├── .gitignore ├── Exercise_03_1.ipynb ├── Exercise_03_2.ipynb ├── Exercise_03_2_solution.ipynb ├── Exercise_03_3.ipynb ├── Exercise_03_3_solution.ipynb ├── Exercise_04.ipynb ├── Exercise_04_1.ipynb ├── Exercise_04_1_solution.ipynb ├── Exercise_04_2.ipynb ├── Exercise_04_2_solution.ipynb ├── Exercise_04_3.ipynb ├── Exercise_04_3_solution.ipynb ├── Exercise_05_1.ipynb ├── Exercise_05_1_solution.ipynb ├── Exercise_05_2.ipynb ├── Exercise_05_2_solution.ipynb ├── Exercise_05_3.ipynb ├── Exercise_05_3_solution.ipynb ├── Exercise_07_1.ipynb ├── Exercise_07_1_solution.ipynb ├── Exercise_07_2.ipynb ├── Exercise_07_2_solution.ipynb ├── Exercise_08_1.ipynb ├── Exercise_08_1_solution.ipynb ├── Exercise_08_2.ipynb ├── Exercise_08_2_solution.ipynb ├── Exercise_09_1.ipynb ├── Exercise_09_2.ipynb ├── Exercise_09_2_solution.ipynb ├── Exercise_10_1.ipynb ├── Exercise_10_1_solution.ipynb ├── Exercise_11_1.ipynb ├── Exercise_11_1_solution.ipynb ├── Exercise_12_1.ipynb ├── Exercise_12_1_solution.ipynb ├── Exercise_12_2.ipynb ├── Exercise_12_2_solution.ipynb ├── Exercise_12_3.ipynb ├── Exercise_12_3_solution.ipynb ├── Exercise_16_1.ipynb ├── Exercise_16_1_solution.ipynb ├── Exercise_17_1.ipynb ├── Exercise_17_1_solution.ipynb ├── Exercise_18_1.ipynb ├── Exercise_18_1_solution.ipynb ├── Exercise_18_2.ipynb ├── Exercise_18_2_solution.ipynb ├── LICENSE.md ├── README.md ├── _config.yml ├── edgeconv.py ├── images ├── checkerboard_3_2_task_1.png ├── checkerboard_3_2_task_3.png ├── checkerboard_l1.png ├── checkerboard_l2_high.png ├── checkerboard_l2_low.png ├── checkerboard_l2_moderate.png ├── checkerboard_overtraining.png ├── checkerboard_regularization.png └── checkerboard_tf_playground.png ├── index.md └── requirements.txt /.gitignore: -------------------------------------------------------------------------------- 1 | weights-* 2 | .ipynb_checkpoints/ 3 | *.npz 4 | __pycache__/ 5 | -------------------------------------------------------------------------------- /Exercise_03_1.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 3.1\n", 8 | "\n", 9 | "Congratulations - you have successfully navigated to the exercise page for the book **Deep Learning for Physics Research** \n", 10 | "\n", 11 | "This page hosts additional descriptions as well (where appropriate) example solutions to the exercise problems. While the solutions are available, we recommend you first attempt to solve the problem yourself, before looking up the answer. As many problems are open-ended, the presented solution of course often only represents one possible option how the problem could be solved.\n", 12 | "\n", 13 | "Some helpful links:\n", 14 | " * Python Tutorial (https://docs.python.org/3.7/tutorial/index.html): an introduction to the Python programming language\n", 15 | " \n", 16 | " * Google Colab (https://colab.research.google.com/): for Python development in your web-browser\n", 17 | " * Anaconda (https://www.anaconda.com/products/individual): a Python distribution for local installation\n", 18 | " \n", 19 | " * numpy (https://numpy.org/doc/stable/user/quickstart.html): a widely used library for mathematical operations in Python\n", 20 | " \n", 21 | " * Keras (https://keras.io/): a beginner-friendly deep learning library used in these exercises\n", 22 | " \n", 23 | " * Tensor Flow (https://www.tensorflow.org/): a useful backend for deep learning development\n", 24 | "\n", 25 | " * SciKit Learn (https://scikit-learn.org/stable/): helpful machine learning library \n", 26 | " \n", 27 | " * Seaborn (https://seaborn.pydata.org/): a library for creating nice looking graphs and figures\n" 28 | ] 29 | } 30 | ], 31 | "metadata": { 32 | "kernelspec": { 33 | "display_name": "Python 3", 34 | "language": "python", 35 | "name": "python3" 36 | }, 37 | "language_info": { 38 | "codemirror_mode": { 39 | "name": "ipython", 40 | "version": 3 41 | }, 42 | "file_extension": ".py", 43 | "mimetype": "text/x-python", 44 | "name": "python", 45 | "nbconvert_exporter": "python", 46 | "pygments_lexer": "ipython3", 47 | "version": "3.7.6" 48 | } 49 | }, 50 | "nbformat": 4, 51 | "nbformat_minor": 4 52 | } 53 | -------------------------------------------------------------------------------- /Exercise_03_2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": { 6 | "id": "rF2trPuyzm9C" 7 | }, 8 | "source": [ 9 | "# Exercise 3.2\n" 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 1, 15 | "metadata": { 16 | "id": "ipcsUFDUzm9C" 17 | }, 18 | "outputs": [], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import matplotlib.pyplot as plt" 22 | ] 23 | }, 24 | { 25 | "cell_type": "markdown", 26 | "metadata": { 27 | "id": "MCJe_ITJzm9G" 28 | }, 29 | "source": [ 30 | "**Linear Regression**\n", 31 | "\n", 32 | "The goal of this exercise is to explore a simple linear regression problem based on Portugese white wine.\n", 33 | "\n", 34 | "The dataset is based on \n", 35 | "Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. **Modeling wine preferences by data mining from physicochemical properties**. Published in Decision Support Systems, Elsevier, 47(4):547-553, 2009. \n", 36 | "\n" 37 | ] 38 | }, 39 | { 40 | "cell_type": "code", 41 | "execution_count": 3, 42 | "metadata": { 43 | "colab": { 44 | "base_uri": "https://localhost:8080/" 45 | }, 46 | "id": "NopU99AT9G7s", 47 | "outputId": "d7e8848e-b9c0-4eb4-8f18-5acda9d8c343" 48 | }, 49 | "outputs": [ 50 | { 51 | "name": "stdout", 52 | "output_type": "stream", 53 | "text": [ 54 | "/bin/sh: wget: command not found\r\n" 55 | ] 56 | } 57 | ], 58 | "source": [ 59 | "# The code snippet below is responsible for downloading the dataset\n", 60 | "# - for example when running via Google Colab.\n", 61 | "#\n", 62 | "# You can also directly download the file using the link if you work\n", 63 | "# with a local setup (in that case, ignore the !wget)\n", 64 | "\n", 65 | "!wget https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv" 66 | ] 67 | }, 68 | { 69 | "cell_type": "markdown", 70 | "metadata": { 71 | "id": "zEiZ19s5zm9G" 72 | }, 73 | "source": [ 74 | "**Before we start**\n", 75 | "\n", 76 | "The downloaded file contains data on 4989 wines. For each wine 11 features are recorded (column 0 to 10). The final columns contains the quality of the wine. This is what we want to predict. More information on the features and the quality measurement is provided in the original publication.\n", 77 | "\n", 78 | "List of columns/features: \n", 79 | "0. fixed acidity\n", 80 | "1. volatile acidity\n", 81 | "2. citric acid\n", 82 | "3. residual sugar\n", 83 | "4. chlorides\n", 84 | "5. free sulfur dioxide\n", 85 | "6. total sulfur dioxide\n", 86 | "7. density\n", 87 | "8. pH\n", 88 | "9. sulphates\n", 89 | "10. alcohol\n", 90 | "11. quality\n", 91 | "\n", 92 | "\n", 93 | "\n", 94 | "[file]: https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv" 95 | ] 96 | }, 97 | { 98 | "cell_type": "code", 99 | "execution_count": null, 100 | "metadata": { 101 | "colab": { 102 | "base_uri": "https://localhost:8080/" 103 | }, 104 | "id": "5ONqeI5Uzm9H", 105 | "outputId": "d31ba8d4-cf0a-4f25-8a93-9091c0dd041a" 106 | }, 107 | "outputs": [ 108 | { 109 | "name": "stdout", 110 | "output_type": "stream", 111 | "text": [ 112 | "('data:', (4898, 12))\n", 113 | "First example:\n", 114 | "('Features:', array([7.600e+00, 3.800e-01, 2.800e-01, 4.200e+00, 2.900e-02, 7.000e+00,\n", 115 | " 1.120e+02, 9.906e-01, 3.000e+00, 4.100e-01, 1.260e+01]))\n", 116 | "('Quality:', 6.0)\n" 117 | ] 118 | } 119 | ], 120 | "source": [ 121 | "# Before working with the data, \n", 122 | "# we download and prepare all features\n", 123 | "\n", 124 | "# load all examples from the file\n", 125 | "data = np.genfromtxt('winequality-white.csv',delimiter=\";\",skip_header=1)\n", 126 | "\n", 127 | "print(\"data:\", data.shape)\n", 128 | "\n", 129 | "# Prepare for proper training\n", 130 | "np.random.shuffle(data) # randomly sort examples\n", 131 | "\n", 132 | "# take the first 3000 examples for training\n", 133 | "# (remember array slicing from last week)\n", 134 | "X_train = data[:3000,:11] # all features except last column\n", 135 | "y_train = data[:3000,11] # quality column\n", 136 | "\n", 137 | "# and the remaining examples for testing\n", 138 | "X_test = data[3000:,:11] # all features except last column\n", 139 | "y_test = data[3000:,11] # quality column\n", 140 | "\n", 141 | "print(\"First example:\")\n", 142 | "print(\"Features:\", X_train[0])\n", 143 | "print(\"Quality:\", y_train[0])" 144 | ] 145 | }, 146 | { 147 | "cell_type": "markdown", 148 | "metadata": { 149 | "id": "jiwnyNHpzm9L" 150 | }, 151 | "source": [ 152 | "# Problems\n", 153 | "\n", 154 | "\n", 155 | "* First we want to understand the data better. Plot (`plt.hist`) the distribution of each of the features for the training data as well as the 2D distribution (either `plt.scatter` or `plt.hist2d`) of each feature versus quality. Also calculate the correlation coefficient (`np.corrcoef`) for each feature with quality. Which feature by itself seems most predictive for the quality?\n", 156 | "\n", 157 | "* Calculate the linear regression weights. Numpy provides functions for matrix multiplication (`np.matmul`), matrix transposition (`.T`) and matrix inversion (`np.linalg.inv`).\n", 158 | "\n", 159 | "* Use the weights to predict the quality for the test dataset. How\n", 160 | "does your predicted quality compare with the true quality of the test data? Calculate the correlation coefficient between predicted and true quality and draw a scatter plot." 161 | ] 162 | }, 163 | { 164 | "cell_type": "markdown", 165 | "metadata": {}, 166 | "source": [ 167 | "# Hints" 168 | ] 169 | }, 170 | { 171 | "cell_type": "markdown", 172 | "metadata": {}, 173 | "source": [ 174 | "Formally, we want to find weights $w_i$ that minimize:\n", 175 | "$$\n", 176 | "\\sum_{j}\\left(\\sum_{i} X_{i j} w_{i}-y_{j}\\right)^{2}\n", 177 | "$$\n", 178 | "The index $i$ denotes the different features (properties of the wines) while the index $j$ runs over the different wines. The matrix $X_{ij}$ contains the training data, $y_j$ is the 'true' quality for sample $j$. The weights can be found by taking the first derivative of the above expression with respect to the weights and setting it to zero (the standard strategy for finding an extremum), and solving the corresponding system of equations (for a detailed derivation, see [here](https://en.wikipedia.org/wiki/Ordinary_least_squares)). The result is:\n", 179 | "$$\n", 180 | "\\overrightarrow{\\mathbf{w}}=\\left(\\mathbf{X}^{T} \\mathbf{X}\\right)^{-1} \\mathbf{X}^{T} \\overrightarrow{\\mathbf{y}}\n", 181 | "$$\n", 182 | "\n", 183 | "In the end, you should have as many components of $w_i$ as there are features in the data (i.e. eleven in this case). \n", 184 | "\n", 185 | "You can use `.shape` to inspect the dimensions of numpy tensors.\n" 186 | ] 187 | } 188 | ], 189 | "metadata": { 190 | "colab": { 191 | "collapsed_sections": [], 192 | "name": "Exercise 4", 193 | "provenance": [] 194 | }, 195 | "kernelspec": { 196 | "display_name": "Python 3", 197 | "language": "python", 198 | "name": "python3" 199 | }, 200 | "language_info": { 201 | "codemirror_mode": { 202 | "name": "ipython", 203 | "version": 3 204 | }, 205 | "file_extension": ".py", 206 | "mimetype": "text/x-python", 207 | "name": "python", 208 | "nbconvert_exporter": "python", 209 | "pygments_lexer": "ipython3", 210 | "version": "3.6.9" 211 | } 212 | }, 213 | "nbformat": 4, 214 | "nbformat_minor": 1 215 | } 216 | -------------------------------------------------------------------------------- /Exercise_03_3.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 3.3\n", 8 | "## Checkerboard\n", 9 | "\n", 10 | "Open the Tensorflow Playground (www.playground.tensorflow.org) and select on the left the checkerboard pattern as the data basis.\n", 11 | "\n", 12 | "The data is taken from a two-dimensional probability distribution and is represented by the value pairs $x_1$ and $x_2$. The regions $x1$, $x_2 > 0$ and $x_1$, $x_2 < 0$ are shown by one color. For value pairs with $x_1 > 0$, $x_2 < 0$ and $x_1 < 0$, $x_2 > 0$, the regions are indicated by a different color. \n", 13 | "\n", 14 | "In features, select the two independent variables $x_1$ and $x_2$ and start the network training. The network learns that $x_1$ and $x_2$ are for these data not independent variables, but are taken from the probability distribution of the checkerboard pattern.\n", 15 | "\n", 16 | "[![Checkerboard](./images/checkerboard_tf_playground.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=4,2&seed=0.20784&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false)\n", 17 | "\n", 18 | "## Tasks\n", 19 | "1. Try various settings for the number of layers and neurons using `ReLU` as activation function. What is the smallest network that gives a good fit result?\n", 20 | "2. What do you observe when training networks with the same settings multiple times? Explain your observations.\n", 21 | "3. Try additional input features: Which one is most helpful?\n" 22 | ] 23 | } 24 | ], 25 | "metadata": { 26 | "kernelspec": { 27 | "display_name": "Python 3", 28 | "language": "python", 29 | "name": "python3" 30 | }, 31 | "language_info": { 32 | "codemirror_mode": { 33 | "name": "ipython", 34 | "version": 3 35 | }, 36 | "file_extension": ".py", 37 | "mimetype": "text/x-python", 38 | "name": "python", 39 | "nbconvert_exporter": "python", 40 | "pygments_lexer": "ipython3", 41 | "version": "3.6.9" 42 | } 43 | }, 44 | "nbformat": 4, 45 | "nbformat_minor": 4 46 | } 47 | -------------------------------------------------------------------------------- /Exercise_03_3_solution.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 3.3 - Solution\n", 8 | "## Checkerboard\n", 9 | "\n", 10 | "Open the Tensorflow Playground (www.playground.tensorflow.org) and select on the left the checkerboard pattern as the data basis.\n", 11 | "\n", 12 | "The data is taken from a two-dimensional probability distribution and is represented by the value pairs $x_1$ and $x_2$. The regions $x1$, $x_2 > 0$ and $x_1$, $x_2 < 0$ are shown by one color. For value pairs with $x_1 > 0$, $x_2 < 0$ and $x_1 < 0$, $x_2 > 0$, the regions are indicated by a different color. \n", 13 | "\n", 14 | "In features, select the two independent variables $x_1$ and $x_2$ and start the network training. The network learns that $x_1$ and $x_2$ are for these data not independent variables, but are taken from the probability distribution of the checkerboard pattern.\n", 15 | "\n", 16 | "[![Checkerboard](./images/checkerboard_tf_playground.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=4,2&seed=0.20784&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false)\n", 17 | "\n", 18 | "## Tasks\n", 19 | "1. Try various settings for the number of layers and neurons using `ReLU` as activation function. What is the smallest network that gives a good fit result?\n", 20 | "2. What do you observe when training networks with the same settings multiple times? Explain your observations.\n", 21 | "3. Try additional input features: Which one is most helpful?\n" 22 | ] 23 | }, 24 | { 25 | "cell_type": "markdown", 26 | "metadata": {}, 27 | "source": [ 28 | "## Solutions\n", 29 | "Hint: click on the images to open the correct playground settings needed to solve the task, respectively." 