, layers, activations, targets, learning_rate=0.001, epochs=100\n", + " inputs, layers, activation_funcs, targets, learning_rate=0.001, epochs=100\n", "):\n", " for i in range(epochs):\n", - " layers_grad = gradient_func(inputs, layers, activations, targets)\n", + " layers_grad = gradient_func(inputs, layers, activation_funcs, targets)\n", " for (W, b), (W_g, b_g) in zip(layers, layers_grad):\n", " W -= ...\n", " b -= ..." @@ -749,7 +782,7 @@ ], "metadata": { "kernelspec": { - "display_name": ".venv", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -763,7 +796,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.7" + "version": "3.9.15" } }, "nbformat": 4, diff --git a/doc/LectureNotes/_build/html/exercisesweek42.html b/doc/LectureNotes/_build/html/exercisesweek42.html index f4d0fc025..a4004e731 100644 --- a/doc/LectureNotes/_build/html/exercisesweek42.html +++ b/doc/LectureNotes/_build/html/exercisesweek42.html @@ -51,6 +51,8 @@ const thebe_selector_output = ".output, .cell_output" + + @@ -460,8 +462,8 @@

Applied Data Analysis and Machine Learning
  • - - Exercise 6 - Training on real data + + Exercise 7 - Training on real data (Optional)
    • @@ -525,8 +527,8 @@

    Contents

  • - - Exercise 6 - Training on real data + + Exercise 7 - Training on real data (Optional)
    • @@ -543,14 +545,15 @@

    Contents

    Exercises week 42

    -

    October 11-18, 2024

    +

    October 14-18, 2024

    Date: Deadline is Friday October 18 at midnight

    Overarching aims of the exercises this week

    -

    The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.

    -

    This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.

    -

    If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.

    +

    This week, you will implement the entire feed-forward pass of a neural network! Next week you will compute the gradient of the network by implementing back-propagation manually, and by using autograd which does back-propagation for you (much easier!). Next week, you will also use the gradient to optimize the network with a gradient method! However, there is an optional exercise this week to get started on training the network and getting good results!

    +

    We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.

    +

    If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1zKibVQf-iAYaAn2-GlKfgRjHtLnPlBX4#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.

    +

    First, here are some functions you are going to need, don’t change this cell. If you are unable to import autograd, just swap in normal numpy until you want to do the final optional exercise.

    import autograd.numpy as np  # We need to use this numpy wrapper to make automatic differentiation work later
@@ -762,9 +765,9 @@ 
    Exercise 4 - Custom activation for each layerfeed_forward function which accepts a list of activation functions as an argument, and which evaluates these activation functions at each layer.
    
 
    
 
    
-
    def feed_forward(input, layers, activations):
+
    def feed_forward(input, layers, activation_funcs):
     a = input
-    for (W, b), activation in zip(layers, activations):
+    for (W, b), activation_func in zip(layers, activation_funcs):
         z = ...
         a = ...
     return a
@@ -772,21 +775,22 @@ 
    Exercise 4 - Custom activation for each layer
 
    
 
    network_input_size = ...
 layer_output_sizes = [...]
-activations = [...]
+activation_funcs = [ReLU, ReLU, sigmoid]
 layers = ...
 
 x = np.random.randn(network_input_size)
-feed_forward(x, layers, activations)
+feed_forward(x, layers, activation_funcs)
 
    
 
    
 
    
 
    
+
    c) How does the output of the network change if you use sigmoid in the hidden layers and ReLU in the output layer?
    
 
    
 
    
 
    Exercise 5 - Processing multiple inputs at once
    
@@ -816,9 +820,9 @@ 
    Exercise 5 - Processing multiple inputs at once
    inputs = np.random.rand(1000, 4)
 
 
-def feed_forward_batch(inputs, layers, activations):
+def feed_forward_batch(inputs, layers, activation_funcs):
     a = inputs
-    for (W, b), activation in zip(layers, activations):
+    for (W, b), activation_func in zip(layers, activation_funcs):
         z = ...
         a = ...
     return a
@@ -831,11 +835,11 @@ 
    Exercise 5 - Processing multiple inputs at once
 
    network_input_size = ...
 layer_output_sizes = [...]
-activations = [...]
+activation_funcs = [...]
 layers = create_layers_batch(network_input_size, layer_output_sizes)
 
 x = np.random.randn(network_input_size)
-feed_forward_batch(inputs, layers, activations)
+feed_forward_batch(inputs, layers, activation_funcs)
 
    
 
    
 
    
@@ -881,7 +885,7 @@ 
    Exercise 6 - Predicting on real data
 
    
@@ -894,7 +898,7 @@ 
    Exercise 6 - Predicting on real data
 
    
-
    predictions = feed_forward_batch(inputs, layers, activations)
+
    predictions = feed_forward_batch(inputs, layers, activation_funcs)
 
    
 
    
 
    
@@ -908,27 +912,37 @@ 
    Exercise 6 - Predicting on real data
-
    Exercise 6 - Training on real data
    
+
    
+
    Exercise 7 - Training on real data (Optional)
    
 
    To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.
    
-
    The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is “most certain” on the correct target.
    
+
    Since we are doing a classification task with multiple output classes, we use the cross-entropy loss function, which can evaluate performance on classification tasks. It sees if your prediction is “most certain” on the correct target.
    
 
    
 
    
-
    from autograd import grad
+
    def cross_entropy(predict, target):
+    return np.sum(-target * np.log(predict))
 
 
-def cost(input, layers, activations, target):
-    predict = feed_forward_batch(input, layers, activations)
+def cost(input, layers, activation_funcs, target):
+    predict = feed_forward_batch(input, layers, activation_funcs)
     return cross_entropy(predict, target)
-
-
-def cross_entropy(predict, target):
-    return np.sum(-target * np.log(predict))
+
    
+
    
+
    
+
    
+
    To improve our network on whatever prediction task we have given it, we need to use a sensible cost function, take the gradient of that cost function with respect to our network parameters, the weights and biases, and then update the weights and biases using these gradients. To clarify, we need to find and use these
    
+
    
+\[
+\frac{\partial C}{\partial W}, \frac{\partial C}{\partial b}
+\]
    
+
    Now we need to compute these gradients. This is pretty hard to do for a neural network, we will use most of next week to do this, but we can also use autograd to just do it for us, which is what we always do in practice. With the code cell below, we create a function which takes all of these gradients for us.
    
