{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "YyREI41Y-UuT" }, "source": [ "## CS535/EE514 - Spring 2022 - Assignment 5 \n", "\n", "\n", "\n", "#### Important Instructions and Submission Guidelines:\n", "- ## Important Instructions and Submission Guidelines:\n", "- Submit your code both as notebook file (.ipynb) and python script (.py) on LMS. Naming convention for submission of this notebook is `RollNumber_partA_PA5.ipynb` where. For example: `23100042_partA_PA5.ipynb`\n", "- All the cells must be run once before submission. If your submission's cells are not showing the results (plots etc.), marks wil be deducted\n", "- Only the code written within this notebook's marked areas will be considered while grading. No other files will be entertained\n", "- You are advised to follow good programming practies including approriate variable naming and making use of logical comments.\n", "\n", "\n", "The university honor code should be maintained. Any violation, if found, will result in disciplinary action. \n" ] }, { "cell_type": "markdown", "metadata": { "id": "Bm73jREWNf7J" }, "source": [ "Often in pratical situations, raw machine learning architecture and code is hidden behind libraries and simplfied toolkits. The purpose of this assignment is to lift that curtain and get you hands-on exprience working with the mathematical fundamentals of neural network architectures. After this, you'll know exactly how a network leverages 'gradient descent' to find optimal solutions and how forward and backward passes are implemented mathematically and in code." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Hf0nYQPsMXYf" }, "outputs": [], "source": [ "rollnumber = None" ] }, { "cell_type": "markdown", "metadata": { "id": "o9WfA6k3Gamc" }, "source": [ "This is the dataset that we are goint to use. As you can see there are two classes and there is a non-linear relationship between them. We are going to build a Neural Network from scratch to learn this non-linear relationship." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 314 }, "id": "Gmds9e122AG8", "outputId": "1874ecca-e625-4cde-d54b-11751511d591" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(500, 1) (500, 2)\n" ] }, { "data": { "text/plain": [ "[Text(0.5, 0, 'Feature 1'), Text(0, 0.5, 'Feature 2')]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_moons\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "points = 500\n", "\n", "X_train, y_train = make_moons(points, noise=0.10)\n", "\n", "y_train = y_train.reshape(points,1)\n", "print(y_train.shape,X_train.shape)\n", "\n", "plt.scatter(X_train[:,0], X_train[:,1], c=y_train, cmap=plt.cm.Spectral);\n", "plt.gca().set(xlabel='Feature 1', ylabel='Feature 2')\n" ] }, { "cell_type": "markdown", "metadata": { "id": "qrK9-wONM_7t" }, "source": [ "In the first part, you are going to build a neural network with 1 input layer and 1 output layer.