30 | ] 31 | }, 32 | { 33 | "cell_type": "markdown", 34 | "metadata": {}, 35 | "source": [ 36 | "### Task 1\n", 37 | "Try various settings for the number of layers and neurons using ReLU as activation function. What is the smallest network that gives a good fit result?\n" 38 | ] 39 | }, 40 | { 41 | "cell_type": "markdown", 42 | "metadata": {}, 43 | "source": [ 44 | "[![Checkerboard](./images/checkerboard_tf_playground.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=3&seed=0.10528&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false)\n", 45 | "\n", 46 | " A network with a single layer holding 3 nodes. However, this configuration is not stable.\n", 47 | "\n", 48 | "A network with a single layer, holding 4 nodes, is way more stable. " 49 | ] 50 | }, 51 | { 52 | "cell_type": "markdown", 53 | "metadata": {}, 54 | "source": [ 55 | "### Task 2\n", 56 | "What do you observe when training networks with the same settings multiple times? Explain your observations." 57 | ] 58 | }, 59 | { 60 | "cell_type": "markdown", 61 | "metadata": {}, 62 | "source": [ 63 | " Due to the random initialization of weights, the network training always develops a little bit differently, leading to different results. " 64 | ] 65 | }, 66 | { 67 | "cell_type": "markdown", 68 | "metadata": {}, 69 | "source": [ 70 | "### Task 3\n", 71 | "Try additional input features: Which one is most helpful?" 72 | ] 73 | }, 74 | { 75 | "cell_type": "markdown", 76 | "metadata": {}, 77 | "source": [ 78 | "[![Checkerboard](./images/checkerboard_3_2_task_3.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=&seed=0.10528&showTestData=false&discretize=false&percTrainData=50&x=false&y=false&xTimesY=true&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false)\n", 79 | "\n", 80 | " Obviously, the $x_1\\cdot x_2$ feature is most helpful. " 81 | ] 82 | } 83 | ], 84 | "metadata": { 85 | "kernelspec": { 86 | "display_name": "Python 3", 87 | "language": "python", 88 | "name": "python3" 89 | }, 90 | "language_info": { 91 | "codemirror_mode": { 92 | "name": "ipython", 93 | "version": 3 94 | }, 95 | "file_extension": ".py", 96 | "mimetype": "text/x-python", 97 | "name": "python", 98 | "nbconvert_exporter": "python", 99 | "pygments_lexer": "ipython3", 100 | "version": "3.6.9" 101 | } 102 | }, 103 | "nbformat": 4, 104 | "nbformat_minor": 4 105 | } 106 | -------------------------------------------------------------------------------- /Exercise_04.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": { 6 | "id": "rF2trPuyzm9C" 7 | }, 8 | "source": [ 9 | "# In-Class Basics\n" 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": null, 15 | "metadata": { 16 | "id": "ipcsUFDUzm9C" 17 | }, 18 | "outputs": [], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import matplotlib.pyplot as plt" 22 | ] 23 | }, 24 | { 25 | "cell_type": "markdown", 26 | "metadata": { 27 | "id": "MCJe_ITJzm9G" 28 | }, 29 | "source": [ 30 | "**Linear Regression**\n", 31 | "\n", 32 | "The goal of this week's exercise is to explore a simple linear regression problem based on Portugese white wine.\n", 33 | "\n", 34 | "The dataset is based on \n", 35 | "Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. **Modeling wine preferences by data mining from physicochemical properties**. Published in Decision Support Systems, Elsevier, 47(4):547-553, 2009. \n", 36 | "\n" 37 | ] 38 | }, 39 | { 40 | "cell_type": "code", 41 | "execution_count": null, 42 | "metadata": { 43 | "colab": { 44 | "base_uri": "https://localhost:8080/" 45 | }, 46 | "id": "NopU99AT9G7s", 47 | "outputId": "d7e8848e-b9c0-4eb4-8f18-5acda9d8c343", 48 | "scrolled": true 49 | }, 50 | "outputs": [ 51 | { 52 | "name": "stdout", 53 | "output_type": "stream", 54 | "text": [ 55 | "--2021-05-10 08:16:34-- https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 56 | "Resolving archive.ics.uci.edu (archive.ics.uci.edu)... 128.195.10.252\n", 57 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 58 | "Retrying.\n", 59 | "\n", 60 | "--2021-05-10 08:17:07-- (try: 2) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 61 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 62 | "Retrying.\n", 63 | "\n", 64 | "--2021-05-10 08:17:41-- (try: 3) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 65 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 66 | "Retrying.\n", 67 | "\n", 68 | "--2021-05-10 08:18:16-- (try: 4) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 69 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 70 | "Retrying.\n", 71 | "\n", 72 | "--2021-05-10 08:18:52-- (try: 5) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 73 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 74 | "Retrying.\n", 75 | "\n", 76 | "--2021-05-10 08:19:28-- (try: 6) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 77 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 78 | "Retrying.\n", 79 | "\n", 80 | "--2021-05-10 08:20:06-- (try: 7) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 81 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 82 | "Retrying.\n", 83 | "\n", 84 | "--2021-05-10 08:20:45-- (try: 8) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 85 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 86 | "Retrying.\n", 87 | "\n", 88 | "--2021-05-10 08:21:25-- (try: 9) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 89 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 90 | "Retrying.\n", 91 | "\n", 92 | "--2021-05-10 08:22:06-- (try:10) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 93 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 94 | "Retrying.\n", 95 | "\n", 96 | "--2021-05-10 08:22:48-- (try:11) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 97 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 98 | "Retrying.\n", 99 | "\n", 100 | "--2021-05-10 08:23:30-- (try:12) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 101 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 102 | "Retrying.\n", 103 | "\n", 104 | "--2021-05-10 08:24:12-- (try:13) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 105 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 106 | "Retrying.\n", 107 | "\n", 108 | "--2021-05-10 08:24:54-- (try:14) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 109 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 110 | "Retrying.\n", 111 | "\n", 112 | "--2021-05-10 08:25:36-- (try:15) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 113 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 114 | "Retrying.\n", 115 | "\n", 116 | "--2021-05-10 08:26:18-- (try:16) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 117 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 118 | "Retrying.\n", 119 | "\n", 120 | "--2021-05-10 08:27:00-- (try:17) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 121 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 122 | "Retrying.\n", 123 | "\n", 124 | "--2021-05-10 08:27:42-- (try:18) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 125 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 126 | "Retrying.\n", 127 | "\n", 128 | "--2021-05-10 08:28:24-- (try:19) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 129 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 130 | "Retrying.\n", 131 | "\n", 132 | "--2021-05-10 08:29:06-- (try:20) https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 133 | "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... failed: Connection timed out.\n", 134 | "Giving up.\n", 135 | "\n" 136 | ] 137 | } 138 | ], 139 | "source": [ 140 | "# The code snippet below is responsible for downloading the dataset to\n", 141 | "# Google. You can directly download the file using the link\n", 142 | "# if you work with a local anaconda setup\n", 143 | "\n", 144 | "# Temporarily replaced link as the ML dataset archive seems to be down\n", 145 | "#!wget https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv\n", 146 | "!wget https://raw.githubusercontent.com/zygmuntz/wine-quality/master/winequality/winequality-white.csv" 147 | ] 148 | }, 149 | { 150 | "cell_type": "markdown", 151 | "metadata": { 152 | "id": "zEiZ19s5zm9G" 153 | }, 154 | "source": [ 155 | "**Before we start**\n", 156 | "\n", 157 | "The downloaded file contains data on 4989 wines. For each wine 11 features are recorded (column 0 to 10). The final columns contains the quality of the wine. This is what we want to predict.\n", 158 | "\n", 159 | "List of columns/features: \n", 160 | "0. fixed acidity\n", 161 | "1. volatile acidity\n", 162 | "2. citric acid\n", 163 | "3. residual sugar\n", 164 | "4. chlorides\n", 165 | "5. free sulfur dioxide\n", 166 | "6. total sulfur dioxide\n", 167 | "7. density\n", 168 | "8. pH\n", 169 | "9. sulphates\n", 170 | "10. alcohol\n", 171 | "11. quality\n", 172 | "\n", 173 | "\n", 174 | "\n", 175 | "[file]: https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": null, 181 | "metadata": { 182 | "colab": { 183 | "base_uri": "https://localhost:8080/" 184 | }, 185 | "id": "5ONqeI5Uzm9H", 186 | "outputId": "d31ba8d4-cf0a-4f25-8a93-9091c0dd041a" 187 | }, 188 | "outputs": [ 189 | { 190 | "name": "stdout", 191 | "output_type": "stream", 192 | "text": [ 193 | "('data:', (4898, 12))\n", 194 | "First example:\n", 195 | "('Features:', array([7.600e+00, 3.800e-01, 2.800e-01, 4.200e+00, 2.900e-02, 7.000e+00,\n", 196 | " 1.120e+02, 9.906e-01, 3.000e+00, 4.100e-01, 1.260e+01]))\n", 197 | "('Quality:', 6.0)\n" 198 | ] 199 | } 200 | ], 201 | "source": [ 202 | "# load all examples from the file\n", 203 | "data = np.genfromtxt('winequality-white.csv',delimiter=\";\",skip_header=1)\n", 204 | "\n", 205 | "print(\"data:\", data.shape)\n", 206 | "\n", 207 | "# Prepare for proper training\n", 208 | "np.random.shuffle(data) # randomly sort examples\n", 209 | "\n", 210 | "# take the first 3000 examples for training\n", 211 | "# (remember array slicing from last week)\n", 212 | "X_train = data[:3000,:11] # all features except last column\n", 213 | "y_train = data[:3000,11] # quality column\n", 214 | "\n", 215 | "# and the remaining examples for testing\n", 216 | "X_test = data[3000:,:11] # all features except last column\n", 217 | "y_test = data[3000:,11] # quality column\n", 218 | "\n", 219 | "print(\"First example:\")\n", 220 | "print(\"Features:\", X_train[0])\n", 221 | "print(\"Quality:\", y_train[0])" 222 | ] 223 | }, 224 | { 225 | "cell_type": "markdown", 226 | "metadata": { 227 | "id": "jiwnyNHpzm9L" 228 | }, 229 | "source": [ 230 | "# Homework\n", 231 | "\n", 232 | "1. First we want to understand the data better. Plot (`plt.hist`) the distribution of each of the features for the training data as well as the 2D distribution (either `plt.scatter` or `plt.hist2d`) of each feature versus quality. Also calculate the correlation coefficient (`np.corrcoef`) for each feature with quality. Which feature by itself seems most\n", 233 | " predictive for the quality?\n", 234 | "\n", 235 | "2. Calculate the linear regression weights as derived in the lecture. Numpy provides functions for matrix multiplication (`np.matmul`), matrix transposition (`.T`) and matrix inversion (`np.linalg.inv`).\n", 236 | "\n", 237 | "3. Use the weights to predict the quality for the test dataset. How does your predicted quality compare with the true quality of the test data? Calculate the correlation coefficient between predicted and true quality and draw the scatter plot. " 238 | ] 239 | }, 240 | { 241 | "cell_type": "code", 242 | "execution_count": null, 243 | "metadata": { 244 | "id": "MzzCP2ST898a" 245 | }, 246 | "outputs": [], 247 | "source": [ 248 | "x = np.random.uniform(size=(3,4))" 249 | ] 250 | }, 251 | { 252 | "cell_type": "code", 253 | "execution_count": null, 254 | "metadata": { 255 | "colab": { 256 | "base_uri": "https://localhost:8080/" 257 | }, 258 | "id": "MlbmmHoA9BJQ", 259 | "outputId": "98e65963-3173-46c7-f47b-6b9a6714c187" 260 | }, 261 | "outputs": [ 262 | { 263 | "data": { 264 | "text/plain": [ 265 | "array([[0.27061972, 0.85093187, 0.06038869, 0.6430975 ],\n", 266 | " [0.05802941, 0.1492127 , 0.93073299, 0.70555297],\n", 267 | " [0.4806267 , 0.27201085, 0.75607278, 0.88637951]])" 268 | ] 269 | }, 270 | "execution_count": 27, 271 | "metadata": { 272 | "tags": [] 273 | }, 274 | "output_type": "execute_result" 275 | } 276 | ], 277 | "source": [ 278 | "x" 279 | ] 280 | }, 281 | { 282 | "cell_type": "code", 283 | "execution_count": null, 284 | "metadata": { 285 | "id": "MqRyPzzN-ar0" 286 | }, 287 | "outputs": [], 288 | "source": [] 289 | }, 290 | { 291 | "cell_type": "code", 292 | "execution_count": null, 293 | "metadata": { 294 | "colab": { 295 | "base_uri": "https://localhost:8080/" 296 | }, 297 | "id": "HiYXwCle9Fow", 298 | "outputId": "949146bf-7184-488f-a347-4af589917bf6" 299 | }, 300 | "outputs": [ 301 | { 302 | "data": { 303 | "text/plain": [ 304 | "0.14921269768865764" 305 | ] 306 | }, 307 | "execution_count": 28, 308 | "metadata": { 309 | "tags": [] 310 | }, 311 | "output_type": "execute_result" 312 | } 313 | ], 314 | "source": [ 315 | "x[1,1]" 316 | ] 317 | }, 318 | { 319 | "cell_type": "code", 320 | "execution_count": null, 321 | "metadata": { 322 | "colab": { 323 | "base_uri": "https://localhost:8080/" 324 | }, 325 | "id": "0M56hD2R9VYo", 326 | "outputId": "7199e2d2-4d5d-4500-ea8a-37c9c12046b5" 327 | }, 328 | "outputs": [ 329 | { 330 | "name": "stdout", 331 | "output_type": "stream", 332 | "text": [ 333 | "[[0.93073299 0.70555297]\n", 334 | " [0.75607278 0.88637951]]\n" 335 | ] 336 | } 337 | ], 338 | "source": [ 339 | "f = x[1:,2:]\n", 340 | "print(f)" 341 | ] 342 | }, 343 | { 344 | "cell_type": "code", 345 | "execution_count": null, 346 | "metadata": { 347 | "colab": { 348 | "base_uri": "https://localhost:8080/" 349 | }, 350 | "id": "J3f29BC99cDK", 351 | "outputId": "91dd6002-c95f-47ea-de6f-ba4279175b8d" 352 | }, 353 | "outputs": [ 354 | { 355 | "name": "stdout", 356 | "output_type": "stream", 357 | "text": [ 358 | "[[9.99000000e+02 7.05552973e-01]\n", 359 | " [7.56072781e-01 8.86379512e-01]]\n" 360 | ] 361 | } 362 | ], 363 | "source": [ 364 | "f[0,0] = 999\n", 365 | "print(f)" 366 | ] 367 | }, 368 | { 369 | "cell_type": "code", 370 | "execution_count": null, 371 | "metadata": { 372 | "colab": { 373 | "base_uri": "https://localhost:8080/" 374 | }, 375 | "id": "ZnvjBmbs9hdq", 376 | "outputId": "c30f3f02-c9a9-42ae-da07-af13151e6596" 377 | }, 378 | "outputs": [ 379 | { 380 | "data": { 381 | "text/plain": [ 382 | "array([[2.70619720e-01, 8.50931871e-01, 6.03886907e-02, 6.43097505e-01],\n", 383 | " [5.80294054e-02, 1.49212698e-01, 9.99000000e+02, 7.05552973e-01],\n", 384 | " [4.80626701e-01, 2.72010854e-01, 7.56072781e-01, 8.86379512e-01]])" 385 | ] 386 | }, 387 | "execution_count": 35, 388 | "metadata": { 389 | "tags": [] 390 | }, 391 | "output_type": "execute_result" 392 | } 393 | ], 394 | "source": [ 395 | "x" 396 | ] 397 | }, 398 | { 399 | "cell_type": "code", 400 | "execution_count": null, 401 | "metadata": { 402 | "id": "c4kcHKQP-tTp" 403 | }, 404 | "outputs": [], 405 | "source": [] 406 | } 407 | ], 408 | "metadata": { 409 | "colab": { 410 | "collapsed_sections": [], 411 | "name": "Exercise 4", 412 | "provenance": [] 413 | }, 414 | "kernelspec": { 415 | "display_name": "Python 2", 416 | "language": "python", 417 | "name": "python2" 418 | }, 419 | "language_info": { 420 | "codemirror_mode": { 421 | "name": "ipython", 422 | "version": 3 423 | }, 424 | "file_extension": ".py", 425 | "mimetype": "text/x-python", 426 | "name": "python", 427 | "nbconvert_exporter": "python", 428 | "pygments_lexer": "ipython3", 429 | "version": "3.6.9" 430 | } 431 | }, 432 | "nbformat": 4, 433 | "nbformat_minor": 1 434 | } 435 | -------------------------------------------------------------------------------- /Exercise_04_1.