+
    
+
    
+
    from autograd import grad
 
 
 gradient_func = grad(
-    cross_entropy, 1
-)  # Taking the gradient wrt. the second input to the cost function
+    cost, 1
+)  # Taking the gradient wrt. the second input to the cost function, i.e. the layers
 
    
 
    
 
    
@@ -937,7 +951,9 @@ 
    Exercise 6 - Training on real datagradient_func function to take the gradient of the cross entropy wrt. the weights and biases of the network. Check the shapes of what’s inside. What does the grad func from autograd actually do?
    
 
    
 
    
-
    layers_grad = gradient_func(inputs, layers, activations, targets)  # Don't change this
+
    layers_grad = gradient_func(
+    inputs, layers, activation_funcs, targets
+)  # Don't change this
 
    
 
    
 
    
@@ -946,10 +962,10 @@ 
    Exercise 6 - Training on real data
 
    
 
    def train_network(
-    inputs, layers, activations, targets, learning_rate=0.001, epochs=100
+    inputs, layers, activation_funcs, targets, learning_rate=0.001, epochs=100
 ):
     for i in range(epochs):
-        layers_grad = gradient_func(inputs, layers, activations, targets)
+        layers_grad = gradient_func(inputs, layers, activation_funcs, targets)
         for (W, b), (W_g, b_g) in zip(layers, layers_grad):
             W -= ...
             b -= ...
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index a9e5c206c..a7411b8d7 100644
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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations  with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Project 2 on Machine Learning, deadline November 4 (Midnight)","Teaching schedule with links to material","1. 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","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with examples"],titleterms:{"0":39,"1":[0,15,16,17,18,22,25,31,32,38,39],"11":38,"14":39,"16":35,"2":[0,15,16,17,18,22,26,31,32,33,38,39],"2023":29,"2024":[25,36,37,38,39],"21":[],"23":36,"26":32,"27":36,"3":[0,15,16,22,31,32,38,39],"30":37,"34":[15,31],"35":[16,32],"36":[17,33],"37":[18,34],"38":[19,35],"39":[20,21,36],"4":[0,22,26,32,39],"40":[21,37],"41":[21,38],"42":[22,39],"5":[0,22],"6":22,"7":[25,38],"9":34,"case":[8,10,28,32,33,35,36],"class":[35,38],"do":[1,33,34,36,37,38,39],"final":[12,21,26,32,33,36,37,38,39],"float":38,"function":[0,1,6,7,8,10,11,12,13,21,25,26,28,31,32,33,34,35,36,37,38,39],"import":[5,21,24,31,32,33,37,38,39],"new":[4,33,34,38],A:[0,1,4,8,9,21,31,33,34,35,37,38,39],AND:[37,38],And:[21,31,32,33,35,36,37],But:[21,36,37],For:32,In:[29,38],Is:[38,39],Ising:6,OR:[37,38],The:[0,1,2,3,5,6,7,8,9,11,12,17,23,31,32,33,34,35,36,37,38,39],To:[31,32],With:[4,33],about:[31,32],abov:[33,38,39],activ:[1,12,22,26,33,37,38,39],ad:[0,6,17,25,31,32,37,38,39],adaboost:10,adagrad:[13,21,36,37],adam:[13,21,36,37],adapt:[10,21,36,37],adjust:[1,39],advanc:[21,37],adversari:4,again:[3,9,35],ai:[25,31],aim:[8,9,17,18,19,20,21,22,31],aka:[31,32],al:[21,37],algebra:[24,31],algorithm:[9,10,11,12,21,26,32,36,37,38,39],algortithm:[13,35,36],all:[8,38,39],an:[0,4,10,31,38],analys:[5,32],analysi:[0,5,6,11,23,25,26,28,31,32,33,34,38],analyt:[0,16,17,21],analyz:[38,39],ani:[13,35,36],anoth:[9,33,34],appli:23,approach:[0,8,14,31,34,36,37],approxim:[12,38],architectur:[1,39],argument:[36,37],arrai:[24,31],artifici:[37,38],assist:29,assumpt:[33,34],august:32,autocorrel:28,autograd:[2,13,21,36,37],automat:[13,21,36,37,38],avoid:[],b:[17,25,26,36],back:[1,11,12,38,39],background:[23,25,26,34],bag:10,base:[13,21,34,36,37],basic:[0,5,7,9,10,11,24,32,33,34,35,38],batch:[1,36,37,38,39],bay:[5,33,34],befor:11,bengio:[38,39],beta:[33,34],better:[8,37,38],bia:[6,25,34],bias:[38,39],binari:[1,39],bind:31,bird:10,boldsymbol:[32,33,34],book:[38,39],boost:10,bootstrap:[6,10,34],boston:0,breast:[1,39],brief:[31,34,35,36],bring:[12,38,39],build:[1,3,9,39],c:[25,26,31],calcul:32,can:[21,31,34,36,37,38],cancer:[1,7,9,11,35,39],cart:9,center:32,central:[13,23,28,34,35,36],chain:[12,38,39],challeng:35,chang:10,channel:31,chi:[0,31],choic:[38,39],choos:[1,39],cifar01:3,classic:11,classif:[1,9,10,26,35,39],classifi:[8,35],clip:[1,38,39],cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,21,26,31,32,33,34,35,36,37,38,39],collect:[1,3,39],come:35,commun:31,compact:[35,38,39],compar:[2,10],comparison:33,compet:[21,36,37],complet:[32,38,39],complex:[0,6,25,32],complic:[6,36,37,38],compon:11,comput:[9,36,37],computation:34,computerlab:31,con:9,concept:28,condit:[33,34,35,36],confid:34,conjug:[13,36],consider:[38,39],construct:[38,39],continu:37,contn:31,convex:[8,13,35,36],convolut:[3,12,37,38],correctli:[33,34],correl:[11,32,35],correspond:[35,36],cost:[1,10,32,33,34,35,36,38,39],count:38,cours:[23,30,31],covari:[5,11,28,32],cover:31,critic:26,cross:[6,25,34,35],custom:22,cython:31,d:[25,26],data:[0,1,3,6,7,9,11,15,16,22,23,25,28,31,32,33,35,38,39],dataset:[1,3,39],deadlin:[25,26,31],decai:[2,36,37],decis:[9,10],decomposit:[5,11,17,24,32],deep:[1,2,31,35,38,39],defin:[1,31,38,39],definit:[38,39],degre:[0,32],deliveri:[25,26],delta:34,dens:[0,31],deriv:[5,12,32,33,34,35,36,38,39],descent:[2,10,13,21,26,35,36,37],descript:25,design:32,detail:[3,31],develop:[1,39],diagon:11,differ:[8,26,36,37],different:21,differenti:[2,13,36,37,38],diffus:2,dimension:[2,3,8,25,32],directli:[36,37],disadvantag:9,discret:28,discuss:35,distribut:[5,28,33,34],distrubut:34,doe:[32,33,37,38],domain:28,dot:36,down:[1,38,39],dropout:[1,38,39],e:[25,26],each:[22,35],economi:32,electron:[25,26],element:[0,28,31,36,37],elimin:24,elu:[38,39],energi:31,ensembl:10,entri:[38,39],entropi:[9,35],environ:[0,15,31],equat:[0,2,12,31,32,33,35,36,38,39],error:[0,10,31,32,34],essenti:31,estim:[33,34],et:[21,37],etc:31,euler:2,evalu:[1,26,38,39],exampl:[0,1,2,3,4,6,7,8,9,10,21,31,32,33,34,35,36,37,38,39],exercis:[0,6,15,16,17,18,19,20