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": { 6 | "id": "rF2trPuyzm9C" 7 | }, 8 | "source": [ 9 | "# Exercise 4.1\n" 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 3, 15 | "metadata": { 16 | "id": "ipcsUFDUzm9C" 17 | }, 18 | "outputs": [], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import matplotlib.pyplot as plt" 22 | ] 23 | }, 24 | { 25 | "cell_type": "markdown", 26 | "metadata": { 27 | "id": "MCJe_ITJzm9G" 28 | }, 29 | "source": [ 30 | "**Disclaimer**\n", 31 | "\n", 32 | "The book mistakently refers to the page for Exercise 4.2 when introducting Exercise 4.1, etc. Of course, these numbers should match: Book Exercise 4.1 is discussed under Exercise 4.1 \n", 33 | "\n", 34 | "**Simple Network**\n", 35 | "\n", 36 | "We continue with the dataset first encountered in Exercise 3.2. Please refer to the discussion there for an introduction to the data and the learning objective.\n", 37 | "\n", 38 | "Here, we manually implement a simple network architecture" 39 | ] 40 | }, 41 | { 42 | "cell_type": "code", 43 | "execution_count": 1, 44 | "metadata": { 45 | "colab": { 46 | "base_uri": "https://localhost:8080/" 47 | }, 48 | "id": "NopU99AT9G7s", 49 | "outputId": "d7e8848e-b9c0-4eb4-8f18-5acda9d8c343" 50 | }, 51 | "outputs": [ 52 | { 53 | "name": "stdout", 54 | "output_type": "stream", 55 | "text": [ 56 | "/bin/sh: wget: command not found\r\n" 57 | ] 58 | } 59 | ], 60 | "source": [ 61 | "# The code snippet below is responsible for downloading the dataset\n", 62 | "# - for example when running via Google Colab.\n", 63 | "#\n", 64 | "# You can also directly download the file using the link if you work\n", 65 | "# with a local setup (in that case, ignore the !wget)\n", 66 | "\n", 67 | "!wget https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv" 68 | ] 69 | }, 70 | { 71 | "cell_type": "code", 72 | "execution_count": 5, 73 | "metadata": { 74 | "colab": { 75 | "base_uri": "https://localhost:8080/" 76 | }, 77 | "id": "5ONqeI5Uzm9H", 78 | "outputId": "d31ba8d4-cf0a-4f25-8a93-9091c0dd041a" 79 | }, 80 | "outputs": [ 81 | { 82 | "name": "stdout", 83 | "output_type": "stream", 84 | "text": [ 85 | "data: (4898, 12)\n", 86 | "First example:\n", 87 | "Features: [5.900e+00 3.400e-01 2.200e-01 2.400e+00 3.000e-02 1.900e+01 1.350e+02\n", 88 | " 9.894e-01 3.410e+00 7.800e-01 1.390e+01]\n", 89 | "Quality: 7.0\n" 90 | ] 91 | } 92 | ], 93 | "source": [ 94 | "# Before working with the data, \n", 95 | "# we download and prepare all features\n", 96 | "\n", 97 | "# load all examples from the file\n", 98 | "data = np.genfromtxt('winequality-white.csv',delimiter=\";\",skip_header=1)\n", 99 | "\n", 100 | "print(\"data:\", data.shape)\n", 101 | "\n", 102 | "# Prepare for proper training\n", 103 | "np.random.shuffle(data) # randomly sort examples\n", 104 | "\n", 105 | "# take the first 3000 examples for training\n", 106 | "# (remember array slicing from last week)\n", 107 | "X_train = data[:3000,:11] # all features except last column\n", 108 | "y_train = data[:3000,11] # quality column\n", 109 | "\n", 110 | "# and the remaining examples for testing\n", 111 | "X_test = data[3000:,:11] # all features except last column\n", 112 | "y_test = data[3000:,11] # quality column\n", 113 | "\n", 114 | "print(\"First example:\")\n", 115 | "print(\"Features:\", X_train[0])\n", 116 | "print(\"Quality:\", y_train[0])" 117 | ] 118 | }, 119 | { 120 | "cell_type": "markdown", 121 | "metadata": { 122 | "id": "jiwnyNHpzm9L" 123 | }, 124 | "source": [ 125 | "# Problems\n", 126 | "\n", 127 | "The goal is to implement the training of a neural network with one input layer, one hidden layer, and one output layer using gradient descent. We first (below) define the matrices and initialise with random values. We need W, b, W' and b'. The shapes will be:\n", 128 | " * W: (number of hidden nodes, number of inputs) named `W`\n", 129 | " * b: (number of hidden nodes) named `b`\n", 130 | " * W': (number of hidden nodes) named `Wp`\n", 131 | " * b': (one) named `bp`\n", 132 | "\n", 133 | "Your tasks are: \n", 134 | " * Implement a forward pass of the network as `dnn` (see below)\n", 135 | " * Implement a function that uses one data point to update the weights using gradient descent. You can follow the `update_weights` skeleton below\n", 136 | " * Now you can use the code below (training loop and evaluation) to train the network for multiple data points and even over several epochs. Try to find a set of hyperparameters (number of nodes in the hidden layer, learning rate, number of training epochs) that gives stable results. What is the best result (as measured by the loss on the training sample) you can get?" 137 | ] 138 | }, 139 | { 140 | "cell_type": "code", 141 | "execution_count": 8, 142 | "metadata": {}, 143 | "outputs": [ 144 | { 145 | "name": "stdout", 146 | "output_type": "stream", 147 | "text": [ 148 | "(50, 11)\n" 149 | ] 150 | } 151 | ], 152 | "source": [ 153 | "# Initialise weights with suitable random distributions\n", 154 | "hidden_nodes = 50 # number of nodes in the hidden layer\n", 155 | "n_inputs = 11 # input features in the dataset\n", 156 | "\n", 157 | "# See section 4.3 of the book for more information on\n", 158 | "# how to initialise network parameters\n", 159 | "W = np.random.randn(hidden_nodes,11)*np.sqrt(2./n_inputs)\n", 160 | "b = np.random.randn(hidden_nodes)*np.sqrt(2./n_inputs)\n", 161 | "Wp = np.random.randn(hidden_nodes)*np.sqrt(2./hidden_nodes)\n", 162 | "bp = np.random.randn((1))\n", 163 | "\n", 164 | "print(W.shape)" 165 | ] 166 | }, 167 | { 168 | "cell_type": "code", 169 | "execution_count": 6, 170 | "metadata": {}, 171 | "outputs": [], 172 | "source": [ 173 | "# You can use this implementation of the ReLu activation function\n", 174 | "def relu(x):\n", 175 | " return np.maximum(x, 0)" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": 7, 181 | "metadata": {}, 182 | "outputs": [], 183 | "source": [ 184 | "def dnn(x,W,b,Wp,bp):\n", 185 | " # TODO Calculate and return network output of forward pass\n", 186 | " # See Hint 1 for additional information\n", 187 | " return -1 # change to the calculated output" 188 | ] 189 | }, 190 | { 191 | "cell_type": "code", 192 | "execution_count": 11, 193 | "metadata": {}, 194 | "outputs": [], 195 | "source": [ 196 | "def update_weights(x,y, W, b, Wp, bp):\n", 197 | " \n", 198 | " learning_rate = 0.01\n", 199 | "\n", 200 | " # TODO: Calculate the network output (use the function dnn defined above)\n", 201 | " \n", 202 | " # TODO: Derive the gradient for each of W,b,Wp,bp by taking the partial\n", 203 | " # derivative of the loss function with respect to the variable and\n", 204 | " # then implement the resulting weight-update procedure\n", 205 | " # See Hint 2 for additional information\n", 206 | "\n", 207 | " # You might need these numpy functions:\n", 208 | " # np.dot, np.outer, np.heaviside\n", 209 | " # Hint: Use .shape and print statements to make sure all operations\n", 210 | " # do what you want them to \n", 211 | " \n", 212 | " # TODO: Update the weights/bias following the rule: weight_new = weight_old - learning_rate * gradient \n", 213 | "\n", 214 | " return -1 # no return value needed, you can modify the weights in-place" 215 | ] 216 | }, 217 | { 218 | "cell_type": "markdown", 219 | "metadata": {}, 220 | "source": [ 221 | "# Training loop and evaluation below" 222 | ] 223 | }, 224 | { 225 | "cell_type": "code", 226 | "execution_count": null, 227 | "metadata": {}, 228 | "outputs": [], 229 | "source": [ 230 | "# The code below implements the training.\n", 231 | "# If you correctly implement dnn and update_weights above, \n", 232 | "# you should not need to change anything below. \n", 233 | "# (apart from increasing the number of epochs)\n", 234 | "\n", 235 | "train_losses = []\n", 236 | "test_losses = []\n", 237 | "\n", 238 | "# How many epochs to train\n", 239 | "# This will just train for one epoch\n", 240 | "# You will want a higher number once everything works\n", 241 | "n_epochs = 1 \n", 242 | "\n", 243 | "# Loop over the epochs\n", 244 | "for ep in range(n_epochs):\n", 245 | " \n", 246 | " # Each epoch is a complete over the training data\n", 247 | " for i in range(X_train.shape[0]):\n", 248 | " \n", 249 | " # pick one example\n", 250 | " x = X_train[i]\n", 251 | " y = y_train[i]\n", 252 | "\n", 253 | " # use it to update the weights\n", 254 | " update_weights(x,y,W,b,Wp,bp)\n", 255 | " \n", 256 | " # Calculate predictions for the full training and testing sample\n", 257 | " y_pred_train = [dnn(x,W,b,Wp,bp)[0] for x in X_train]\n", 258 | " y_pred = [dnn(x,W,b,Wp,bp)[0] for x in X_test]\n", 259 | "\n", 260 | " # Calculate aver loss / example over the epoch\n", 261 | " train_loss = sum((y_pred_train-y_train)**2) / y_train.shape[0]\n", 262 | " test_loss = sum((y_pred-y_test)**2) / y_test.shape[0] \n", 263 | " \n", 264 | " # print some information\n", 265 | " print(\"Epoch:\",ep, \"Train Loss:\", train_loss, \"Test Loss:\", test_loss)\n", 266 | " \n", 267 | " # and store the losses for later use\n", 268 | " train_losses.append(train_loss)\n", 269 | " test_losses.append(test_loss)\n", 270 | " \n", 271 | " \n", 272 | "# After the training:\n", 273 | " \n", 274 | "# Prepare scatter plot\n", 275 | "y_pred = [dnn(x,W,b,Wp,bp)[0] for x in X_test]\n", 276 | "\n", 277 | "print(\"Best loss:\", min(test_losses), \"Final loss:\", test_losses[-1])\n", 278 | "\n", 279 | "print(\"Correlation coefficient:\", np.corrcoef(y_pred,y_test)[0,1])\n", 280 | "plt.scatter(y_pred_train,y_train)\n", 281 | "plt.xlabel(\"Predicted\")\n", 282 | "plt.ylabel(\"True\")\n", 283 | "plt.show()\n", 284 | "\n", 285 | "# Prepare and loss over time\n", 286 | "plt.plot(train_losses,label=\"train\")\n", 287 | "plt.plot(test_losses,label=\"test\")\n", 288 | "plt.legend()\n", 289 | "plt.xlabel(\"Epoch\")\n", 290 | "plt.ylabel(\"Loss\")\n", 291 | "plt.show()\n" 292 | ] 293 | }, 294 | { 295 | "cell_type": "markdown", 296 | "metadata": {}, 297 | "source": [ 298 | "# Hint 1" 299 | ] 300 | }, 301 | { 302 | "cell_type": "markdown", 303 | "metadata": {}, 304 | "source": [ 305 | "We want a network with one hidden layer. As activiation in the hidden layer $\\sigma$ we apply element-wise ReLu, while no activation is used for the output layer. The forward pass of the network then reads:\n", 306 | "$$\\hat{y}=\\mathbf{W}^{\\prime} \\sigma(\\mathbf{W} \\vec{x}+\\vec{b})+b^{\\prime}$$" 307 | ] 308 | }, 309 | { 310 | "cell_type": "markdown", 311 | "metadata": {}, 312 | "source": [ 313 | "# Hint 2" 314 | ] 315 | }, 316 | { 317 | "cell_type": "markdown", 318 | "metadata": {}, 319 | "source": [ 320 | "For the regression problem the objective function is the mean squared error between the prediction and the true label $y$: \n", 321 | "$$\n", 322 | "L=(\\hat{y}-y)^{2}\n", 323 | "$$\n", 324 | "\n", 325 | "Taking the partial derivatives - and diligently the applying chain rule - with respect to the different objects yields:\n", 326 | "\n", 327 | "$$\n", 328 | "\\begin{aligned}\n", 329 | "\\frac{\\partial L}{\\partial b^{\\prime}} &=2(\\hat{y}-y) \\\\\n", 330 | "\\frac{\\partial L}{\\partial b_{k}} &=2(\\hat{y}-y) \\mathbf{W}_{k}^{\\prime} \\theta\\left(\\sum_{i} \\mathbf{W}_{i k} x_{i}+b_{k}\\right) \\\\\n", 331 | "\\frac{\\partial L}{\\partial \\mathbf{W}_{k}^{\\prime}} &=2(\\hat{y}-y) \\sigma\\left(\\sum_{i} \\mathbf{W}_{i k} x_{i}+b_{k}\\right) \\\\\n", 332 | "\\frac{\\partial L}{\\partial \\mathbf{W}_{k m}} &=2(\\hat{y}-y) \\mathbf{W}_{m}^{\\prime} \\theta\\left(\\sum_{i} \\mathbf{W}_{i k} x_{i}+b_{m}\\right) x_{k}\n", 333 | "\\end{aligned}\n", 334 | "$$\n", 335 | "\n", 336 | "Here, $\\Theta$ denotes the Heaviside step function." 337 | ] 338 | }, 339 | { 340 | "cell_type": "code", 341 | "execution_count": null, 342 | "metadata": {}, 343 | "outputs": [], 344 | "source": [] 345 | } 346 | ], 347 | "metadata": { 348 | "colab": { 349 | "collapsed_sections": [], 350 | "name": "Exercise 4", 351 | "provenance": [] 352 | }, 353 | "kernelspec": { 354 | "display_name": "Python 3", 355 | "language": "python", 356 | "name": "python3" 357 | }, 358 | "language_info": { 359 | "codemirror_mode": { 360 | "name": "ipython", 361 | "version": 3 362 | }, 363 | "file_extension": ".py", 364 | "mimetype": "text/x-python", 365 | "name": "python", 366 | "nbconvert_exporter": "python", 367 | "pygments_lexer": "ipython3", 368 | "version": "3.6.9" 369 | } 370 | }, 371 | "nbformat": 4, 372 | "nbformat_minor": 1 373 | } 374 | -------------------------------------------------------------------------------- /Exercise_04_2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 4.2\n", 8 | "## Linear regression\n", 9 | "In this task we will design and train a linear model using [Keras](https://keras.io/).\n", 10 | "\n", 11 | "### Tasks\n", 12 | "1. Complete the implemetation of the `LinearLayer`\n", 13 | "2. Define a meaningful objective\n", 14 | "3. Implement gradient descent and train the linear model for 80 epochs." 15 | ] 16 | }, 17 | { 18 | "cell_type": "code", 19 | "execution_count": 3, 20 | "metadata": {}, 21 | "outputs": [], 22 | "source": [ 23 | "import tensorflow as tf\n", 24 | "from tensorflow import keras\n", 25 | "import numpy as np\n", 26 | "import matplotlib.pyplot as plt\n", 27 | "\n", 28 | "layers = keras.layers" 29 | ] 30 | }, 31 | { 32 | "cell_type": "markdown", 33 | "metadata": {}, 34 | "source": [ 35 | "### Simulation of data\n", 36 | "Let's first simulate some noisy data" 37 | ] 38 | }, 39 | { 40 | "cell_type": "code", 41 | "execution_count": 2, 42 | "metadata": {}, 43 | "outputs": [ 44 | { 45 | "name": "stdout", 46 | "output_type": "stream", 47 | "text": [ 48 | "x.shape: (100, 1)\n", 49 | "y.shape: (100,)\n" 50 | ] 51 | } 52 | ], 53 | "source": [ 54 | "np.random.seed(1904)\n", 55 | "x = np.float32(np.linspace(-1, 1, 100)[:,np.newaxis])\n", 56 | "y = np.float32(2 * x[:,0] + 0.3 * np.random.randn(100))\n", 57 | "print(\"x.shape:\", x.shape)\n", 58 | "print(\"y.shape:\", y.shape)" 59 | ] 60 | }, 61 | { 62 | "cell_type": "markdown", 63 | "metadata": {}, 64 | "source": [ 65 | "### Implement linear model" 66 | ] 67 | }, 68 | { 69 | "cell_type": "markdown", 70 | "metadata": {}, 71 | "source": [ 72 | "Now, we have to design a linear layer that maps from the input $x$ to the output $y$ using a single adaptive weight $w$:\n", 73 | " \n", 74 | "$$y = w \\cdot x$$\n", 75 | "\n", 76 | "### Task 1\n", 77 | "Complete the implementation of the `LinearLayer` by adding the linear transformation in the `call` function." 78 | ] 79 | }, 80 | { 81 | "cell_type": "code", 82 | "execution_count": null, 83 | "metadata": {}, 84 | "outputs": [], 85 | "source": [ 86 | "class LinearLayer(layers.Layer):\n", 87 | "\n", 88 | " def __init__(self, units=1, input_dim=1): # when intializing the layer the weights have to be initialized\n", 89 | " super(LinearLayer, self).__init__()\n", 90 | " w_init = tf.random_normal_initializer()\n", 91 | " self.w = tf.Variable(initial_value=w_init(shape=(input_dim, units), dtype=\"float32\"),\n", 92 | " trainable=True)\n", 93 | "\n", 94 | " def call(self, inputs): # when calling the layer the linear transformation has to be performed\n", 95 | " return ..." 96 | ] 97 | }, 98 | { 99 | "cell_type": "markdown", 100 | "metadata": {}, 101 | "source": [ 102 | "Build a model using the implemented layer." 103 | ] 104 | }, 105 | { 106 | "cell_type": "code", 107 | "execution_count": null, 108 | "metadata": {}, 109 | "outputs": [], 110 | "source": [ 111 | "model = keras.models.Sequential()\n", 112 | "model.add(LinearLayer(units=1, input_dim=1))" 113 | ] 114 | }, 115 | { 116 | "cell_type": "code", 117 | "execution_count": null, 118 | "metadata": {}, 119 | "outputs": [], 120 | "source": [ 121 | "model.build((None, 1))\n", 122 | "print(model.summary())" 123 | ] 124 | }, 125 | { 126 | "cell_type": "markdown", 127 | "metadata": {}, 128 | "source": [ 129 | "### Performance before the training\n", 130 | "Plot data and model before the training" 131 | ] 132 | }, 133 | { 134 | "cell_type": "code", 135 | "execution_count": null, 136 | "metadata": {}, 137 | "outputs": [], 138 | "source": [ 139 | "y_pred = model(x)\n", 140 | "\n", 141 | "fig, ax = plt.subplots(1)\n", 142 | "ax.plot(x, y, 'bo', label='data')\n", 143 | "ax.plot(x, y_pred, 'r-', label='model')\n", 144 | "ax.set(xlabel='$x$', ylabel='$y$')\n", 145 | "ax.grid()\n", 146 | "ax.legend(loc='lower right')\n", 147 | "plt.tight_layout()" 148 | ] 149 | }, 150 | { 151 | "cell_type": "markdown", 152 | "metadata": {}, 153 | "source": [ 154 | "### Task 2: Define the objective function\n", 155 | "Define a meaningful objective here (regression task). \n", 156 | "Note that you can use `tf.reduce_mean()` to average your loss estimate over the full data set (100 points)." 157 | ] 158 | }, 159 | { 160 | "cell_type": "code", 161 | "execution_count": null, 162 | "metadata": {}, 163 | "outputs": [], 164 | "source": [ 165 | "def loss(x, y):\n", 166 | " return ...." 167 | ] 168 | }, 169 | { 170 | "cell_type": "markdown", 171 | "metadata": {}, 172 | "source": [ 173 | "### Task 3 - Train the model using gradient descent\n", 174 | "'Train' the linear model for 80 epochs (or iterations) with a meaningful learning rate and implement gradient descent. \n", 175 | "Hint: you can access the adaptive parameters using `model.trainable_weights` and perform $w' \\rightarrow w-z$ using `w.assign_sub(z)`" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": null, 181 | "metadata": {}, 182 | "outputs": [], 183 | "source": [ 184 | "epochs = ... # number of epochs\n", 185 | "lr = ... # learning rate\n", 186 | "\n", 187 | "for epoch in range(epochs):\n", 188 | "\n", 189 | " with tf.GradientTape() as tape:\n", 190 | " output = model(x, training=True)\n", 191 | " # Compute loss value\n", 192 | " loss_value = loss(tf.convert_to_tensor(y), output)\n", 193 | " grads = tape.gradient(...)\n", 194 | " \n", 195 | " for weight, grad in zip(model.trainable_weights, grads):\n", 196 | " weight.assign_sub(...)\n", 197 | "\n", 198 | " print(\"Current loss at epoch %d: %.4f\" % (epoch, float(loss_value)))" 199 | ] 200 | }, 201 | { 202 | "cell_type": "markdown", 203 | "metadata": {}, 204 | "source": [ 205 | "### Performance of the fitted model\n", 206 | "Plot data and model after the training" 207 | ] 208 | }, 209 | { 210 | "cell_type": "code", 211 | "execution_count": null, 212 | "metadata": {}, 213 | "outputs": [], 214 | "source": [ 215 | "fig, ax = plt.subplots(1)\n", 216 | "\n", 217 | "y_pred = model(x)\n", 218 | "\n", 219 | "ax.plot(x, y, 'bo', label='data')\n", 220 | "ax.plot(x, y_pred, 'r-', label='model')\n", 221 | "ax.set(xlabel='$x$', ylabel='$y$')\n", 222 | "ax.grid()\n", 223 | "ax.legend(loc='lower right')\n", 224 | "plt.tight_layout()" 225 | ] 226 | } 227 | ], 228 | "metadata": { 229 | "kernelspec": { 230 | "display_name": "Python 3", 231 | "language": "python", 232 | "name": "python3" 233 | }, 234 | "language_info": { 235 | "codemirror_mode": { 236 | "name": "ipython", 237 | "version": 3 238 | }, 239 | "file_extension": ".py", 240 | "mimetype": "text/x-python", 241 | "name": "python", 242 | "nbconvert_exporter": "python", 243 | "pygments_lexer": "ipython3", 244 | "version": "3.6.9" 245 | } 246 | }, 247 | "nbformat": 4, 248 | "nbformat_minor": 4 249 | } 250 | -------------------------------------------------------------------------------- /Exercise_04_3.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 4.3\n", 8 | "## Classification\n", 9 | "In the following tasks, we will repeatedly use some basic functions (e.g., the softmax function or the cross-entropy) of the [Keras](https://keras.io/) Library. To familiarize with them, we will implement the most important of them ourselves in this task.\n", 10 | "\n", 11 | "Suppose we want to classify some data (4 samples) into 3 distinct classes: 0, 1, and 2.\n", 12 | "We have set up a network with a pre-activation output `z` in the last layer.\n", 13 | "Applying softmax will give the final model output.\n", 14 | "\n", 15 | "input X ---> some network --> `z`
\n", 16 | "--> `y_model = softmax(z)`\n", 17 | "\n", 18 | "We quantify the agreement between truth (y) and model using categorical cross-entropy.\n", 19 | "\n", 20 | "$$J = - \\sum_i (y_i * \\log(y_\\mathrm{model}(x_i))$$\n", 21 | "\n", 22 | "In the following you are to implement softmax and categorical cross-entropy\n", 23 | "and evaluate them values given the values for `z`." 24 | ] 25 | }, 26 | { 27 | "cell_type": "code", 28 | "execution_count": 1, 29 | "metadata": {}, 30 | "outputs": [], 31 | "source": [ 32 | "import numpy as np" 33 | ] 34 | }, 35 | { 36 | "cell_type": "markdown", 37 | "metadata": {}, 38 | "source": [ 39 | "##### Data: 4 samples with the following class labels (input features X irrelevant here)" 40 | ] 41 | }, 42 | { 43 | "cell_type": "code", 44 | "execution_count": 2, 45 | "metadata": {}, 46 | "outputs": [], 47 | "source": [ 48 | "y_cl = np.array([0, 0, 2, 1])" 49 | ] 50 | }, 51 | { 52 | "cell_type": "markdown", 53 | "metadata": {}, 54 | "source": [ 55 | "##### output of the last network layer before applying softmax" 56 | ] 57 | }, 58 | { 59 | "cell_type": "code", 60 | "execution_count": 3, 61 | "metadata": {}, 62 | "outputs": [], 63 | "source": [ 64 | "z = np.array([\n", 65 | " [4, 5, 1],\n", 66 | " [-1, -2, -3],\n", 67 | " [0.1, 0.2, 0.3],\n", 68 | " [-1, 17, 1]\n", 69 | " ]).astype(np.float32)" 70 | ] 71 | }, 72 | { 73 | "cell_type": "markdown", 74 | "metadata": {}, 75 | "source": [ 76 | "## Task 1)\n", 77 | "Write a function that turns any class labels `y_cl` into one-hot encodings `y`.\n", 78 | "\n", 79 | "0 --> (1, 0, 0)
\n", 80 | "1 --> (0, 1, 0)
\n", 81 | "2 --> (0, 0, 1)
\n", 82 | "\n", 83 | "Make sure that `np.shape(y) = (4, 3)` for `np.shape(y_cl) = (4)`.\n", 84 | "\n" 85 | ] 86 | }, 87 | { 88 | "cell_type": "code", 89 | "execution_count": null, 90 | "metadata": {}, 91 | "outputs": [], 92 | "source": [] 93 | }, 94 | { 95 | "cell_type": "markdown", 96 | "metadata": {}, 97 | "source": [ 98 | "## Task 2)\n", 99 | "Write a function that returns the softmax of the input `z` along the last axis" 100 | ] 101 | }, 102 | { 103 | "cell_type": "code", 104 | "execution_count": null, 105 | "metadata": {}, 106 | "outputs": [], 107 | "source": [] 108 | }, 109 | { 110 | "cell_type": "markdown", 111 | "metadata": {}, 112 | "source": [ 113 | "## Task 3)\n", 114 | "Compute the categorical cross-entropy between data and model" 115 | ] 116 | }, 117 | { 118 | "cell_type": "code", 119 | "execution_count": null, 120 | "metadata": {}, 121 | "outputs": [], 122 | "source": [] 123 | }, 124 | { 125 | "cell_type": "markdown", 126 | "metadata": {}, 127 | "source": [ 128 | "## Task 4)\n", 129 | "Determine which calsses are predicted by the model (maximum prediction)" 130 | ] 131 | }, 132 | { 133 | "cell_type": "code", 134 | "execution_count": null, 135 | "metadata": {}, 136 | "outputs": [], 137 | "source": [] 138 | }, 139 | { 140 | "cell_type": "markdown", 141 | "metadata": {}, 142 | "source": [ 143 | "## Task 5)\n", 144 | "Estimate how many samples are classified correctly (accuracy)" 145 | ] 146 | }, 147 | { 148 | "cell_type": "code", 149 | "execution_count": null, 150 | "metadata": {}, 151 | "outputs": [], 152 | "source": [] 153 | } 154 | ], 155 | "metadata": { 156 | "kernelspec": { 157 | "display_name": "Python 3", 158 | "language": "python", 159 | "name": "python3" 160 | }, 161 | "language_info": { 162 | "codemirror_mode": { 163 | "name": "ipython", 164 | "version": 3 165 | }, 166 | "file_extension": ".py", 167 | "mimetype": "text/x-python", 168 | "name": "python", 169 | "nbconvert_exporter": "python", 170 | "pygments_lexer": "ipython3", 171 | "version": "3.6.9" 172 | } 173 | }, 174 | "nbformat": 4, 175 | "nbformat_minor": 4 176 | } 177 | -------------------------------------------------------------------------------- /Exercise_04_3_solution.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 4.3 - Solution\n", 8 | "## Classification\n", 9 | "In the following tasks, we will repeatedly use some basic functions (e.g., the softmax function or the cross-entropy) of the [Keras](https://keras.io/) Library. To familiarize with them, we will implement the most important of them ourselves in this task.\n", 10 | "\n", 11 | "Suppose we want to classify some data (4 samples) into 3 distinct classes: 0, 1, and 2.\n", 12 | "We have set up a network with a pre-activation output `z` in the last layer.\n", 13 | "Applying softmax will give the final model output.\n", 14 | "\n", 15 | "input X ---> some network --> `z`
\n", 16 | "--> `y_model = softmax(z)`\n", 17 | "\n", 18 | "We quantify the agreement between truth (y) and model using categorical cross-entropy.\n", 19 | "\n", 20 | "$$J = - \\sum_i (y_i * \\log(y_\\mathrm{model}(x_i))$$\n", 21 | "\n", 22 | "In the following you are to implement softmax and categorical cross-entropy\n", 23 | "and evaluate them values given the values for `z`." 24 | ] 25 | }, 26 | { 27 | "cell_type": "code", 28 | "execution_count": 1, 29 | "metadata": {}, 30 | "outputs": [], 31 | "source": [ 32 | "import numpy as np" 33 | ] 34 | }, 35 | { 36 | "cell_type": "markdown", 37 | "metadata": {}, 38 | "source": [ 39 | "##### Data: 4 samples with the following class labels (input features X irrelevant here)" 40 | ] 41 | }, 42 | { 43 | "cell_type": "code", 44 | "execution_count": 2, 45 | "metadata": {}, 46 | "outputs": [], 47 | "source": [ 48 | "y_cl = np.array([0, 0, 2, 1])" 49 | ] 50 | }, 51 | { 52 | "cell_type": "markdown", 53 | "metadata": {}, 54 | "source": [ 55 | "##### output of the last network layer before applying softmax" 56 | ] 57 | }, 58 | { 59 | "cell_type": "code", 60 | "execution_count": 3, 61 | "metadata": {}, 62 | "outputs": [], 63 | "source": [ 64 | "z = np.array([\n", 65 | " [4, 5, 1],\n", 66 | " [-1, -2, -3],\n", 67 | " [0.1, 0.2, 0.3],\n", 68 | " [-1, 17, 1]\n", 69 | " ]).astype(np.float32)" 70 | ] 71 | }, 72 | { 73 | "cell_type": "markdown", 74 | "metadata": {}, 75 | "source": [ 76 | "## Task 1)\n", 77 | "Write a function that turns any class labels `y_cl` into one-hot encodings `y`.\n", 78 | "\n", 79 | "0 --> (1, 0, 0)
\n", 80 | "1 --> (0, 1, 0)
\n", 81 | "2 --> (0, 0, 1)
\n", 82 | "\n", 83 | "Make sure that `np.shape(y) = (4, 3)` for `np.shape(y_cl) = (4)`.\n", 84 | "\n" 85 | ] 86 | }, 87 | { 88 | "cell_type": "code", 89 | "execution_count": 4, 90 | "metadata": {}, 91 | "outputs": [ 92 | { 93 | "name": "stdout", 94 | "output_type": "stream", 95 | "text": [ 96 | "one-hot encoding of data labels\n", 97 | "[[1. 0. 0.]\n", 98 | " [1. 0. 0.]\n", 99 | " [0. 0. 1.]\n", 100 | " [0. 1. 0.]]\n" 101 | ] 102 | } 103 | ], 104 | "source": [ 105 | "def to_onehot(y_cl, num_classes):\n", 106 | " y = np.zeros((len(y_cl), num_classes))\n", 107 | " y[np.arange(4), y_cl] = 1\n", 108 | " return y\n", 109 | "\n", 110 | "y = to_onehot(y_cl, num_classes=3)\n", 111 | "print('one-hot encoding of data labels')\n", 112 | "print(y)" 113 | ] 114 | }, 115 | { 116 | "cell_type": "markdown", 117 | "metadata": {}, 118 | "source": [ 119 | "## Task 2)\n", 120 | "Write a function that returns the softmax of the input `z` along the last axis" 121 | ] 122 | }, 123 | { 124 | "cell_type": "code", 125 | "execution_count": 5, 126 | "metadata": {}, 127 | "outputs": [ 128 | { 129 | "name": "stdout", 130 | "output_type": "stream", 131 | "text": [ 132 | "softmax(z)\n", 133 | "[[2.6538792e-01 7.2139925e-01 1.3212887e-02]\n", 134 | " [6.6524100e-01 2.4472848e-01 9.0030573e-02]\n", 135 | " [3.0060962e-01 3.3222499e-01 3.6716542e-01]\n", 136 | " [1.5229979e-08 9.9999994e-01 1.1253517e-07]]\n" 137 | ] 138 | } 139 | ], 140 | "source": [ 141 | "def softmax(z):\n", 142 | " expz = np.exp(z).T\n", 143 | " return (expz / np.sum(expz, axis=0)).T\n", 144 | "\n", 145 | "y_model = softmax(z)\n", 146 | "print('softmax(z)')\n", 147 | "print(y_model)" 148 | ] 149 | }, 150 | { 151 | "cell_type": "markdown", 152 | "metadata": {}, 153 | "source": [ 154 | "## Task 3)\n", 155 | "Compute the categorical cross-entropy between data and model" 156 | ] 157 | }, 158 | { 159 | "cell_type": "code", 160 | "execution_count": 6, 161 | "metadata": {}, 162 | "outputs": [ 163 | { 164 | "name": "stdout", 165 | "output_type": "stream", 166 | "text": [ 167 | "cross entropy = 0.684028\n" 168 | ] 169 | } 170 | ], 171 | "source": [ 172 | "crossentropy = -np.mean(np.sum(y * np.log(y_model), axis=1))\n", 173 | "crossentropy = -np.mean(np.log(y_model[np.arange(4), y_cl])) # alternative formulation\n", 174 | "print('cross entropy = %f' % crossentropy)" 175 | ] 176 | }, 177 | { 178 | "cell_type": "markdown", 179 | "metadata": {}, 180 | "source": [ 181 | "## Task 4)\n", 182 | "Determine which calsses are predicted by the model (maximum prediction)" 183 | ] 184 | }, 185 | { 186 | "cell_type": "code", 187 | "execution_count": 7, 188 | "metadata": {}, 189 | "outputs": [ 190 | { 191 | "name": "stdout", 192 | "output_type": "stream", 193 | "text": [ 194 | "\n", 195 | "true class labels = [0 0 2 1]\n", 196 | "predicted class labels = [1 0 2 1]\n" 197 | ] 198 | } 199 | ], 200 | "source": [ 201 | "y_model_cl = np.argmax(y_model, axis=1)\n", 202 | "print('\\ntrue class labels = ', y_cl)\n", 203 | "print('predicted class labels =', y_model_cl)" 204 | ] 205 | }, 206 | { 207 | "cell_type": "markdown", 208 | "metadata": {}, 209 | "source": [ 210 | "## Task 5)\n", 211 | "Estimate how many samples are classified correctly (accuracy)" 212 | ] 213 | }, 214 | { 215 | "cell_type": "code", 216 | "execution_count": 8, 217 | "metadata": {}, 218 | "outputs": [ 219 | { 220 | "name": "stdout", 221 | "output_type": "stream", 222 | "text": [ 223 | "accuracy = 0.75\n" 224 | ] 225 | } 226 | ], 227 | "source": [ 228 | "accuracy = np.mean(y_model_cl == y_cl)\n", 229 | "print('accuracy = %.2f' % accuracy)" 230 | ] 231 | } 232 | ], 233 | "metadata": { 234 | "kernelspec": { 235 | "display_name": "Python 3", 236 | "language": "python", 237 | "name": "python3" 238 | }, 239 | "language_info": { 240 | "codemirror_mode": { 241 | "name": "ipython", 242 | "version": 3 243 | }, 244 | "file_extension": ".py", 245 | "mimetype": "text/x-python", 246 | "name": "python", 247 | "nbconvert_exporter": "python", 248 | "pygments_lexer": "ipython3", 249 | "version": "3.6.9" 250 | } 251 | }, 252 | "nbformat": 4, 253 | "nbformat_minor": 4 254 | } 255 | -------------------------------------------------------------------------------- /Exercise_05_1.