,21,22,31,32,38],expect:[18,28,33,34],expens:34,experi:28,explicit:[38,39],explod:[38,39],explor:[0,15,16,31],exponenti:2,express:[17,18,32,35,36,38,39],extend:[35,36,38],extrapol:4,extrem:[10,31],ey:10,f:[25,26],fall:29,famili:[1,31,32,38,39],famou:24,fantast:32,featur:[9,24,32],feed:[1,12,37,38,39],find:[34,36],fine:[1,38,39],first:[4,12,26,31,32,33,35,36,38,39],fit:[0,10,31,33],fix:32,fold:[34,35],forc:3,forest:10,format:[25,26,31],forward:[1,2,12,37,38,39],fourier:3,frank:[6,25,32],freedom:[0,32],frequent:32,frequentist:[0,31],fridai:[],from:[5,10,12,21,26,32,33,34,35,36,37,38,39],full:[2,39],funtion:[38,39],further:[3,5,32],g:25,gan:4,gate:[37,38,39],gaussian:24,gd:[13,21,36,37],gener:[4,9,31,38],geometr:[11,35,36],get:[21,37,38],gini:9,glorot:[38,39],good:[0,31],goodfellow:[21,37],grade:[29,31],gradient:[1,2,10,13,21,26,35,36,37,38,39],grid:35,group:35,growth:2,ha:23,hand:[38,39],handl:[24,31,32],happen:[33,34],hard:[],hessian:[32,35,36],hidden:[2,38,39],h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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations  with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Project 2 on Machine Learning, deadline November 4 (Midnight)","Teaching schedule with links to material","1. 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","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with 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],histogram:34,homework:[35,36],homogen:[38,39],hous:0,how:35,hyperbol:[37,38,39],hyperparamet:[1,38,39],hyperplan:8,i:1,id3:9,idea:11,ideal:[35,36],ident:[33,34],identifi:34,ii:31,iid:[33,34],illustr:[33,37,38],implement:[1,37,39],implic:[5,32],improv:[1,36,39],includ:[13,21,35,36,37,38],increment:11,independ:[33,34],index:9,inform:29,ingredi:38,init:39,input:[2,22,38,39],insight:[38,39],instal:[23,25,31],instructor:29,intercept:32,intermedi:38,interpret:[5,11,31,32,33,34,35,36],interv:34,introduc:[11,13,21,32,36,37],introduct:[0,6,23,24,25,26,31,37,38],invers:[5,24,33],invert:32,iter:[10,36],its:32,jacobian:32,jax:[13,21,36,37],job:[37,38],julia:31,jungl:10,k:[34,35,38,39],kera:[1,3,39],kernel:[8,11],l:[38,39],lab:[34,35,36,37],lagrangian:8,lambda:35,lasso:[5,6,25,32,33,34,35,37],last:[32,35,37,38,39],later:[5,32,39],layer:[1,2,3,12,22,38,39],layout:[38,39],learn:[0,1,2,11,13,14,15,16,21,23,25,26,31,32,33,34,35,36,37,38,39],least:[5,6,18,25,31,32,33],lectur:[31,32,33,34,35,36,37,38,39],level:10,librari:[23,31],likelihood:[7,33,34,35],limit:[1,13,28,34,35,36,37,38,39],linear:[0,8,13,24,26,31,32,33,35],link:[5,11,27,30,32,33,34],list:[38,39],literatur:[25,26],logist:[7,26,31,35,36,37,38,39],loop:[36,37],loss:[32,35,36],lu:24,machin:[0,8,13,23,25,26,31,35,36],made:[33,34],main:[28,31],make:[0,9,10,15,16,31,32],mani:[10,12],manipul:32,margin:[33,34],mass:31,materi:[25,27,31,32,33,34,35,38,39],math:[5,32],mathemat:[3,5,8,32,36,37,38,39],matric:[5,24,31,33],matrix:[1,5,11,12,24,31,32,33,35,36,37,39],matter:[0,31],max:32,maximum:[33,34,35],mean:[0,32,33,35],measur:35,meet:[5,10,28,31,32],mercer:8,method:[6,9,10,13,21,25,31,34,35,36,37,39],midnight:[25,26],min:32,mini:[36,37],minibatch:[21,36,37],minim:[31,35],ml:31,mle:[33,34],mlp:12,mnist:[3,4],mode:38,model:[0,1,4,6,12,31,37,38,39],moment:[36,37],momentum:[13,21,36,37],mondai:[32,33,34,35,36,37,38],moon:[8,9],more:[3,6,21,24,25,31,32,33,34,35,36,37,38,39],multi:[37,38,39],multiclass:39,multilay:[12,37,38],multipl:[1,3,22,39],multipli:8,multivari:38,need:[25,31],network:[1,2,3,4,7,12,26,31,35,37,38,39],neural:[1,2,3,4,7,12,26,31,37,38,39],neuron:[37,38],newton:[21,35,36,37],nn:[38,39],node:[38,39],noeds:39,noen:21,non:8,none:[36,37],normal:[0,1,34,38,39],notat:[12,37],note:[21,25,32,33,37],novemb:26,now:[1,9,13,21,33,34,36,37,39],nuclear:[0,31],nueral:35,numba:31,number:[0,2,21,28,32,36,37,38],numer:[2,25,26,28],numpi:[21,24,31,36,37],object:[3,39],observ:[38,39],obtain:11,octob:[25,38,39],od:2,off:[6,25],ol:[5,6,21,25,33,34,36,37],onc:22,one:[2,12,35,36,38,39],ones:[37,38,39],oper:[24,38],optim:[1,8,13,23,31,32,35,36,37,38,39],option:22,order:[13,21,36,37],ordinari:[5,6,18,25,31,32,33],organ:[0,31],orient:39,oslo:30,other:[4,9,11,12,24,25,31,32,35,37,38,39],ouput:[38,39],our:[0,4,5,11,13,31,32,35,36,38,39],outcom:[23,31],output:[2,38,39],over:[38,39],overarch:[0,4,8,9,17,18,19,20,21,22,31,32,38],overview:[10,31,36,37],own:[0,10,11,15,16,26,31,32],packag:[24,31],panda:[31,32],paper:[25,38,39],parallel:38,paramet:[31,32,35,36,37,38,39],part:[13,23,25,26,32,35,36,38,39],partial:2,pass:[1,39],pca:11,pdf:28,pencil:25,percepetron:[38,39],perceptron:[12,37,38,39],perform:[1,9,39],period:3,perspect:[1,38,39],plan:[32,33,34,35,36,37,38],plot:[34,35],point:[4,38],poisson:2,polynomi:[3,33],popul:2,popular:31,practic:[13,21,29,31,36,37],pre:[1,3,39],preambl:25,predict:[4,22],predictor:35,preprocess:32,prerequisit:[3,23,31],princip:11,principl:3,pro:9,probabl:[5,28,33,34],problem:[1,2,13,21,31,32,33,35,36,37,38,39],procedur:[9,31],process:[1,3,22,39],product:36,program:[2,13,25,26,35,36,38],project:[6,25,26,31,35],prop:[13,36,37],propag:[1,12,38,39],properti:[5,28,32,35],python:[0,9,15,23,24,31],quick:8,r:31,random:[10,11,28,35],raphson:[35,36],rate:[21,36,37,39],read:[9,31,32,34,35,37,38,39],real:[6,22,25,31,38],recommend:[31,32,38,39],rectangular:33,recurr:[4,12,37,38],recurs:[36,37],reduc:[0,32,38],reduct:3,refer:25,reformul:2,regress:[0,5,6,7,9,10,13,17,18,25,26,31,32,33,34,35,36,37,38],regular:[1,35,39],relat:32,relev:[30,32,35,37,38,39],relu:[1,38,39],remark:3,remind:[6,8,31,35,36,38,39],repeat:32,replac:[13,36,37],report:[25,26],repositori:34,repres:[],requir:[2,23],resampl:[6,25,34],rescal:[6,33],residu:32,resourc:2,result:[32,33,38,39],revers:38,revisit:[13,35,36],rewrit:[31,32,34],rewritten:35,ridg:[0,5,6,17,18,25,32,33,34,35,36,37],rm:[13,36,37],rmsprop:[21,36,37],root:[38,39],rule:[12,38,39],s:[8,10,21,34,35,36,37],same:[13,21,34,36,37],sampl:11,scale:32,schedul:[27,31,39],schemat:9,scheme:2,scienc:31,scikit:[0,1,11,15,16,31,32,33,34,35,36,39],search:35,second:[13,21,36,37],select:35,semest:29,sensit:[35,36],septemb:[33,34,35,36,37],seriou:38,session:[32,33,34,35,36,37,38,39],set:[0,2,3,9,12,15,31,32,35,38,39],sgd:[13,36,37],should:[1,38,39],sigmoid:[38,39],similar:[13,21,36,37],simpl:[0,4,9,13,31,32,33,35,36,37,38,39],simpler:38,singl:[10,37,38],singular:[5,11,17,32],size:32,slightli:[36,37],smarter:38,soft:8,softmax:[1,39],softwar:[25,31],solv:[2,33,35,36],solver:13,some:[13,24,32,35,36,38],specifi:2,split:[0,15,16,31,32],squar:[0,5,6,10,18,25,31,32,33],standard:[13,32,34,36],start:[21,37],state:[0,31],statist:[5,6,23,28,31,33,34],steepest:[10,13,35,36],step:[26,34,35,36,37],still:32,stochast:[13,21,26,28,36,37],stop:[36,37],strongli:31,studi:35,subtract:32,suggest:[31,35,37],sum:[34,38,39],summari:[29,31,37],superposit:3,supervis:[1,38,39],support:8,svd:[5,32,33],syntax:36,systemat:3,t:[32,33],taken:[21,37],teach:[27,29],teacher:[29,31],technic:33,techniqu:[6,11,25],technolog:23,tensorflow:[1,3,39],tent:31,term:[34,38,39],test:[0,1,15,16,26,31,32,33,39],text:31,textbook:[30,31],than:[35,36],theorem:[5,8,11,12,28,33,34,38],theori:28,thi:[17,18,19,20,21,22,31,38],think:32,three:[38,39],through:38,thursdai:[],time:[36,37],tip:[13,21,36,37],togeth:[12,38,39],tool:[25,31],top:[1,38,39],topic:31,toward:11,trade:[6,25],tradeoff:[6,34],train:[0,1,4,15,16,22,31,32,38,39],transform:3,tree:[9,10],tuesdai:[33,37,38,39],tune:[1,38,39],two:[3,8,23,25,32,35,38,39],type:[2,4,12,31,37,38],uio:31,understand:34,univers:[12,30,38],unsupervis:14,unsupport:36,up:[0,2,9,12,15,21,31,32,34,35,37,38,39],updat:[38,39],us:[0,1,2,3,7,13,21,23,25,26,31,32,35,36,37,38,39],usag:[33,34,39],valid:[6,25,34,35],valu:[5,11,17,18,28,32,33,34,35],vanish:[38,39],vari:[21,36,37],variabl:[28,35,36],varianc:[6,25,33,34],variou:[0,15,26,31,34,35],vector:[8,12,24,31,32,37],veri:[],video:[35,36,37],view:[0,4,10,32,38],visual:[1,9,39],vs:3,wai:[9,21,34,37,38],warm:[21,37],wave:2,we:[21,31,36,37,38,39],wednesdai:[33,37,38,39],week:[15,16,17,18,19,20,21,22,31,32,33,34,35,36,37,38,39],weekend:35,weekli:27,weight:39,what:[0,31,32,33,34],when:[36,37],which:[1,21,36,37,38,39],why:[31,32,34,37,38],wisconsin:[7,35],word:38,wrap:[32,34],write:[4,11,25,26,33,39],x:[32,33],xgboost:10,xor:[37,38,39],yet:33,your:[0,10,15,16,26,31,32],yourself:35,z_j:[38,39]}})
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb
index 03a26374e..c51e82193 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.ipynb
@@ -3,9 +3,7 @@
   {
    "cell_type": "markdown",
    "id": "4b4c06bc",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "\n",
@@ -15,13 +13,11 @@
   {
    "cell_type": "markdown",
    "id": "bcb25e64",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "# Exercises week 42\n",
     "\n",
-    "**October 11-18, 2024**\n",
+    "**October 14-18, 2024**\n",
     "\n",
     "Date: **Deadline is Friday October 18 at midnight**\n"
    ]
@@ -29,17 +25,17 @@
   {
    "cell_type": "markdown",
    "id": "bb01f126",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "# Overarching aims of the exercises this week\n",
     "\n",
-    "The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.\n",
+    "This week, you will implement the entire feed-forward pass of a neural network! Next week you will compute the gradient of the network by implementing back-propagation manually, and by using autograd which does back-propagation for you (much easier!). Next week, you will also use the gradient to optimize the network with a gradient method! However, there is an optional exercise this week to get started on training the network and getting good results!\n",
     "\n",
-    "This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n",
+    "We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n",
     "\n",
-    "If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n"
+    "If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1zKibVQf-iAYaAn2-GlKfgRjHtLnPlBX4#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n",
+    "\n",
+    "First, here are some functions you are going to need, don't change this cell. If you are unable to import autograd, just swap in normal numpy until you want to do the final optional exercise.\n"
    ]
   },
   {
@@ -382,9 +378,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def feed_forward(input, layers, activations):\n",
+    "def feed_forward(input, layers, activation_funcs):\n",
     "    a = input\n",
-    "    for (W, b), activation in zip(layers, activations):\n",
+    "    for (W, b), activation_func in zip(layers, activation_funcs):\n",
     "        z = ...\n",
     "        a = ...\n",
     "    return a"
@@ -395,9 +391,9 @@
    "id": "8f7df363",
    "metadata": {},
    "source": [
-    "**b)** Make a list with three activation functions(don't call them yet! you can make a list with function names as elements, and then call these elements of the list later), two ReLU and one sigmoid. (If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n",
+    "**b)** You are now given a list with three activation functions, two ReLU and one sigmoid. (Don't call them yet! you can make a list with function names as elements, and then call these elements of the list later. If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n",
     "\n",
-    "Then evaluate a network with three layers and these activation functions.\n"
+    "Evaluate a network with three layers and these activation functions.\n"
    ]
   },
   {
@@ -409,11 +405,19 @@
    "source": [
     "network_input_size = ...\n",
     "layer_output_sizes = [...]\n",
-    "activations = [...]\n",
+    "activation_funcs = [ReLU, ReLU, sigmoid]\n",
     "layers = ...\n",
     "\n",