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 5.1\n", 8 | "## Overtraining and Regularization:\n", 9 | "Open the Tensorflow Playground\n", 10 | "(https://playground.tensorflow.org) and select on the left the checkerboard\n", 11 | "pattern as the data basis (see [Exercise 3.3](Exercise_3_3.ipynb)). As input features, select the two\n", 12 | "independent variables $x_1$ and $x_2$ and set the noise to $50\\%$.\n", 13 | "\n", 14 | "\n", 15 | "[![Checkerboard](./images/checkerboard_regularization.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=50&networkShape=6,6,6,6,6&seed=0.82577&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 16 | "\n", 17 | "\n", 18 | "## Tasks\n", 19 | "1. Choose a deep (many layers) and wide (many nodes) network and train it for more than 1000 epochs. Comment on your observations.\n", 20 | "2. Apply L2 regularization to reduce overfitting. Try low and high regularization rates. What do you observe?\n", 21 | "3. Compare the effects of L1 and L2 regularization." 22 | ] 23 | } 24 | ], 25 | "metadata": { 26 | "kernelspec": { 27 | "display_name": "Python 3", 28 | "language": "python", 29 | "name": "python3" 30 | }, 31 | "language_info": { 32 | "codemirror_mode": { 33 | "name": "ipython", 34 | "version": 3 35 | }, 36 | "file_extension": ".py", 37 | "mimetype": "text/x-python", 38 | "name": "python", 39 | "nbconvert_exporter": "python", 40 | "pygments_lexer": "ipython3", 41 | "version": "3.6.9" 42 | } 43 | }, 44 | "nbformat": 4, 45 | "nbformat_minor": 4 46 | } 47 | -------------------------------------------------------------------------------- /Exercise_05_1_solution.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 5.1 - Solution\n", 8 | "## Overtraining and Regularization:\n", 9 | "Open the Tensorflow Playground\n", 10 | "(https://playground.tensorflow.org) and select on the left the checkerboard\n", 11 | "pattern as the data basis (see [Exercise 3.3](Exercise_3_3.ipynb)). As input features, select the two\n", 12 | "independent variables $x_1$ and $x_2$ and set the noise to $50\\%$.\n", 13 | "\n", 14 | "\n", 15 | "[![Checkerboard](./images/checkerboard_regularization.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=50&networkShape=6,6,6,6,6&seed=0.82577&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 16 | "\n", 17 | "## Tasks\n", 18 | "1. Choose a deep (many layers) and wide (many nodes) network and train it for more than 1000 epochs. Comment on your observations.\n", 19 | "2. Apply L2 regularization to reduce overfitting. Try low and high regularization rates. What do you observe?\n", 20 | "3. Compare the effects of L1 and L2 regularization." 21 | ] 22 | }, 23 | { 24 | "cell_type": "markdown", 25 | "metadata": {}, 26 | "source": [ 27 | "## Solutions" 28 | ] 29 | }, 30 | { 31 | "cell_type": "markdown", 32 | "metadata": {}, 33 | "source": [ 34 | "### Task 1.\n", 35 | "Choose a deep (many layers) and wide (many nodes) network and train it for more than 1000 epochs. Comment on your observations.\n" 36 | ] 37 | }, 38 | { 39 | "cell_type": "markdown", 40 | "metadata": {}, 41 | "source": [ 42 | "[![Checkerboard](./images/checkerboard_overtraining.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=50&networkShape=6,6,6,6&seed=0.38222&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 43 | "\n", 44 | "Overtraining is observed (the network learns statistical fluctuations)." 45 | ] 46 | }, 47 | { 48 | "cell_type": "markdown", 49 | "metadata": {}, 50 | "source": [ 51 | "## Task 2\n", 52 | "Apply L2 regularization to reduce overfitting. Try low and high regularization rates. What do you observe?\n", 53 | "\n", 54 | "#### Low regularization rates" 55 | ] 56 | }, 57 | { 58 | "cell_type": "markdown", 59 | "metadata": {}, 60 | "source": [ 61 | "[![Checkerboard](./images/checkerboard_l2_low.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0.001&noise=50&networkShape=6,6,6,6,6&seed=0.82577&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 62 | "\n", 63 | " For very low regularization rates ($\\lambda \\rightarrow 0$), the L2 norm penalty is only hardly considered in the training. Thus, the network is still overfitting. \n", 64 | "\n", 65 | "#### High regularization rates\n", 66 | "[![Checkerboard](./images/checkerboard_l2_high.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=10&noise=50&networkShape=6,6,6,6,6&seed=0.82577&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 67 | "\n", 68 | "\n", 69 | " For high regularization rates ($\\lambda >> 0$), almost only the L2 norm penalty is considered in training. Thus, all adaptive parameters are pushed to zero. \n", 70 | "\n", 71 | "#### Moderate regularization rates\n", 72 | "[![Checkerboard](./images/checkerboard_l2_moderate.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=10&noise=50&networkShape=6,6,6,6,6&seed=0.82577&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 73 | "\n", 74 | " For moderate regularization rates, no overtraining can be observed.\n" 75 | ] 76 | }, 77 | { 78 | "cell_type": "markdown", 79 | "metadata": {}, 80 | "source": [ 81 | "## Task 3\n", 82 | "Compare the effects of L1 and L2 regularization." 83 | ] 84 | }, 85 | { 86 | "cell_type": "markdown", 87 | "metadata": {}, 88 | "source": [ 89 | "[![Checkerboard](./images/checkerboard_l1.png)](https://playground.tensorflow.org/#activation=relu&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=50&networkShape=6,6,6,6,6&seed=0.82577&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=false&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=true)\n", 90 | "\n", 91 | "As was observed in Task 1 and Task 2, L2 regularization with moderate regularization rates pushes the weights to smaller values — but not to zero. \n", 92 | "\n", 93 | "In contrast, L1 regularization pushes certain, unimportant weights to zero. Therefore, L1 regularization can, in principle, be used as a feature-selection technique." 94 | ] 95 | } 96 | ], 97 | "metadata": { 98 | "kernelspec": { 99 | "display_name": "Python 3", 100 | "language": "python", 101 | "name": "python3" 102 | }, 103 | "language_info": { 104 | "codemirror_mode": { 105 | "name": "ipython", 106 | "version": 3 107 | }, 108 | "file_extension": ".py", 109 | "mimetype": "text/x-python", 110 | "name": "python", 111 | "nbconvert_exporter": "python", 112 | "pygments_lexer": "ipython3", 113 | "version": "3.6.9" 114 | } 115 | }, 116 | "nbformat": 4, 117 | "nbformat_minor": 4 118 | } 119 | -------------------------------------------------------------------------------- /Exercise_05_2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 5.2\n", 8 | "## Interpolation\n", 9 | "In this task, we implement a simple NN to learn a complicated function." 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 2, 15 | "metadata": {}, 16 | "outputs": [], 17 | "source": [ 18 | "import numpy as np\n", 19 | "from tensorflow import keras\n", 20 | "import matplotlib.pyplot as plt\n", 21 | "\n", 22 | "layers = keras.layers" 23 | ] 24 | }, 25 | { 26 | "cell_type": "markdown", 27 | "metadata": {}, 28 | "source": [ 29 | "### Generation of data" 30 | ] 31 | }, 32 | { 33 | "cell_type": "code", 34 | "execution_count": 2, 35 | "metadata": {}, 36 | "outputs": [], 37 | "source": [ 38 | "def some_complicated_function(x):\n", 39 | " return (\n", 40 | " (np.abs(x)) ** 0.5\n", 41 | " + 0.1 * x\n", 42 | " + 0.01 * x ** 2\n", 43 | " + 1\n", 44 | " - np.sin(x)\n", 45 | " + 0.5 * np.exp(x / 10.0)\n", 46 | " ) / (0.5 + np.abs(np.cos(x)))" 47 | ] 48 | }, 49 | { 50 | "cell_type": "markdown", 51 | "metadata": {}, 52 | "source": [ 53 | "Let's simulate the train data" 54 | ] 55 | }, 56 | { 57 | "cell_type": "code", 58 | "execution_count": 3, 59 | "metadata": {}, 60 | "outputs": [], 61 | "source": [ 62 | "N_train = 10 ** 4 # number of training samples\n", 63 | "# Note: \"[:, np.newaxis]\" reshapes array to (N,1) as required by our DNN (we input one feature per sample)\n", 64 | "xtrain = np.random.uniform(-10, 10, N_train)[:, np.newaxis]\n", 65 | "ytrain = some_complicated_function(xtrain) + np.random.randn(xtrain.shape[0]) # train data includes some noise" 66 | ] 67 | }, 68 | { 69 | "cell_type": "code", 70 | "execution_count": 4, 71 | "metadata": {}, 72 | "outputs": [ 73 | { 74 | "name": "stdout", 75 | "output_type": "stream", 76 | "text": [ 77 | "xtrain.shape (10000, 1)\n", 78 | "ytrain.shape (10000, 10000)\n" 79 | ] 80 | } 81 | ], 82 | "source": [ 83 | "print(\"xtrain.shape\", xtrain.shape)\n", 84 | "print(\"ytrain.shape\", ytrain.shape)" 85 | ] 86 | }, 87 | { 88 | "cell_type": "markdown", 89 | "metadata": {}, 90 | "source": [ 91 | "Simulate test data" 92 | ] 93 | }, 94 | { 95 | "cell_type": "code", 96 | "execution_count": 5, 97 | "metadata": {}, 98 | "outputs": [], 99 | "source": [ 100 | "N_test = 10000 # number of testing samples\n", 101 | "xtest = np.linspace(-10, 10, N_test)\n", 102 | "ytest = some_complicated_function(xtest)" 103 | ] 104 | }, 105 | { 106 | "cell_type": "code", 107 | "execution_count": 6, 108 | "metadata": {}, 109 | "outputs": [ 110 | { 111 | "name": "stdout", 112 | "output_type": "stream", 113 | "text": [ 114 | "xtest.shape (10000,)\n", 115 | "ytest.shape (10000,)\n" 116 | ] 117 | } 118 | ], 119 | "source": [ 120 | "print(\"xtest.shape\", xtest.shape)\n", 121 | "print(\"ytest.shape\", ytest.shape)" 122 | ] 123 | }, 124 | { 125 | "cell_type": "markdown", 126 | "metadata": {}, 127 | "source": [ 128 | "### Define Model\n", 129 | "\n", 130 | "Define the number of nodes, the number of layers, and choose an activation function.\n", 131 | "Use `keras.regularizers` to use parameter norm penalties or add a dropout layer via `layers.Dropout(fraction)`.\n", 132 | "\n", 133 | "You may use the skeleton below:" 134 | ] 135 | }, 136 | { 137 | "cell_type": "code", 138 | "execution_count": null, 139 | "metadata": {}, 140 | "outputs": [], 141 | "source": [ 142 | "nb_nodes = 1\n", 143 | "nb_layers = 1\n", 144 | "activation = \"\"\n", 145 | "\n", 146 | "model = keras.models.Sequential(name=\"1Dfit\")\n", 147 | "model.add(layers.Dense(nb_nodes, activation=activation, input_dim=xtrain.shape[1])) # first layer\n", 148 | "\n", 149 | "model.add(layers.Dense(1)) # final layer\n", 150 | "\n", 151 | "print(model.summary())" 152 | ] 153 | }, 154 | { 155 | "cell_type": "markdown", 156 | "metadata": {}, 157 | "source": [ 158 | "### Compile the model (set an objective and choose an optimizer)" 159 | ] 160 | }, 161 | { 162 | "cell_type": "markdown", 163 | "metadata": {}, 164 | "source": [ 165 | "Choose an optimizer from `keras.optimizers`, e.g., `adam = keras.optimizers.Adam(lr=0.001)`.\n", 166 | "\n", 167 | "Further, choose the correct objective (loss) for this regression task." 168 | ] 169 | }, 170 | { 171 | "cell_type": "code", 172 | "execution_count": 8, 173 | "metadata": {}, 174 | "outputs": [], 175 | "source": [ 176 | "model.compile(loss=\"\", optimizer=)" 177 | ] 178 | }, 179 | { 180 | "cell_type": "markdown", 181 | "metadata": {}, 182 | "source": [ 183 | "### Train the model" 184 | ] 185 | }, 186 | { 187 | "cell_type": "markdown", 188 | "metadata": {}, 189 | "source": [ 190 | "Train the network for a couple of epochs and save the model several times in between." 191 | ] 192 | }, 193 | { 194 | "cell_type": "code", 195 | "execution_count": null, 196 | "metadata": {}, 197 | "outputs": [], 198 | "source": [ 199 | "epochs = \n", 200 | "save_period = # after how many epochs the model should be saved?\n", 201 | "\n", 202 | "chkpnt_saver = keras.callbacks.ModelCheckpoint(\"weights-{epoch:02d}.hdf5\", save_weights_only=True, save_freq=save_period)\n", 203 | "\n", 204 | "results = model.fit(\n", 205 | " xtrain,\n", 206 | " ytrain,\n", 207 | " batch_size=64,\n", 208 | " epochs=epochs,\n", 209 | " verbose=1,\n", 210 | " callbacks=[chkpnt_saver]\n", 211 | " )" 212 | ] 213 | }, 214 | { 215 | "cell_type": "markdown", 216 | "metadata": {}, 217 | "source": [ 218 | "Compare the performance of the model during the training. You may use the skeleton below:" 219 | ] 220 | }, 221 | { 222 | "cell_type": "code", 223 | "execution_count": null, 224 | "metadata": {}, 225 | "outputs": [], 226 | "source": [ 227 | "fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(12, 8))\n", 228 | "\n", 229 | "ax1.plot(xtest, ytest, color=\"black\", label=\"data\")\n", 230 | "saved_epochs = range(save_period, epochs + 1, save_period)\n", 231 | "\n", 232 | "colors = [plt.cm.jet((i + 1) / float(len(saved_epochs) + 1)) for i in range(len(saved_epochs))]\n", 233 | "\n", 234 | "for i, epoch in enumerate(saved_epochs):\n", 235 | " model.load_weights(\"weights-{epoch:02d}.hdf5\".format(epoch=epoch))\n", 236 | " ypredict = model.predict(xtest).squeeze()\n", 237 | " ax1.plot(xtest.squeeze(), ypredict, color=colors[i], label=epoch)\n", 238 | " ax2.plot(epoch, results.history[\"loss\"][epoch - 1], color=colors[i], marker=\"o\")\n", 239 | "\n", 240 | "ax1.set(xlabel=\"x\", ylabel=\"some_complicated_function(x)\", xlim=(-10, 13), title=\"\")\n", 241 | "ax1.grid(True)\n", 242 | "ax1.legend(loc=\"upper right\", title=\"Epochs\")\n", 243 | "\n", 244 | "ax2.plot(results.history[\"loss\"], color=\"black\")\n", 245 | "ax2.set(xlabel=\"epoch\", ylabel=\"loss\")\n", 246 | "ax2.grid(True)\n", 247 | "ax2.semilogy()\n", 248 | "\n", 249 | "plt.show()" 250 | ] 251 | } 252 | ], 253 | "metadata": { 254 | "kernelspec": { 255 | "display_name": "Python 3", 256 | "language": "python", 257 | "name": "python3" 258 | }, 259 | "language_info": { 260 | "codemirror_mode": { 261 | "name": "ipython", 262 | "version": 3 263 | }, 264 | "file_extension": ".py", 265 | "mimetype": "text/x-python", 266 | "name": "python", 267 | "nbconvert_exporter": "python", 268 | "pygments_lexer": "ipython3", 269 | "version": "3.6.9" 270 | } 271 | }, 272 | "nbformat": 4, 273 | "nbformat_minor": 4 274 | } 275 | -------------------------------------------------------------------------------- /Exercise_05_3.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": { 6 | "id": "WSW9BmePM7zZ" 7 | }, 8 | "source": [ 9 | "# Exercise 5.3: Neural Networks in Keras" 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 1, 15 | "metadata": { 16 | "id": "t02FemO-M7za" 17 | }, 18 | "outputs": [], 19 | "source": [ 20 | "import numpy as np\n", 21 | "import matplotlib.pyplot as plt\n", 22 | "\n", 23 | "# See https://keras.io/\n", 24 | "# for extennsive documentation\n", 25 | "import tensorflow as tf\n", 26 | "from tensorflow import keras\n", 27 | "\n", 28 | "from keras.models import Sequential\n", 29 | "from keras.layers import Dense" 30 | ] 31 | }, 32 | { 33 | "cell_type": "markdown", 34 | "metadata": { 35 | "id": "IrvyHKHTM7ze" 36 | }, 37 | "source": [ 38 | "Let us visit the problem of wine quality prediction previ- ously encountered in Exercises 3.2 and 4.1 one final time. After linear regression and a self-made network, we can now explore the comfort provided by the Keras library." 