     "x = np.random.randn(network_input_size)\n",
-    "feed_forward(x, layers, activations)"
+    "feed_forward(x, layers, activation_funcs)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c914fd0",
+   "metadata": {},
+   "source": [
+    "**c)** How does the output of the network change if you use sigmoid in the hidden layers and ReLU in the output layer?\n"
    ]
   },
   {
@@ -480,9 +484,9 @@
     "inputs = np.random.rand(1000, 4)\n",
     "\n",
     "\n",
-    "def feed_forward_batch(inputs, layers, activations):\n",
+    "def feed_forward_batch(inputs, layers, activation_funcs):\n",
     "    a = inputs\n",
-    "    for (W, b), activation in zip(layers, activations):\n",
+    "    for (W, b), activation_func in zip(layers, activation_funcs):\n",
     "        z = ...\n",
     "        a = ...\n",
     "    return a"
@@ -505,11 +509,11 @@
    "source": [
     "network_input_size = ...\n",
     "layer_output_sizes = [...]\n",
-    "activations = [...]\n",
+    "activation_funcs = [...]\n",
     "layers = create_layers_batch(network_input_size, layer_output_sizes)\n",
     "\n",
     "x = np.random.randn(network_input_size)\n",
-    "feed_forward_batch(inputs, layers, activations)"
+    "feed_forward_batch(inputs, layers, activation_funcs)"
    ]
   },
   {
@@ -584,7 +588,7 @@
    "id": "0362c4a9",
    "metadata": {},
    "source": [
-    "**a)** What should the input size for the network be with this dataset? What should the output shape of the last layer be?\n"
+    "**a)** What should the input size for the network be with this dataset? What should the output size of the last layer be?\n"
    ]
   },
   {
@@ -621,7 +625,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "predictions = feed_forward_batch(inputs, layers, activations)"
+    "predictions = feed_forward_batch(inputs, layers, activation_funcs)"
    ]
   },
   {
@@ -647,7 +651,7 @@
    "id": "334560b6",
    "metadata": {},
    "source": [
-    "# Exercise 6 - Training on real data\n",
+    "# Exercise 7 - Training on real data (Optional)\n",
     "\n",
     "To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.\n"
    ]
@@ -657,31 +661,58 @@
    "id": "700cabe4",
    "metadata": {},
    "source": [
-    "The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n"
+    "Since we are doing a classification task with multiple output classes, we use the cross-entropy loss function, which can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56bef776",
+   "id": "f30e6e2c",
    "metadata": {},
    "outputs": [],
    "source": [
-    "from autograd import grad\n",
-    "\n",
+    "def cross_entropy(predict, target):\n",
+    "    return np.sum(-target * np.log(predict))\n",
     "\n",
-    "def cost(input, layers, activations, target):\n",
-    "    predict = feed_forward_batch(input, layers, activations)\n",
-    "    return cross_entropy(predict, target)\n",
     "\n",
+    "def cost(input, layers, activation_funcs, target):\n",
+    "    predict = feed_forward_batch(input, layers, activation_funcs)\n",
+    "    return cross_entropy(predict, target)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ea9c1a4",
+   "metadata": {},
+   "source": [
+    "To improve our network on whatever prediction task we have given it, we need to use a sensible cost function, take the gradient of that cost function with respect to our network parameters, the weights and biases, and then update the weights and biases using these gradients. To clarify, we need to find and use these\n",
     "\n",
-    "def cross_entropy(predict, target):\n",
-    "    return np.sum(-target * np.log(predict))\n",
+    "$$\n",
+    "\\frac{\\partial C}{\\partial W}, \\frac{\\partial C}{\\partial b}\n",
+    "$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6c753e3b",
+   "metadata": {},
+   "source": [
+    "Now we need to compute these gradients. This is pretty hard to do for a neural network, we will use most of next week to do this, but we can also use autograd to just do it for us, which is what we always do in practice. With the code cell below, we create a function which takes all of these gradients for us.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "56bef776",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from autograd import grad\n",
     "\n",
     "\n",
     "gradient_func = grad(\n",
-    "    cross_entropy, 1\n",
-    ")  # Taking the gradient wrt. the second input to the cost function"
+    "    cost, 1\n",
+    ")  # Taking the gradient wrt. the second input to the cost function, i.e. the layers"
    ]
   },
   {
@@ -701,7 +732,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "layers_grad = gradient_func(inputs, layers, activations, targets)  # Don't change this"
+    "layers_grad = gradient_func(\n",
+    "    inputs, layers, activation_funcs, targets\n",
+    ")  # Don't change this"
    ]
   },
   {
@@ -720,10 +753,10 @@
    "outputs": [],
    "source": [
     "def train_network(\n",
-    "    inputs, layers, activations, targets, learning_rate=0.001, epochs=100\n",
+    "    inputs, layers, activation_funcs, targets, learning_rate=0.001, epochs=100\n",
     "):\n",
     "    for i in range(epochs):\n",
-    "        layers_grad = gradient_func(inputs, layers, activations, targets)\n",
+    "        layers_grad = gradient_func(inputs, layers, activation_funcs, targets)\n",
     "        for (W, b), (W_g, b_g) in zip(layers, layers_grad):\n",
     "            W -= ...\n",
     "            b -= ..."
@@ -766,7 +799,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": ".venv",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.py b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.py
index 073fceec2..2e54b4645 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.py
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek42.py
@@ -8,18 +8,20 @@
 