39 | ] 40 | }, 41 | { 42 | "cell_type": "code", 43 | "execution_count": null, 44 | "metadata": { 45 | "colab": { 46 | "base_uri": "https://localhost:8080/" 47 | }, 48 | "id": "-H-L5egsM7ze", 49 | "outputId": "82d3f95f-59b1-43e3-e8d7-4d939ea7eec6" 50 | }, 51 | "outputs": [], 52 | "source": [ 53 | "# The code snippet below is responsible for downloading the dataset to\n", 54 | "# Google. You can directly download the file using the link\n", 55 | "# if you work with a local anaconda setup\n", 56 | "!wget https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv" 57 | ] 58 | }, 59 | { 60 | "cell_type": "code", 61 | "execution_count": null, 62 | "metadata": { 63 | "colab": { 64 | "base_uri": "https://localhost:8080/" 65 | }, 66 | "id": "mDToshKJNWGY", 67 | "outputId": "8cce4ba8-392b-43a1-d659-26aa95d21113" 68 | }, 69 | "outputs": [], 70 | "source": [ 71 | "# load all examples from the file\n", 72 | "data = np.genfromtxt('winequality-white.csv',delimiter=\";\",skip_header=1)\n", 73 | "\n", 74 | "print(\"data:\", data.shape)\n", 75 | "\n", 76 | "# Prepare for proper training\n", 77 | "np.random.shuffle(data) # randomly sort examples\n", 78 | "\n", 79 | "# take the first 3000 examples for training\n", 80 | "X_train = data[:3000,:11] # all features except last column\n", 81 | "y_train = data[:3000,11] # quality column\n", 82 | "\n", 83 | "# and the remaining examples for testing\n", 84 | "X_test = data[3000:,:11] # all features except last column\n", 85 | "y_test = data[3000:,11] # quality column\n", 86 | "\n", 87 | "print(\"First example:\")\n", 88 | "print(\"Features:\", X_train[0])\n", 89 | "print(\"Quality:\", y_train[0])\n" 90 | ] 91 | }, 92 | { 93 | "cell_type": "markdown", 94 | "metadata": { 95 | "id": "VXx8BXB_M7zi" 96 | }, 97 | "source": [ 98 | "Below is the simple network from exercise 4.1 implemented using Keras. In addition to the network we define the loss function and optimiser." 99 | ] 100 | }, 101 | { 102 | "cell_type": "code", 103 | "execution_count": null, 104 | "metadata": { 105 | "id": "Z0HMdw9eM7zi" 106 | }, 107 | "outputs": [], 108 | "source": [ 109 | "# See: https://keras.io/api/models/sequential/ and \n", 110 | "# https://keras.io/api/layers/core_layers/dense/\n", 111 | "# We can use the Sequential class to very easiliy\n", 112 | "# build a simple architecture\n", 113 | "model = Sequential()\n", 114 | "# 11 inputs, 20 outputs, relu\n", 115 | "model.add(Dense(20, input_dim=11, activation='relu')) \n", 116 | "# 20 inputs (automatically detected by Keras), 1 output, linear activation\n", 117 | "model.add(Dense(1, activation='linear'))\n", 118 | "\n", 119 | "\n", 120 | "# Set loss function and optimiser algorithm\n", 121 | "model.compile(loss='mse', # mean squared error\n", 122 | " optimizer='sgd'# stochastic gradient descent\n", 123 | " ) " 124 | ] 125 | }, 126 | { 127 | "cell_type": "markdown", 128 | "metadata": { 129 | "id": "I98jdZcqM7zm" 130 | }, 131 | "source": [ 132 | "# Training and evaluation below\n", 133 | "\n", 134 | "The code below trains the network for 5 epochs using the loss function and optimiser defined above. Each example is individually passed to the network" 135 | ] 136 | }, 137 | { 138 | "cell_type": "code", 139 | "execution_count": null, 140 | "metadata": {}, 141 | "outputs": [], 142 | "source": [ 143 | "history = model.fit(X_train, y_train, \n", 144 | " validation_data=(X_test, y_test),\n", 145 | " epochs=5, batch_size=1)\n" 146 | ] 147 | }, 148 | { 149 | "cell_type": "code", 150 | "execution_count": null, 151 | "metadata": {}, 152 | "outputs": [], 153 | "source": [ 154 | "# The history object returned by the model training above \n", 155 | "# contains the values of the loss function (the mean-squared-error)\n", 156 | "# at different epochs\n", 157 | "# We discard the first epoch as the loss value is very high,\n", 158 | "# obscuring the rest of the distribution\n", 159 | "train_loss = history.history[\"loss\"][1:]\n", 160 | "test_loss = history.history[\"val_loss\"][1:]" 161 | ] 162 | }, 163 | { 164 | "cell_type": "code", 165 | "execution_count": null, 166 | "metadata": {}, 167 | "outputs": [], 168 | "source": [ 169 | "# Prepare and plot loss over time\n", 170 | "plt.plot(train_loss,label=\"train\")\n", 171 | "plt.plot(test_loss,label=\"test\")\n", 172 | "plt.legend()\n", 173 | "plt.xlabel(\"Epoch-1\")\n", 174 | "plt.ylabel(\"Loss\")\n", 175 | "plt.show()" 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": null, 181 | "metadata": {}, 182 | "outputs": [], 183 | "source": [ 184 | "# After the training:\n", 185 | "\n", 186 | "# Prepare scatter plot\n", 187 | "y_pred = model.predict(X_test)[:,0]\n", 188 | "\n", 189 | "print(\"Correlation coefficient:\", np.corrcoef(y_pred,y_test)[0,1])\n", 190 | "plt.scatter(y_pred,y_test)\n", 191 | "plt.xlabel(\"Predicted\")\n", 192 | "plt.ylabel(\"True\")\n", 193 | "plt.show()" 194 | ] 195 | }, 196 | { 197 | "cell_type": "code", 198 | "execution_count": null, 199 | "metadata": {}, 200 | "outputs": [], 201 | "source": [ 202 | "np.corrcoef(y_pred,y_test)" 203 | ] 204 | }, 205 | { 206 | "cell_type": "markdown", 207 | "metadata": { 208 | "id": "KI7zcK_uM7zp" 209 | }, 210 | "source": [ 211 | "\n", 212 | "# Problems\n", 213 | "\n", 214 | "* Use the notebook as starting point. It already contains the simple network from Exercise 4.1 implemented in Keras.\n", 215 | "\n", 216 | "* Currently, SGD is used without momentum. Try training with a momentum term. Replace SGD with the Adam optimizer and train using that. (See: https://keras.io/api/optimizers/)\n", 217 | "* Add two more hidden layers to the network (you can choose the number of nodes but make sure to apply the ReLu activation function after each) and train again.\n", 218 | "* Test differet numbers of examples (i.e. change the batch batch size) to be simulataneously used by the network. " 219 | ] 220 | }, 221 | { 222 | "cell_type": "code", 223 | "execution_count": null, 224 | "metadata": { 225 | "id": "2mUTzx7h2mKJ" 226 | }, 227 | "outputs": [], 228 | "source": [] 229 | } 230 | ], 231 | "metadata": { 232 | "colab": { 233 | "collapsed_sections": [], 234 | "name": "Exercise 6 - Solution", 235 | "provenance": [] 236 | }, 237 | "kernelspec": { 238 | "display_name": "Python 3", 239 | "language": "python", 240 | "name": "python3" 241 | }, 242 | "language_info": { 243 | "codemirror_mode": { 244 | "name": "ipython", 245 | "version": 3 246 | }, 247 | "file_extension": ".py", 248 | "mimetype": "text/x-python", 249 | "name": "python", 250 | "nbconvert_exporter": "python", 251 | "pygments_lexer": "ipython3", 252 | "version": "3.7.6" 253 | } 254 | }, 255 | "nbformat": 4, 256 | "nbformat_minor": 1 257 | } 258 | -------------------------------------------------------------------------------- /Exercise_07_1.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 7.1\n", 8 | "### Classification of magnetic phases using fully-connected networks\n", 9 | "\n", 10 | "Imagine a 2-dimensional lattice arrangement of $n \\times n$ magnetic dipole moments (spins) that can be in one of two states ($+1$ or $−1$, Ising model).\n", 11 | "With interactions between spins being short ranged, each spin interacts only with its four neighbors.\n", 12 | "The probability to find a spin in one of the orientations is a function of temperature $T$ according to $p \\sim e^{−a/T},\\;a = \\mathrm{const.}$).\n", 13 | "\n", 14 | "At extremely low temperatures $T \\rightarrow 0$, neighboring spins have a very low probability of different orientations, so that a uniform overall state (ferromagnetic state) is adopted, characterized by $+1$ or $−1$.\n", 15 | "At very high temperatures $T \\rightarrow \\infty$, a paramagnetic phase with random spin alignment results, yielding $50\\%$ of $+1$ and $0%$ of $−1$ orientations.\n", 16 | "Below a critical temperature $0 < T < T_c$, stable ferromagnetic domains emerge, with both orientations being equally probable in the absence of an external magnetic field.\n", 17 | "The spin-spin correlation function diverges at $T_c$, whereas the correlation decays for $T > T_c$.\n", 18 | "\n", 19 | "The data for this task contain the $n \\times n$ dipole orientations on the lattice for different temperatures $T$.\n", 20 | "Classify the two magnetic phases (paramagnetic/ferromagnetic)!" 21 | ] 22 | }, 23 | { 24 | "cell_type": "code", 25 | "execution_count": 6, 26 | "metadata": {}, 27 | "outputs": [ 28 | { 29 | "name": "stdout", 30 | "output_type": "stream", 31 | "text": [ 32 | "keras version 2.4.0\n" 33 | ] 34 | } 35 | ], 36 | "source": [ 37 | "from tensorflow import keras\n", 38 | "import numpy as np\n", 39 | "callbacks = keras.callbacks\n", 40 | "layers = keras.layers\n", 41 | "\n" 42 | ] 43 | }, 44 | { 45 | "cell_type": "markdown", 46 | "metadata": {}, 47 | "source": [ 48 | "### Load and prepare dataset\n", 49 | "See https://doi.org/10.1038/nphys4035 for more information" 50 | ] 51 | }, 52 | { 53 | "cell_type": "code", 54 | "execution_count": 2, 55 | "metadata": {}, 56 | "outputs": [], 57 | "source": [ 58 | "import gdown\n", 59 | "url = \"https://drive.google.com/u/0/uc?export=download&confirm=HgGH&id=1Ihxt1hb3Kyv0IrjHlsYb9x9QY7l7n2Sl\"\n", 60 | "output = 'ising_data.npz'\n", 61 | "gdown.download(url, output, quiet=True)\n", 62 | "\n", 63 | "f = np.load(output, allow_pickle=True)\n", 64 | "n_train = 20000\n", 65 | "\n", 66 | "x_train, x_test = f[\"C\"][:n_train], f[\"C\"][n_train:]\n", 67 | "T_train, T_test = f[\"T\"][:n_train], f[\"T\"][n_train:]" 68 | ] 69 | }, 70 | { 71 | "cell_type": "code", 72 | "execution_count": 3, 73 | "metadata": {}, 74 | "outputs": [ 75 | { 76 | "data": { 77 | "image/png": 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\n", 78 | "text/plain": [ 79 | "
" 80 | ] 81 | }, 82 | "metadata": { 83 | "needs_background": "light" 84 | }, 85 | "output_type": "display_data" 86 | } 87 | ], 88 | "source": [ 89 | "import matplotlib.pyplot as plt\n", 90 | "\n", 91 | "for i,j in enumerate(np.random.choice(n_train, 6)):\n", 92 | " plt.subplot(2,3,i+1)\n", 93 | " image = x_train[j]\n", 94 | " plot = plt.imshow(image)\n", 95 | " plt.title(\"T: %.2f\" % T_train[j])\n", 96 | "\n", 97 | "plt.tight_layout()\n", 98 | "plt.show()" 99 | ] 100 | }, 101 | { 102 | "cell_type": "code", 103 | "execution_count": 4, 104 | "metadata": {}, 105 | "outputs": [ 106 | { 107 | "data": { 108 | "text/plain": [ 109 | "Text(0, 0.5, 'frequency')" 110 | ] 111 | }, 112 | "execution_count": 4, 113 | "metadata": {}, 114 | "output_type": "execute_result" 115 | }, 116 | { 117 | "data": { 118 | "image/png": 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\n", 119 | "text/plain": [ 120 | "
" 121 | ] 122 | }, 123 | "metadata": { 124 | "needs_background": "light" 125 | }, 126 | "output_type": "display_data" 127 | } 128 | ], 129 | "source": [ 130 | "plt.hist(T_test)\n", 131 | "plt.xlabel(\"T\")\n", 132 | "plt.ylabel(\"frequency\")" 133 | ] 134 | }, 135 | { 136 | "cell_type": "markdown", 137 | "metadata": {}, 138 | "source": [ 139 | "#### Set up training data - define magnetic phases" 140 | ] 141 | }, 142 | { 143 | "cell_type": "code", 144 | "execution_count": 5, 145 | "metadata": {}, 146 | "outputs": [], 147 | "source": [ 148 | "Tc = 2.27\n", 149 | "y_train, y_test = T_train > Tc, T_test > Tc" 150 | ] 151 | }, 152 | { 153 | "cell_type": "markdown", 154 | "metadata": {}, 155 | "source": [ 156 | " ### Task\n", 157 | "\n", 158 | " - evaluate the test accuracy for a fully-connected network,\n", 159 | " - plot the test accuracy vs. temperature.\n" 160 | ] 161 | } 162 | ], 163 | "metadata": { 164 | "kernelspec": { 165 | "display_name": "Python 3", 166 | "language": "python", 167 | "name": "python3" 168 | }, 169 | "language_info": { 170 | "codemirror_mode": { 171 | "name": "ipython", 172 | "version": 3 173 | }, 174 | "file_extension": ".py", 175 | "mimetype": "text/x-python", 176 | "name": "python", 177 | "nbconvert_exporter": "python", 178 | "pygments_lexer": "ipython3", 179 | "version": "3.6.9" 180 | } 181 | }, 182 | "nbformat": 4, 183 | "nbformat_minor": 4 184 | } 185 | -------------------------------------------------------------------------------- /Exercise_08_1.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 8.1\n", 8 | "### Classification of magnetic phases using CNNs\n", 9 | "\n", 10 | "Imagine a 2-dimensional lattice arrangement of $n \\times n$ magnetic dipole moments (spins) that can be in one of two states ($+1$ or $−1$, Ising model).\n", 11 | "With interactions between spins being short ranged, each spin interacts only with its four neighbors.\n", 12 | "The probability to find a spin in one of the orientations is a function of temperature $T$ according to $p \\sim e^{−a/T},\\;a = \\mathrm{const.}$).\n", 13 | "\n", 14 | "At extremely low temperatures $T \\rightarrow 0$, neighboring spins have a very low probability of different orientations, so that a uniform overall state (ferromagnetic state) is adopted, characterized by $+1$ or $−1$.\n", 15 | "At very high temperatures $T \\rightarrow \\infty$, a paramagnetic phase with random spin alignment results, yielding $50\\%$ of $+1$ and $0%$ of $−1$ orientations.\n", 16 | "Below a critical temperature $0 < T < T_c$, stable ferromagnetic domains emerge, with both orientations being equally probable in the absence of an external magnetic field.\n", 17 | "The spin-spin correlation function diverges at $T_c$, whereas the correlation decays for $T > T_c$.\n", 18 | "\n", 19 | "The data for this task contain the $n \\times n$ dipole orientations on the lattice for different temperatures $T$.\n", 20 | "Classify the two magnetic phases (paramagnetic/ferromagnetic) using a convolutional neural network!" 21 | ] 22 | }, 23 | { 24 | "cell_type": "code", 25 | "execution_count": 6, 26 | "metadata": {}, 27 | "outputs": [ 28 | { 29 | "name": "stdout", 30 | "output_type": "stream", 31 | "text": [ 32 | "keras 2.4.0\n" 33 | ] 34 | } 35 | ], 36 | "source": [ 37 | "from tensorflow import keras\n", 38 | "import numpy as np\n", 39 | "callbacks = keras.callbacks\n", 40 | "layers = keras.layers\n", 41 | "\n" 42 | ] 43 | }, 44 | { 45 | "cell_type": "markdown", 46 | "metadata": {}, 47 | "source": [ 48 | "### Load and prepare dataset\n", 49 | "See https://doi.org/10.1038/nphys4035 for more information" 50 | ] 51 | }, 52 | { 53 | "cell_type": "code", 54 | "execution_count": 2, 55 | "metadata": {}, 56 | "outputs": [], 57 | "source": [ 58 | "import gdown\n", 59 | "url = \"https://drive.google.com/u/0/uc?export=download&confirm=HgGH&id=1Ihxt1hb3Kyv0IrjHlsYb9x9QY7l7n2Sl\"\n", 60 | "output = 'ising_data.npz'\n", 61 | "gdown.download(url, output, quiet=True)\n", 62 | "\n", 63 | "f = np.load(output, allow_pickle=True)\n", 64 | "n_train = 20000\n", 65 | "\n", 66 | "x_train, x_test = f[\"C\"][:n_train], f[\"C\"][n_train:]\n", 67 | "T_train, T_test = f[\"T\"][:n_train], f[\"T\"][n_train:]" 68 | ] 69 | }, 70 | { 71 | "cell_type": "code", 72 | "execution_count": 3, 73 | "metadata": {}, 74 | "outputs": [ 75 | { 76 | "data": { 77 | "image/png": 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\n", 78 | "text/plain": [ 79 | "