 # # Exercises week 42
 # 
-# **October 11-18, 2024**
+# **October 14-18, 2024**
 # 
 # Date: **Deadline is Friday October 18 at midnight**
 # 
 
 # # Overarching aims of the exercises this week
 # 
-# The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.
+# This week, you will implement the entire feed-forward pass of a neural network! Next week you will compute the gradient of the network by implementing back-propagation manually, and by using autograd which does back-propagation for you (much easier!). Next week, you will also use the gradient to optimize the network with a gradient method! However, there is an optional exercise this week to get started on training the network and getting good results!
 # 
-# This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.
+# We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.
 # 
-# If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.
+# If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1zKibVQf-iAYaAn2-GlKfgRjHtLnPlBX4#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.
+# 
+# First, here are some functions you are going to need, don't change this cell. If you are unable to import autograd, just swap in normal numpy until you want to do the final optional exercise.
 # 
 
 # In[1]:
@@ -213,17 +215,17 @@ def feed_forward_all_relu(layers, input):
 # In[ ]:
 
 
-def feed_forward(input, layers, activations):
+def feed_forward(input, layers, activation_funcs):
     a = input
-    for (W, b), activation in zip(layers, activations):
+    for (W, b), activation_func in zip(layers, activation_funcs):
         z = ...
         a = ...
     return a
 
 
-# **b)** Make a list with three activation functions(don't call them yet! you can make a list with function names as elements, and then call these elements of the list later), two ReLU and one sigmoid. (If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)
+# **b)** You are now given a list with three activation functions, two ReLU and one sigmoid. (Don't call them yet! you can make a list with function names as elements, and then call these elements of the list later. If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)
 # 
-# Then evaluate a network with three layers and these activation functions.
+# Evaluate a network with three layers and these activation functions.
 # 
 
 # In[ ]:
@@ -231,12 +233,15 @@ def feed_forward(input, layers, activations):
 
 network_input_size = ...
 layer_output_sizes = [...]
-activations = [...]
+activation_funcs = [ReLU, ReLU, sigmoid]
 layers = ...
 
 x = np.random.randn(network_input_size)
-feed_forward(x, layers, activations)
+feed_forward(x, layers, activation_funcs)
+
 
+# **c)** How does the output of the network change if you use sigmoid in the hidden layers and ReLU in the output layer?
+# 
 
 # # Exercise 5 - Processing multiple inputs at once
 # 
@@ -274,9 +279,9 @@ def create_layers_batch(network_input_size, layer_output_sizes):
 inputs = np.random.rand(1000, 4)
 
 
-def feed_forward_batch(inputs, layers, activations):
+def feed_forward_batch(inputs, layers, activation_funcs):
     a = inputs
-    for (W, b), activation in zip(layers, activations):
+    for (W, b), activation_func in zip(layers, activation_funcs):
         z = ...
         a = ...
     return a
@@ -290,11 +295,11 @@ def feed_forward_batch(inputs, layers, activations):
 
 network_input_size = ...
 layer_output_sizes = [...]
-activations = [...]
+activation_funcs = [...]
 layers = create_layers_batch(network_input_size, layer_output_sizes)
 
 x = np.random.randn(network_input_size)
-feed_forward_batch(inputs, layers, activations)
+feed_forward_batch(inputs, layers, activation_funcs)
 
 
 # You should use this batched approach moving forward, as it will lead to much more compact code. However, remember that each input is still treated separately, and that you will need to keep in mind the transposed weight matrix and other details when implementing backpropagation.
@@ -341,7 +346,7 @@ def accuracy(predictions, targets):
     return accuracy_score(one_hot_predictions, targets)
 
 
-# **a)** What should the input size for the network be with this dataset? What should the output shape of the last layer be?
+# **a)** What should the input size for the network be with this dataset? What should the output size of the last layer be?
 # 
 
 # **b)** Create a network with two hidden layers, the first with sigmoid activation and the last with softmax, the first layer should have 8 "nodes", the second has the number of nodes you found in exercise a). Softmax returns a "probability distribution", in the sense that the numbers in the output are positive and add up to 1 and, their magnitude are in some sense relative to their magnitude before going through the softmax function. Remember to use the batched version of the create_layers and feed forward functions.
@@ -360,7 +365,7 @@ def accuracy(predictions, targets):
 # In[ ]:
 
 
-predictions = feed_forward_batch(inputs, layers, activations)
+predictions = feed_forward_batch(inputs, layers, activation_funcs)
 
 
 # **d)** Compute the accuracy of your model using the accuracy function defined above. Recreate your model a couple times and see how the accuracy changes.
@@ -372,32 +377,45 @@ def accuracy(predictions, targets):
 print(accuracy(predictions, targets))
 
 
-# # Exercise 6 - Training on real data
+# # Exercise 7 - Training on real data (Optional)
 # 
 # To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.
 # 
 
-# The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is "most certain" on the correct target.
+# Since we are doing a classification task with multiple output classes, we use the cross-entropy loss function, which can evaluate performance on classification tasks. It sees if your prediction is "most certain" on the correct target.
 # 
 
 # In[ ]:
 
 
-from autograd import grad
+def cross_entropy(predict, target):
+    return np.sum(-target * np.log(predict))
 
 
-def cost(input, layers, activations, target):
-    predict = feed_forward_batch(input, layers, activations)
+def cost(input, layers, activation_funcs, target):
+    predict = feed_forward_batch(input, layers, activation_funcs)
     return cross_entropy(predict, target)
 
 
-def cross_entropy(predict, target):
-    return np.sum(-target * np.log(predict))
+# To improve our network on whatever prediction task we have given it, we need to use a sensible cost function, take the gradient of that cost function with respect to our network parameters, the weights and biases, and then update the weights and biases using these gradients. To clarify, we need to find and use these
+# 
+# $$
+# \frac{\partial C}{\partial W}, \frac{\partial C}{\partial b}
+# $$
+# 
+
+# Now we need to compute these gradients. This is pretty hard to do for a neural network, we will use most of next week to do this, but we can also use autograd to just do it for us, which is what we always do in practice. With the code cell below, we create a function which takes all of these gradients for us.
+# 
+
+# In[ ]:
+
+
+from autograd import grad
 
 
 gradient_func = grad(
-    cross_entropy, 1
-)  # Taking the gradient wrt. the second input to the cost function
+    cost, 1
+)  # Taking the gradient wrt. the second input to the cost function, i.e. the layers
 
 
 # **a)** What shape should the gradient of the cost function wrt. weights and biases be?
@@ -408,7 +426,9 @@ def cross_entropy(predict, target):
 # In[ ]:
 
 
-layers_grad = gradient_func(inputs, layers, activations, targets)  # Don't change this
+layers_grad = gradient_func(
+    inputs, layers, activation_funcs, targets
+)  # Don't change this
 