" 80 | ] 81 | }, 82 | "metadata": { 83 | "needs_background": "light" 84 | }, 85 | "output_type": "display_data" 86 | } 87 | ], 88 | "source": [ 89 | "import matplotlib.pyplot as plt\n", 90 | "\n", 91 | "for i,j in enumerate(np.random.choice(n_train, 6)):\n", 92 | " plt.subplot(2,3,i+1)\n", 93 | " image = x_train[j]\n", 94 | " plot = plt.imshow(image)\n", 95 | " plt.title(\"T: %.2f\" % T_train[j])\n", 96 | "\n", 97 | "plt.tight_layout()\n", 98 | "plt.show()" 99 | ] 100 | }, 101 | { 102 | "cell_type": "code", 103 | "execution_count": 4, 104 | "metadata": {}, 105 | "outputs": [ 106 | { 107 | "data": { 108 | "text/plain": [ 109 | "Text(0, 0.5, 'frequency')" 110 | ] 111 | }, 112 | "execution_count": 4, 113 | "metadata": {}, 114 | "output_type": "execute_result" 115 | }, 116 | { 117 | "data": { 118 | "image/png": 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\n", 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" 121 | ] 122 | }, 123 | "metadata": { 124 | "needs_background": "light" 125 | }, 126 | "output_type": "display_data" 127 | } 128 | ], 129 | "source": [ 130 | "plt.hist(T_test)\n", 131 | "plt.xlabel(\"T\")\n", 132 | "plt.ylabel(\"frequency\")" 133 | ] 134 | }, 135 | { 136 | "cell_type": "markdown", 137 | "metadata": {}, 138 | "source": [ 139 | "#### Set up training data - define magnetic phases" 140 | ] 141 | }, 142 | { 143 | "cell_type": "code", 144 | "execution_count": 5, 145 | "metadata": {}, 146 | "outputs": [], 147 | "source": [ 148 | "Tc = 2.27\n", 149 | "y_train, y_test = T_train > Tc, T_test > Tc" 150 | ] 151 | }, 152 | { 153 | "cell_type": "markdown", 154 | "metadata": {}, 155 | "source": [ 156 | " ### Task\n", 157 | "\n", 158 | " - evaluate the test accuracy for a convolutional network,\n", 159 | " - plot the test accuracy vs. temperature.\n", 160 | " - compare to the results obtained using a fully-connected network (Exercise 7.1)" 161 | ] 162 | } 163 | ], 164 | "metadata": { 165 | "kernelspec": { 166 | "display_name": "Python 3", 167 | "language": "python", 168 | "name": "python3" 169 | }, 170 | "language_info": { 171 | "codemirror_mode": { 172 | "name": "ipython", 173 | "version": 3 174 | }, 175 | "file_extension": ".py", 176 | "mimetype": "text/x-python", 177 | "name": "python", 178 | "nbconvert_exporter": "python", 179 | "pygments_lexer": "ipython3", 180 | "version": "3.6.9" 181 | } 182 | }, 183 | "nbformat": 4, 184 | "nbformat_minor": 4 185 | } 186 | -------------------------------------------------------------------------------- /Exercise_12_2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Exercise 12.2\n", 8 | "## Activation maximization\n", 9 | "In this task, we use the approach of activation maximization to visualize to which patterns features of a CNN trained using on MNIST are sensitive. This will give us a deeper understanding of the working principle of CNNs." 10 | ] 11 | }, 12 | { 13 | "cell_type": "code", 14 | "execution_count": 3, 15 | "metadata": {}, 16 | "outputs": [ 17 | { 18 | "name": "stdout", 19 | "output_type": "stream", 20 | "text": [ 21 | "keras version 2.4.0\n" 22 | ] 23 | } 24 | ], 25 | "source": [ 26 | "import tensorflow as tf\n", 27 | "from tensorflow import keras\n", 28 | "import numpy as np\n", 29 | "import matplotlib.pyplot as plt\n", 30 | "\n", 31 | "KTF = keras.backend\n", 32 | "layers = keras.layers\n", 33 | "\n" 34 | ] 35 | }, 36 | { 37 | "cell_type": "markdown", 38 | "metadata": {}, 39 | "source": [ 40 | "### Download and preprocess data" 41 | ] 42 | }, 43 | { 44 | "cell_type": "code", 45 | "execution_count": 2, 46 | "metadata": {}, 47 | "outputs": [], 48 | "source": [ 49 | "(x_train, y_train), (x_test, y_test) = keras.datasets.mnist.load_data()\n", 50 | "x_train = x_train.astype(np.float32)[...,np.newaxis] / 255.\n", 51 | "x_test = x_test.astype(np.float32)[...,np.newaxis] / 255.\n", 52 | "y_train = keras.utils.to_categorical(y_train, 10)\n", 53 | "y_test = keras.utils.to_categorical(y_test, 10)" 54 | ] 55 | }, 56 | { 57 | "cell_type": "markdown", 58 | "metadata": {}, 59 | "source": [ 60 | "### Set up a convolutional neural network with at least 4 CNN layers." 61 | ] 62 | }, 63 | { 64 | "cell_type": "code", 65 | "execution_count": null, 66 | "metadata": {}, 67 | "outputs": [], 68 | "source": [ 69 | "model = keras.models.Sequential()\n", 70 | "\n", 71 | "model.summary()" 72 | ] 73 | }, 74 | { 75 | "cell_type": "markdown", 76 | "metadata": {}, 77 | "source": [ 78 | "#### compile and train model" 79 | ] 80 | }, 81 | { 82 | "cell_type": "code", 83 | "execution_count": null, 84 | "metadata": {}, 85 | "outputs": [], 86 | "source": [ 87 | "model.compile(\n", 88 | " loss='categorical_crossentropy',\n", 89 | " optimizer=keras.optimizers.Adam(lr=1e-3),\n", 90 | " metrics=['accuracy'])\n", 91 | "\n", 92 | "\n", 93 | "results = model.fit(x_train, y_train,\n", 94 | " batch_size=100,\n", 95 | " epochs=3,\n", 96 | " verbose=1,\n", 97 | " validation_split=0.1\n", 98 | " )" 99 | ] 100 | }, 101 | { 102 | "cell_type": "markdown", 103 | "metadata": {}, 104 | "source": [ 105 | "### Implementation of activation maximization\n", 106 | "Select a layer you want to visualize and perform activation maximization." 107 | ] 108 | }, 109 | { 110 | "cell_type": "code", 111 | "execution_count": null, 112 | "metadata": {}, 113 | "outputs": [], 114 | "source": [ 115 | "gradient_updates = 50\n", 116 | "step_size = 1.\n", 117 | "\n", 118 | "def normalize(x):\n", 119 | " '''Normalize gradients via l2 norm'''\n", 120 | " return x / (KTF.sqrt(KTF.mean(KTF.square(x))) + KTF.epsilon())\n" 121 | ] 122 | }, 123 | { 124 | "cell_type": "markdown", 125 | "metadata": {}, 126 | "source": [ 127 | "In the following, implement activation maximization to visualize to which patterns a specific feature map is sensitive:\n", 128 | "- Start from uniform distributed noise 'images' (note that the shape has to be `(1, 28, 28, 1)`, as we use a batch size of `1`).\n", 129 | "- Choose one specific feature map using 'filter_index'.\n", 130 | "- Create a scalar loss as discussed in Chapter 12 (maximize the average feature map activation).\n", 131 | "- Thereafter, add the calculated gradients to your start image (gradient ascent step) and repeat the procedure using gradient_updates = 50. \n", 132 | "You can calculate the gradients using the following expressions: \n", 133 | "`with tf.GradientTape() as gtape:\n", 134 | " grads = gtape.gradient(YOUR_OBJECTIVE, THE_VARIABLE_YOU_WANT_TO_OPTIMIZE) \n", 135 | " grads = normalize(grads)`\n", 136 | "\n", 137 | "- Finally, implement the gradient ascent step (you may use `assign_sub` or `assign_add` to adapt the parameters) and perform 50 updates.\n", 138 | "\n", 139 | "Remember to construct a Keras variable for the input (we want to find an input that 'maximizes' the output, so we build an input that holds adaptive parameters which we can train using TensorFlow / Keras)\n", 140 | "The following code snippet may help you to implement the maximization: " 141 | ] 142 | }, 143 | { 144 | "cell_type": "code", 145 | "execution_count": null, 146 | "metadata": {}, 147 | "outputs": [], 148 | "source": [ 149 | "visualized_feature = []\n", 150 | "layer_dict = layer_dict = dict([(layer.name, layer) for layer in model.layers[:]])\n", 151 | "layer_name = \"conv2d_3\"\n", 152 | "\n", 153 | "layer_output = layer_dict[layer_name].output\n", 154 | "sub_model = keras.models.Model([model.inputs], [layer_output])\n", 155 | "\n", 156 | "for filter_index in range(layer_output.shape[-1]): # iterate over fiters\n", 157 | "\n", 158 | " print('Processing filter %d' % (filter_index+1))\n", 159 | " \n", 160 | " input_img = KTF.variable([0]) # instead of '[0]' use noise as the (start) input image with correct shape\n", 161 | "\n", 162 | " for i in range(gradient_updates):\n", 163 | "\n", 164 | " with tf.GradientTape() as gtape:\n", 165 | " # define a scalar loss using Keras.\n", 166 | " # remember: You would like to maximize the activations in the respective feature map!\n", 167 | " loss = 0 # <--: define your loss HERE\n", 168 | " " 169 | ] 170 | }, 171 | { 172 | "cell_type": "markdown", 173 | "metadata": {}, 174 | "source": [ 175 | "#### Plot images to visualize to which patterns the respective feature maps are sensitive." 176 | ] 177 | }, 178 | { 179 | "cell_type": "code", 180 | "execution_count": null, 181 | "metadata": {}, 182 | "outputs": [], 183 | "source": [ 184 | "def deprocess_image(x):\n", 185 | " # reprocess visualization to format of \"MNIST images\"\n", 186 | " x -= x.mean()\n", 187 | " x /= (x.std() + KTF.epsilon())\n", 188 | " # x *= 0.1\n", 189 | " x += 0.5\n", 190 | " x *= 255\n", 191 | " x = np.clip(x, 0, 255).astype('uint8')\n", 192 | " return x" 193 | ] 194 | }, 195 | { 196 | "cell_type": "code", 197 | "execution_count": null, 198 | "metadata": {}, 199 | "outputs": [], 200 | "source": [ 201 | "plt.figure(figsize=(10,10))\n", 202 | "\n", 203 | "for i, feature_ in enumerate(visualized_feature):\n", 204 | " feature_image = deprocess_image(feature_)\n", 205 | " ax = plt.subplot(8,8, 1+i, )\n", 206 | " plt.imshow(feature_image.squeeze())\n", 207 | " ax.axis('off')\n", 208 | " plt.title(\"feature %s\" % i)\n", 209 | " \n", 210 | "plt.tight_layout()" 211 | ] 212 | } 213 | ], 214 | "metadata": { 215 | "kernelspec": { 216 | "display_name": "Python 3", 217 | "language": "python", 218 | "name": "python3" 219 | }, 220 | "language_info": { 221 | "codemirror_mode": { 222 | "name": "ipython", 223 | "version": 3 224 | }, 225 | "file_extension": ".py", 226 | "mimetype": "text/x-python", 227 | "name": "python", 228 | "nbconvert_exporter": "python", 229 | "pygments_lexer": "ipython3", 230 | "version": "3.6.9" 231 | } 232 | }, 233 | "nbformat": 4, 234 | "nbformat_minor": 4 235 | } 236 | -------------------------------------------------------------------------------- /LICENSE.md: -------------------------------------------------------------------------------- 1 | Creative Commons Attribution-NonCommercial 4.0 International Public 2 | License 3 | 4 | By exercising the Licensed Rights (defined below), You accept and agree 5 | to be bound by the terms and conditions of this Creative Commons 6 | Attribution-NonCommercial 4.0 International Public License ("Public 7 | License"). 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For 348 | the avoidance of doubt, this paragraph does not form part of the 349 | public licenses. 350 | 351 | Creative Commons may be contacted at creativecommons.org. 352 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | # Deep Learning for Physics Research 3 | 4 | This repository contains additional material (exercises) for the textbook *Deep Learning for Physics Research* by 5 | [Martin Erdmann](https://www.physik.rwth-aachen.de/user/erdmann), [Jonas Glombitza](https://www.jonas-glombitza.com/), [Gregor Kasieczka](https://www.physik.uni-hamburg.de/iexp/gruppe-kasieczka.html), and Uwe Klemradt. 6 | 7 | The authors can be contacted under [authors@deeplearningphysics.org](mailto:authors@deeplearningphysics.org). 8 | 9 | For more information on the book, refer to the page by the [publisher](https://worldscientific.com/worldscibooks/10.1142/12294). 10 | 11 | ## Exercises 12 | You can find the exercise page at: http://deeplearningphysics.org 13 | 14 | You can directly open the exercise page in 15 | 16 | [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/master) 17 | [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/DeepLearningForPhysicsResearchBook/deep-learning-physics/HEAD) 18 | 19 | or using the CERN SWAN service 20 | [![SWAN](http://swanserver.web.cern.ch/swanserver/images/badge_swan_white_150.png)](https://cern.ch/swanserver/cgi-bin/go?projurl=https://github.com/DeepLearningForPhysicsResearchBook/deep-learning-physics.git) 21 | 22 | ### Software 23 | The exercises are based on [Keras](https://keras.io/) and [TensorFlow](https://www.tensorflow.org/) v2.4.0. 24 | If you download the repository you can install the software requirements via: 25 | ```bash 26 | pip install -r requirements.txt 27 | ``` 28 | 29 |   30 | ## License 31 | [![CC BY-NC 4.0][cc-by-nc-image]][cc-by-nc] 32 | This work (repository) is licensed under a 33 | [Creative Commons Attribution-NonCommercial 4.0 International License][cc-by-nc]. 34 | 35 | [cc-by-nc]: http://creativecommons.org/licenses/by-nc/4.0/ 36 | [cc-by-nc-image]: https://licensebuttons.net/l/by-nc/4.0/88x31.png 37 | [cc-by-nc-shield]: https://img.shields.io/badge/License-CC%20BY--NC%204.0-lightgrey.svg 38 | 39 | 40 |   41 | ## Citation 42 | 43 | ``` 44 | @book{doi:10.1142/12294, 45 | author = {Erdmann, Martin and Glombitza, Jonas and Kasieczka, Gregor and Klemradt, Uwe}, 46 | title = {Deep Learning for Physics Research}, 47 | publisher = {WORLD SCIENTIFIC}, 48 | year = {2021}, 49 | doi = {10.1142/12294}, 50 | address = {}, 51 | edition = {}, 52 | URL = {http://deeplearningphysics.org}, 53 | eprint = {https://worldscientific.com/doi/pdf/10.1142/12294} 54 | } 55 | ``` 56 | 57 | 58 | 59 | -------------------------------------------------------------------------------- /_config.yml: -------------------------------------------------------------------------------- 1 | theme: jekyll-theme-slate 2 | title: Deep Learning for Physics Research 3 | google_analytics: UA-203084223-2 4 | 5 | -------------------------------------------------------------------------------- /edgeconv.py: -------------------------------------------------------------------------------- 1 | """Implementation of EdgeConv using arbitrary functions as h 2 | for more information see https://git.rwth-aachen.de/niklas.langner/edgeconv_keras 3 | authors: Jonas Glombitza, Niklas Lagner 4 | """ 5 | 6 | import tensorflow as tf 7 | import tensorflow.keras.layers as lay 8 | from tensorflow import keras 9 | 10 | 11 | class SplitLayer(lay.Layer): 12 | """ Custom layer: split layer along specific axis. 13 | eg. split (1,9) into 9 x (1,1) 14 | 15 | Parameters 16 | ---------- 17 | n_splits : int 18 | number of splits 19 | split_axis : int 20 | axis where to split tensor 21 | **kwargs : type 22 | Description of parameter `**kwargs`. 23 | 24 | Attributes 25 | ---------- 26 | n_splits 27 | split_axis 28 | 29 | """ 30 | 31 | def __init__(self, n_splits=12, split_axis=-1, **kwargs): 32 | self.n_splits = n_splits 33 | self.split_axis = split_axis 34 | super(SplitLayer, self).__init__(**kwargs) 35 | 36 | def get_config(self): 37 | config = {'n_splits': self.n_splits, 38 | 'split_axis': self.split_axis} 39 | base_config = super(SplitLayer, self).get_config() 40 | return dict(list(base_config.items()) + list(config.items())) 41 | 42 | def call(self, x): 43 | ''' return array of splitted tensors ''' 44 | sub_tensors = tf.split(x, self.n_splits, axis=self.split_axis) 45 | return sub_tensors 46 | 47 | def compute_output_shape(self, input_shape): 48 | sub_tensor_shape = list(input_shape) 49 | num_channels = sub_tensor_shape[self.split_axis] 50 | sub_tensor_shape[self.split_axis] = int(num_channels / self.n_splits) 51 | sub_tensor_shape = tuple(sub_tensor_shape) 52 | list_of_output_shape = [sub_tensor_shape] * self.n_splits 53 | return list_of_output_shape 54 | 55 | def compute_mask(self, inputs, mask=None): 56 | return self.n_splits * [None] 57 | 58 | 59 | class EdgeConv(lay.Layer): 60 | ''' 61 | Keras layer implementation of EdgeConv. 62 | # Arguments 63 | kernel_func: h-function applied on the points and it's k nearest neighbors. The function should take a list 64 | of two tensors. The first tensor is the vector v_i of the central point, the second tensor is the vector 65 | of one of its neighbors v_j. 66 | :param list: [v_i, v_j] with v_i and v_j being Keras tensors with shape (C_f, ). 67 | :return: Keras tensor of shape (C', ). 68 | next_neighbors: number k of nearest neighbors to consider 69 | agg_func: Aggregation function applied after h. Must take argument "axis=2" to 70 | aggregate over all neighbors. 71 | # Input shape 72 | List of two tensors [points, features] with shape: 73 | `[(batch, P, C_p), (batch, P, C_f)]`. 