 
 # **c)** Finish the `train_network` function.
@@ -418,10 +438,10 @@ def cross_entropy(predict, target):
 
 
 def train_network(
-    inputs, layers, activations, targets, learning_rate=0.001, epochs=100
+    inputs, layers, activation_funcs, targets, learning_rate=0.001, epochs=100
 ):
     for i in range(epochs):
-        layers_grad = gradient_func(inputs, layers, activations, targets)
+        layers_grad = gradient_func(inputs, layers, activation_funcs, targets)
         for (W, b), (W_g, b_g) in zip(layers, layers_grad):
             W -= ...
             b -= ...
diff --git a/doc/LectureNotes/exercisesweek42.ipynb b/doc/LectureNotes/exercisesweek42.ipynb
index c6dd8e5a0..c24e52ac4 100644
--- a/doc/LectureNotes/exercisesweek42.ipynb
+++ b/doc/LectureNotes/exercisesweek42.ipynb
@@ -3,9 +3,7 @@
   {
    "cell_type": "markdown",
    "id": "4b4c06bc",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "\n",
@@ -15,13 +13,11 @@
   {
    "cell_type": "markdown",
    "id": "bcb25e64",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "# Exercises week 42\n",
     "\n",
-    "**October 11-18, 2024**\n",
+    "**October 14-18, 2024**\n",
     "\n",
     "Date: **Deadline is Friday October 18 at midnight**\n"
    ]
@@ -29,17 +25,17 @@
   {
    "cell_type": "markdown",
    "id": "bb01f126",
-   "metadata": {
-    "editable": true
-   },
+   "metadata": {},
    "source": [
     "# Overarching aims of the exercises this week\n",
     "\n",
-    "The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.\n",
+    "This week, you will implement the entire feed-forward pass of a neural network! Next week you will compute the gradient of the network by implementing back-propagation manually, and by using autograd which does back-propagation for you (much easier!). Next week, you will also use the gradient to optimize the network with a gradient method! However, there is an optional exercise this week to get started on training the network and getting good results!\n",
     "\n",
-    "This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n",
+    "We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n",
     "\n",
-    "If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n"
+    "If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1zKibVQf-iAYaAn2-GlKfgRjHtLnPlBX4#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n",
+    "\n",
+    "First, here are some functions you are going to need, don't change this cell. If you are unable to import autograd, just swap in normal numpy until you want to do the final optional exercise.\n"
    ]
   },
   {
@@ -365,9 +361,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def feed_forward(input, layers, activations):\n",
+    "def feed_forward(input, layers, activation_funcs):\n",
     "    a = input\n",
-    "    for (W, b), activation in zip(layers, activations):\n",
+    "    for (W, b), activation_func in zip(layers, activation_funcs):\n",
     "        z = ...\n",
     "        a = ...\n",
     "    return a"
@@ -378,9 +374,9 @@
    "id": "8f7df363",
    "metadata": {},
    "source": [
-    "**b)** Make a list with three activation functions(don't call them yet! you can make a list with function names as elements, and then call these elements of the list later), two ReLU and one sigmoid. (If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n",
+    "**b)** You are now given a list with three activation functions, two ReLU and one sigmoid. (Don't call them yet! you can make a list with function names as elements, and then call these elements of the list later. If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n",
     "\n",
-    "Then evaluate a network with three layers and these activation functions.\n"
+    "Evaluate a network with three layers and these activation functions.\n"
    ]
   },
   {
@@ -392,11 +388,19 @@
    "source": [
     "network_input_size = ...\n",
     "layer_output_sizes = [...]\n",
-    "activations = [...]\n",
+    "activation_funcs = [ReLU, ReLU, sigmoid]\n",
     "layers = ...\n",
     "\n",
     "x = np.random.randn(network_input_size)\n",
-    "feed_forward(x, layers, activations)"
+    "feed_forward(x, layers, activation_funcs)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c914fd0",
+   "metadata": {},
+   "source": [
+    "**c)** How does the output of the network change if you use sigmoid in the hidden layers and ReLU in the output layer?\n"
    ]
   },
   {
@@ -463,9 +467,9 @@
     "inputs = np.random.rand(1000, 4)\n",
     "\n",
     "\n",
-    "def feed_forward_batch(inputs, layers, activations):\n",
+    "def feed_forward_batch(inputs, layers, activation_funcs):\n",
     "    a = inputs\n",
-    "    for (W, b), activation in zip(layers, activations):\n",
+    "    for (W, b), activation_func in zip(layers, activation_funcs):\n",
     "        z = ...\n",
     "        a = ...\n",
     "    return a"
@@ -488,11 +492,11 @@
    "source": [
     "network_input_size = ...\n",
     "layer_output_sizes = [...]\n",
-    "activations = [...]\n",
+    "activation_funcs = [...]\n",
     "layers = create_layers_batch(network_input_size, layer_output_sizes)\n",
     "\n",
     "x = np.random.randn(network_input_size)\n",
-    "feed_forward_batch(inputs, layers, activations)"
+    "feed_forward_batch(inputs, layers, activation_funcs)"
    ]
   },
   {
@@ -567,7 +571,7 @@
    "id": "0362c4a9",
    "metadata": {},
    "source": [
-    "**a)** What should the input size for the network be with this dataset? What should the output shape of the last layer be?\n"
+    "**a)** What should the input size for the network be with this dataset? What should the output size of the last layer be?\n"
    ]
   },
   {
@@ -604,7 +608,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "predictions = feed_forward_batch(inputs, layers, activations)"
+    "predictions = feed_forward_batch(inputs, layers, activation_funcs)"
    ]
   },
   {
@@ -630,7 +634,7 @@
    "id": "334560b6",
    "metadata": {},
    "source": [
-    "# Exercise 6 - Training on real data\n",
+    "# Exercise 7 - Training on real data (Optional)\n",
     "\n",
     "To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.\n"
    ]
@@ -640,31 +644,58 @@
    "id": "700cabe4",
    "metadata": {},
    "source": [
-    "The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n"
+    "Since we are doing a classification task with multiple output classes, we use the cross-entropy loss function, which can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56bef776",
+   "id": "f30e6e2c",
    "metadata": {},
    "outputs": [],
    "source": [
-    "from autograd import grad\n",
-    "\n",
+    "def cross_entropy(predict, target):\n",
+    "    return np.sum(-target * np.log(predict))\n",
     "\n",
-    "def cost(input, layers, activations, target):\n",
-    "    predict = feed_forward_batch(input, layers, activations)\n",
-    "    return cross_entropy(predict, target)\n",
     "\n",
+    "def cost(input, layers, activation_funcs, target):\n",
+    "    predict = feed_forward_batch(input, layers, activation_funcs)\n",
+    "    return cross_entropy(predict, target)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ea9c1a4",
+   "metadata": {},
+   "source": [
+    "To improve our network on whatever prediction task we have given it, we need to use a sensible cost function, take the gradient of that cost function with respect to our network parameters, the weights and biases, and then update the weights and biases using these gradients. To clarify, we need to find and use these\n",
     "\n",
-    "def cross_entropy(predict, target):\n",
-    "    return np.sum(-target * np.log(predict))\n",
+    "$$\n",
+    "\\frac{\\partial C}{\\partial W}, \\frac{\\partial C}{\\partial b}\n",
+    "$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6c753e3b",
+   "metadata": {},
+   "source": [
+    "Now we need to compute these gradients. This is pretty hard to do for a neural network, we will use most of next week to do this, but we can also use autograd to just do it for us, which is what we always do in practice. With the code cell below, we create a function which takes all of these gradients for us.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "56bef776",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from autograd import grad\n",
     "\n",
     "\n",
     "gradient_func = grad(\n",
-    "    cross_entropy, 1\n",
-    ")  # Taking the gradient wrt. the second input to the cost function"
+    "    cost, 1\n",
+    ")  # Taking the gradient wrt. the second input to the cost function, i.e. the layers"
    ]
   },
   {
@@ -684,7 +715,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "layers_grad = gradient_func(inputs, layers, activations, targets)  # Don't change this"
+    "layers_grad = gradient_func(\n",
+    "    inputs, layers, activation_funcs, targets\n",
+    ")  # Don't change this"
    ]
   },
   {
@@ -703,10 +736,10 @@
    "outputs": [],
    "source": [
     "def train_network(\n",
-    "    inputs, layers, activations, targets, learning_rate=0.001, epochs=100\n",
+    "    inputs, layers, activation_funcs, targets, learning_rate=0.001, epochs=100\n",
     "):\n",
     "    for i in range(epochs):\n",
-    "        layers_grad = gradient_func(inputs, layers, activations, targets)\n",
+    "        layers_grad = gradient_func(inputs, layers, activation_funcs, targets)\n",
     "        for (W, b), (W_g, b_g) in zip(layers, layers_grad):\n",
     "            W -= ...\n",
     "            b -= ..."
@@ -749,7 +782,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": ".venv",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -763,7 +796,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.7"
+   "version": "3.9.15"
   }
  },
  "nbformat": 4,