74 | or tensor with shape: 75 | `(batch, P, C)` 76 | if points (coordinates) and features are supposed to be the same. 77 | # Output shape 78 | Tensor with shape: 79 | `(batch, P, C_h)` 80 | with C_h being the output dimension of the h-function. 81 | ''' 82 | 83 | def __init__(self, kernel_func, next_neighbors, agg_func=keras.backend.mean, **kwargs): 84 | self.kernel_func = kernel_func 85 | self.next_neighbors = next_neighbors 86 | self.agg_func = agg_func 87 | if type(agg_func) == str: 88 | raise ValueError("No such agg_func '%s'. When loading the model specify the agg_func '%s' via custom_objects" % (agg_func, agg_func)) 89 | super(EdgeConv, self).__init__(**kwargs) 90 | 91 | def get_config(self): 92 | config = {'next_neighbors': self.next_neighbors, 93 | 'kernel_func': self.kernel_func, 94 | 'agg_func': self.agg_func} 95 | base_config = super(EdgeConv, self).get_config() 96 | return dict(list(base_config.items()) + list(config.items())) 97 | 98 | def build(self, input_shape): 99 | # Create a trainable weight variable for this layer. 100 | try: 101 | p_shape, f_shape = input_shape 102 | except ValueError: 103 | f_shape = input_shape 104 | 105 | if type(self.kernel_func) != keras.models.Model: # for not wrapping model around model when loading model 106 | x = lay.Input((f_shape.as_list()[-1] * 2,)) 107 | a = lay.Reshape((2, f_shape.as_list()[-1]))(x) 108 | x1, x2 = SplitLayer(n_splits=2, split_axis=-2)(a) # (2, C) 109 | x1 = lay.Reshape((f_shape.as_list()[-1],))(x1) 110 | x2 = lay.Reshape((f_shape.as_list()[-1],))(x2) 111 | y = self.kernel_func([x1, x2]) 112 | self.kernel_func = keras.models.Model(x, y) 113 | 114 | super(EdgeConv, self).build(input_shape) # Be sure to call this at the end 115 | 116 | def call(self, x): 117 | try: 118 | points, features = x 119 | except TypeError: 120 | points = features = x 121 | 122 | # distance 123 | D = batch_distance_matrix_general(points, points) # (N, P, P) 124 | _, indices = tf.nn.top_k(-D, k=self.next_neighbors + 1) # (N, P, K+1) 125 | indices = indices[:, :, 1:] # (N, P, K) remove self connection 126 | knn_fts = knn(indices, features) # (N, P, K, C) 127 | knn_fts_center = tf.tile(tf.expand_dims(features, axis=2), (1, 1, self.next_neighbors, 1)) # (N, P, K, C) 128 | knn_fts = tf.concat([knn_fts_center, knn_fts], axis=-1) # (N, P, K, 2*C) 129 | res = lay.TimeDistributed(lay.TimeDistributed(self.kernel_func))(knn_fts) # (N, P, K, C') 130 | # aggregation 131 | agg = self.agg_func(res, axis=2) # (N, P, C') 132 | return agg 133 | 134 | def compute_output_shape(self, input_shape): 135 | self.output_shape = self.kernel_func.get_output_shape_at(-1) 136 | return self.output_shape 137 | 138 | 139 | def batch_distance_matrix_general(A, B): 140 | ''' Calculate elements-wise distance between entries in two tensors ''' 141 | with tf.name_scope('dmat'): 142 | r_A = tf.reduce_sum(A * A, axis=2, keepdims=True) 143 | r_B = tf.reduce_sum(B * B, axis=2, keepdims=True) 144 | m = tf.matmul(A, tf.transpose(B, perm=(0, 2, 1))) 145 | D = r_A - 2 * m + tf.transpose(r_B, perm=(0, 2, 1)) 146 | return D 147 | 148 | 149 | def knn(topk_indices, features): 150 | # topk_indices: (N, P, K) 151 | # features: (N, P, C) 152 | # return: (N, P, K, C) 153 | with tf.name_scope('knn'): 154 | k = tf.shape(topk_indices)[-1] 155 | num_points = tf.shape(features)[-2] 156 | queries_shape = tf.shape(features) 157 | batch_size = queries_shape[0] 158 | batch_indices = tf.tile(tf.reshape(tf.range(batch_size), (-1, 1, 1, 1)), (1, num_points, k, 1)) 159 | indices = tf.concat([batch_indices, tf.expand_dims(topk_indices, axis=3)], axis=3) # (N, P, K, 2) 160 | return tf.gather_nd(features, indices) 161 | -------------------------------------------------------------------------------- /images/checkerboard_3_2_task_1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_3_2_task_1.png -------------------------------------------------------------------------------- /images/checkerboard_3_2_task_3.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_3_2_task_3.png -------------------------------------------------------------------------------- /images/checkerboard_l1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_l1.png -------------------------------------------------------------------------------- /images/checkerboard_l2_high.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_l2_high.png -------------------------------------------------------------------------------- /images/checkerboard_l2_low.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_l2_low.png -------------------------------------------------------------------------------- /images/checkerboard_l2_moderate.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_l2_moderate.png -------------------------------------------------------------------------------- /images/checkerboard_overtraining.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_overtraining.png -------------------------------------------------------------------------------- /images/checkerboard_regularization.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_regularization.png -------------------------------------------------------------------------------- /images/checkerboard_tf_playground.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/DeepLearningForPhysicsResearchBook/deep-learning-physics/41171d6386ec9c8c33f3e4a0bc06022a98d29791/images/checkerboard_tf_playground.png -------------------------------------------------------------------------------- /index.md: -------------------------------------------------------------------------------- 1 | 2 | ## Information 3 | 4 | This page contains additional material for the textbook *Deep Learning for Physics Research* by 5 | [Martin Erdmann](https://www.physik.rwth-aachen.de/user/erdmann), [Jonas Glombitza](https://www.jonas-glombitza.com/), [Gregor Kasieczka](https://www.physik.uni-hamburg.de/iexp/gruppe-kasieczka.html), and Uwe Klemradt. 6 | 7 | The authors can be contacted under [authors@deeplearningphysics.org](mailto:authors@deeplearningphysics.org). 8 | 9 | For more information on the book, refer to the page by the [publisher](https://worldscientific.com/worldscibooks/10.1142/12294). 10 | 11 | ## Exercises 12 | ### Section 1 - Deep Learning Basics 13 | #### Chapter 3 - Building blocks of neural networks 14 | * **3.1: Introduction** ([Download](Exercise_03_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_03_1.ipynb)) 15 | * **3.2: Linear regression (fit)** 16 | Problem ([Download](Exercise_03_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_03_2.ipynb)), Solution ([Download](Exercise_03_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_03_2_solution.ipynb)) 17 | * **3.3: XOR classification** 18 | Problem ([Download](Exercise_03_3.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_03_3.ipynb)), Solution ([Download](Exercise_03_3_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_03_3_solution.ipynb)) 19 | 20 | 21 | #### Chapter 4 - Optimization of network parameters 22 | * **4.1: Manual definition of regression network** 23 | Problem ([Download](Exercise_04_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_04_1.ipynb)), Solution ([Download](Exercise_04_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_04_1_solution.ipynb)) 24 | * **4.2: Linear regression using Keras** 25 | Problem ([Download](Exercise_04_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_04_2.ipynb)), Solution ([Download](Exercise_04_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_04_2_solution.ipynb)) 26 | * **4.3: Classification: metrics, classes, and one-hot encoding** 27 | Problem ([Download](Exercise_04_3.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_04_3.ipynb)), Solution ([Download](Exercise_04_3_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_04_3_solution.ipynb)) 28 | 29 | #### Chapter 5 - Mastering model building 30 | * **5.1: Regularization and parameter norm penalties** 31 | Problem ([Download](Exercise_05_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_05_1.ipynb)), Solution ([Download](Exercise_05_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_05_1_solution.ipynb)) 32 | * **5.2: Interpolation: train a DNN to learn a complicated function** 33 | Problem ([Download](Exercise_05_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_05_2.ipynb)), Solution ([Download](Exercise_05_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_05_2_solution.ipynb)) 34 | * **5.3: Regression with Keras** 35 | Problem ([Download](Exercise_05_3.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_05_3.ipynb)), Solution ([Download](Exercise_05_3_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_05_3_solution.ipynb)) 36 | 37 | 38 | --- 39 | ### Section 2 - Standard Architectures of Deep Networks 40 | 41 | #### Chapter 7 - Fully-connected networks: improving the classic all-rounder 42 | * **7.1: Classification of magnetic phases using fully-connected networks** 43 | Problem ([Download](Exercise_07_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_07_1.ipynb)), Solution ([Download](Exercise_07_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_07_1_solution.ipynb)) 44 | * **7.2: Energy reconstruction of air showers using fully-connected networks** 45 | Problem ([Download](Exercise_07_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_07_2.ipynb)), Solution ([Download](Exercise_07_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_07_2_solution.ipynb)) 46 | 47 | 48 | #### Chapter 8 - Convolutional neural networks and analysis of image-like data 49 | * **8.1: Classification of magnetic phases using convolutional networks** 50 | Problem ([Download](Exercise_08_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_08_1.ipynb)), Solution ([Download](Exercise_08_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_08_1_solution.ipynb)) 51 | * **8.2: Energy reconstruction of air showers using convolutional networks** 52 | Problem ([Download](Exercise_08_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_08_2.ipynb)), Solution ([Download](Exercise_08_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_08_2_solution.ipynb)) 53 | 54 | 55 | 56 | #### Chapter 9 - Recurrent neural networks: time series and variable input 57 | * **9.1: Get in touch with RNNs: learn a sine wave** 58 | Problem ([Download](Exercise_09_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_09_1.ipynb)) 59 | * **9.2: Identification of radio signals using RNNs** 60 | Problem ([Download](Exercise_09_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_09_2.ipynb)), Solution ([Download](Exercise_09_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_09_2_solution.ipynb)) 61 | 62 | #### Chapter 10 - Graph networks and convolutions beyond Euclidean domains 63 | * **10.1: Signal Classification using Dynamic Graph Convolutional Neural Networks** 64 | Problem ([Download](Exercise_10_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_10_1.ipynb)), Solution ([Download](Exercise_10_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_10_1_solution.ipynb)) 65 | * **(16.1: Semi-supervised node classification using graph convolutional networks)** 66 | Problem ([Download](Exercise_16_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_16_1.ipynb)), Solution ([Download](Exercise_16_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_16_1_solution.ipynb)) 67 | 68 | #### Chapter 11 - Multi-task learning, hybrid architectures, and operational reality 69 | * **11.1: Reconstruction of cosmic-ray-induced air showers** 70 | Problem ([Download](Exercise_11_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_11_1.ipynb)), Solution ([Download](Exercise_11_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_11_1_solution.ipynb)) 71 | 72 | --- 73 | ### Section 3 - Introspection, Uncertainties, Objectives 74 | * **12.1: Visualization of weights and activations** 75 | Problem ([Download](Exercise_12_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_12_1.ipynb)), Solution ([Download](Exercise_12_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_12_1_solution.ipynb)) 76 | * **12.2: Feature visualization using activation maximization** 77 | Problem ([Download](Exercise_12_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_12_2.ipynb)), Solution ([Download](Exercise_12_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_12_2_solution.ipynb)) 78 | * **12.3: Discriminative Localization** 79 | Problem ([Download](Exercise_12_3.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_12_3.ipynb)), Solution ([Download](Exercise_12_3_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_12_3_solution.ipynb)) 80 | 81 | --- 82 | ### Section 4 - Deep Learning Advanced Concepts 83 | 84 | #### Chapter 16 - Weakly-supervised classification 85 | * **16.1: Zachary’s karate club - semi-supervised node classification** 86 | Problem ([Download](Exercise_16_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_16_1.ipynb)), Solution ([Download](Exercise_16_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_16_1_solution.ipynb)) 87 | 88 | #### Chapter 17 - Autoencoders: finding and compressing structures in data 89 | * **17.1: Speckle removal with denoising autoencoders** 90 | Problem ([Download](Exercise_17_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_17_1.ipynb)), Solution ([Download](Exercise_17_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_17_1_solution.ipynb)) 91 | 92 | #### Chapter 18 - Generative models: data from noise 93 | * **18.1: Generation of fashion images using Generative Adversarial Networks** 94 | Problem ([Download](Exercise_18_1.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_18_1.ipynb)), Solution ([Download](Exercise_18_1_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_18_1_solution.ipynb)) 95 | * **18.2: Generation of air-shower footprints using WGAN** 96 | Problem ([Download](Exercise_18_2.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_18_2.ipynb)), Solution ([Download](Exercise_18_2_solution.ipynb) - [View](https://nbviewer.jupyter.org/github/DeepLearningForPhysicsResearchBook/deep-learning-physics/blob/main/Exercise_18_2_solution.ipynb)) 97 | 98 | --- 99 | 100 |   101 | ### Citation 102 | 103 | ``` 104 | @book{doi:10.1142/12294, 105 | author = {Erdmann, Martin and Glombitza, Jonas and Kasieczka, Gregor and Klemradt, Uwe}, 106 | title = {Deep Learning for Physics Research}, 107 | publisher = {WORLD SCIENTIFIC}, 108 | year = {2021}, 109 | doi = {10.1142/12294}, 110 | address = {}, 111 | edition = {}, 112 | URL = {http://deeplearningphysics.org}, 113 | eprint = {https://worldscientific.com/doi/pdf/10.1142/12294} 114 | } 115 | ``` 116 | 117 |   118 | ## Errata 119 | 120 | Please report mistakes to [authors@deeplearningphysics.org](mailto:authors@deeplearningphysics.org). 121 | 122 | So far, no errors are known. 123 | 124 | ## Usage 125 | 126 | Note: To improve the exercise page and potentially improve and extend 127 | the scope, we measure the use of the task templates and the interest in 128 | the solutions with the tool Google Analytics. 129 | -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | matplotlib 2 | numpy 3 | tensorflow==2.4.0 4 | seaborn 5 | spektral 6 | gdown --------------------------------------------------------------------------------