\n", "\n", "In the second part, you will be builidng neural network with 1 input layer, 1 hidden layer and 1 output layer.\n", "\n", "You will be implementing forward pass and most importantly backward pass. Coding these algorithms will help solidfy these concepts which are at the core of modern day Machine Learning and Deep Learning." ] }, { "cell_type": "markdown", "metadata": { "id": "64bPJeFFNRVD" }, "source": [ "## Part1" ] }, { "cell_type": "markdown", "metadata": { "id": "5n3LOI96Np7A" }, "source": [ "Use numpy random [normal](https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html) to intialize weight matrix of the right shape." ] }, { "cell_type": "markdown", "metadata": { "id": "CoC6yXe516j_" }, "source": [ "Neural Network that you are going to implement will have one input layer of 2 neurons and an output layer of one neuron" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "yq65RZ5N16j_", "outputId": "6c6f273f-0072-4e9b-defb-5a8d22769529" }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAACDCAYAAACa5Gl6AAAABmJLR0QA/wD/AP+gvaeTAAAQEElEQVR4nO3df0wT5x8H8PfRa8uE4o9lFINocIMykMmmE6YxCmgWnc5pgAUXNGaJy9BN5v5A/QfNYkayLRj/mhq2WNFpcZlusXNiIA4JbqOiC1NBqJgoiogiP1QK7ef7xzcQXa+/27vr7XklTYiWu0/Dp/dcn97zPo6ICAwTetURUlfA/HewZmNEw5qNEQ0vxk5sNhva29vR3d2Nx48f4/Hjx5g0aRImTJiAhIQEJCQkgOM4MUphJBSSZuvt7YXZbEZdXR3Onz8Pq9UKu93u8vlRUVGYNWsWFi9ejNzcXGRnZ4PnRXkfMCLigvVplIhw+vRp7N+/H2azGRzHISsrC4sXL0ZaWhoMBgOmTp2KCRMmICoqCn19fRgaGkJnZydaW1thsVhQW1uLa9euQa/XY+3atdi0aRNefvnlYJTHSK8aFAQnTpygjIwM4jiOcnNzyWg00uDgoF/bslqttGvXLpo5cyapVCpau3YttbW1BaNMRlqmgJqto6ODli1bRhzHUX5+PjU3NwerMBodHaUjR45QamoqRUZGUllZGT158iRo22dE53+zHT9+nCZNmkQGg4HOnj0bzKKeMzIyQnv27KGYmBhKS0ujlpaWkO2LCSnfm81ut9PmzZuJ4zgqKSmh4eHhUBTmpKOjg958803S6XR06tQpUfbJBJVvzTY8PEwFBQUUGRlJ1dXVoSrK7f43bNhAarWajEaj6PtnAuJ9s9ntdiooKKCYmBiqq6sLYU3uORwOKi0tpYiICDp69KhkdTA+877ZNm/eTJGRkZI22rNKSkpIo9FQbW2t1KUw3vGu2Q4fPkwcx0kydLpit9spPz+f9Ho9dXV1SV0O45nJ46Su1WpFRkYGPvzwQ1RUVIg1AeiVgYEBzJkzBzNmzMCZM2fYV17yVu2x2ZYtW4Zbt27BYrFAo9GIVZjXmpqakJWVhe+//x5FRUVSl8O45v4bhJ9++ok4jqPff/9djMOs34qLi0mv11N/f7/UpTCuuR5GiQhz5szBK6+8ApPJJPa7wCcPHjxAYmIiduzYgdLSUqnLYYS5vlL39OnTuHTpEnbs2CFmQX6ZMmUKiouLUVFRgadPn0pdDuOCy2Y7cOAAcnJykJGRIWY9ftuyZQt6e3tx8uRJqUthXBBstrHr0davXy92PX6Li4vD0qVLcejQIalLYVwQbDaz2QwAWL16tajFBKqwsBA1NTUYGhqSuhRGgGCz1dbWIisrC9HR0WLXE5AlS5bAZrOhoaFB6lIYAYLN1tDQgEWLFoldS8CmTp0Kg8GA8+fPS10KI8Cp2Ww2G6xWK9LT06WoJ2BpaWm4evWq1GUwApyarb29HXa7HcnJyVLUEzCDwYDW1lapy2AEODXbvXv3APz/0104iouLQ09Pj9RlMAKcmm1wcBAAwu7DwRidToeBgQGpy2AECJ6zAYBWqw36zq5cuYKenh7cvn076NseExkZieHh4ZBtn/Gf00rgCRMmAACGhoYQExMT1J2lpqYGdXtCBgcHERUVFfL9ML5zOrLpdDoACNuhqL+/P+hvEiY4nJpt+vTpAICbN2+KXkwwdHZ2jr8GRl6cmm3atGmIjo4O2+mD1tZWGAwGqctgBDg1G8dxSEtLQ1NTkxT1BMThcKC5uTlsJ6SVTvDrqsWLF6Ourk7sWgJ2+fJl3L9/H9nZ2VKXwggQbLbc3FxcvXoVVqtV7HoC8uuvvyI2NpYd2WRKsNmys7MRFxeHqqoqsesJyA8//ID4+HicPHlyfL6QkQ/BZuN5HoWFhTh48KDbED85aWxsREtLC9RqNfLy8hAfH48tW7agublZ6tKYMa6WwnR0dBDP83TkyBHRlt8EYuXKlZSZmUlERLdu3aLy8nJKTk4mAJSamkrl5eV09+5diav8T3O/SPmDDz7A5cuXcenSJVnHjjY1NWHevHn4+eefsWLFiuf+z2KxwGg04vDhw+jr60N2djY2btyIVatWyXIdbCjIJNPY/brR69evU2RkJH3zzTfi9L4f7HY7ZWZm0sKFC8nhcLh83pMnT8hkMtGKFSuI53maPHkybdy4kerr60WsVhz3798no9FIGzZsoKSkJFKpVATA5SMqKooyMzOptLSUzpw5QyMjI6Eoy3PWR1lZGel0Ouro6AhFAQHbu3cv8TxPf//9t9e/MzbMJiUlKWaYdTgcZDab6b333iONRkNarZYWLVpEZWVlZDKZ6PLly3Tv3r3x+NmHDx/SrVu36Pz581RZWUnFxcWUkpJCAEiv19Nnn31G7e3twSzRc7M9efKEMjIyaO7cuaIF/3nLYrGQVqulnTt3+r2NpqYm+vTTT+nFF18klUpFS5YsIZPJJLvX6k6YZBp7l2LU2tpKOp2ONmzY4HaoElNXVxclJiZSTk4O2e32gLcXjsNsmGUae5/PdurUKVKr1VRaWhrIDoPi4cOHNHv2bDIYDNTT0xP07YfDMBuGmca+xZwajUaKiIigkpISyY5wXV1dNHv2bJo2bRp1dnaGfH9jw+yUKVMCHmZ7e3sDrieMM419D3A+duwYabVays/PFz01yGKxUGJiIhkMBrpx44ao+w7GMPvOO+/Q559/TqOjo37VEOaZxv5F09fW1pJer6ekpCT6888//dmET+x2O+3du5e0Wi3l5OSEZOj0hT/D7N27d8enIN5++2169OiRT/tUQKax//dB6OrqotzcXFKpVFRcXByUIULIX3/9RfPmzSOe52nnzp1+HxVCxdth9uuvvyae5wkAqdVqMhgMZLVavd6PAjKNA7vDi8PhIKPRSHq9nmJiYmjbtm10586dQDY5rrGxkVauXEkcx9HChQt9mkeTgqdh9tVXXyWO48YnUtVqNU2cONGr5lFIpnFgzTamv7+fysvLKTY2lniep+XLl9PBgwd9Cla22+3U3NxMu3fvptTUVAJAWVlZ9Msvv8hmusVbN2/epC+++GJ8mB37jvbfj4iICOJ5nr777juX2+ro6CCdTkclJSUivgLv9Pf3U1JSEi1ZssSbv5HnAGdfPH36FCdPnsShQ4dQU1MDm80Gg8GAWbNmITk5GVOnTkV0dPT4XfkGBgZw48YNtLW1obm5Gffv38dLL72EgoICFBUVITMzM1ilSYKI0NDQgI8//hitra0YGRlx+dxPPvkEFRUVUKlUz/27gjKNPQc4+2toaAgNDQ2or6/HtWvX0NbWhu7ubgwNDWFwcBCTJ09GdHQ0EhISkJKSgvT0dGRnZyM9PR0REcq5wbPNZkNsbCwePXrk9nkqlQo5OTmorq7GxIkTAQAnTpzAmjVrcO7cOSxcuFCMcv2yadMm/Pjjj7h+/fr46jwBwbkFJOPa8ePHnztXc/fgeX78g4PD4aDXX3+d8vPzpX4JHvX29lJMTAyVl5e7e1pwztkY15YvXz7+KdSbh1qtpsmTJ9NXX31FHMcF9SuoUNq2bRvp9Xp3X2kF95yNeV53dzfi4+NdXu2sUqnGTxk4jgPHcXA4HBgZGUFERARSUlLwzz//iFmy3+7evYuEhARUVVXh/fffF3pKtXyviFSAyMhI/PHHHxgYGMDo6CgAePVzT08P9uzZg5kzZ+LKlSuixFYE6tlMYxfN5vqycEY6RqORtFotDQwMSF2KT4xGI2k0GleXN5mU87FPQZSaacyaTYaUmmnMmk1mlJxpzJpNZpScacyaTWaUnGnMmk1mlJxpzObZZCaUmcY3btxAdHQ0bDYb4uPjg759wH2mMWs2mQllpnFiYmJQtyfEXaYxG0ZlRsmZxqzZZEbJmcas2WRGyZnGrNlkRsmZxqzZZEipmcas2WRIqZnGbOojhDo7O/Htt99icHBwfLHLsz8/evRofE5qYGBgfI5taGgIKpUKixYtwm+//RYW17MB/880zs/Pd7mGhF2pG0I2mw16vR79/f3jq6bsdjscDofH350yZQqio6NhtVqdVlzJUWNjI+bPn48LFy64WhVXzYbRENJoNCgqKgLP8xgZGcHIyIjHRlOpVFi6dClqa2vR1dUFk8kkUrWB+fLLL5GZmel2+aUoRzaZZLpKwmKxYO7cuV4//9n1o0rINH5GaJbyyTTTVTIpKSlul/O5WhmvpExjCuZSvjDIdBVdS0sLlZaWkk6nc/mG85T5oaBM4+A0W5hkuoqiu7ubKioq6LXXXiMAlJSURNu2bRNsNm/SjBSUaRxYs4VZpmvIjI6OUk1NDeXn55NaraaYmBgqKiqimpqa8aHl34uVx+K1+vr6PG5fIZnG/jdbGGa6Bt3YMBkbG0sRERG0YMEC2rdvn+ASvH/HMGzdutWnrDkFZBr73mxhnOkaFA8ePKB9+/bRG2+8QQBo+vTpVFpa6vGcanh4mCZOnEg8z1NlZaVf+w7zTGPfmi3MM1395s0w6Y1du3bRuXPnAqoljDONvW82BWS6+syXYVJMYZpp7H2zKSDT1Suuhklf8m/FEIaZxt41m0IyXV0K1jAptjDLNPbcbArKdHUi12HSV2GSaew5n01Bma4AgIcPH6K6uhr79u3DxYsXMX36dBQWFuKjjz4SZfVRKMk809h9pq5SMl3tdjvq6uqwf/9+nDhxAi+88AJWrVqFdevWITc3V5EXAcgw09j1F/FKyHRVyjCpEK7P2cxmc1hmut65cycsPk3+B7k+Z1uzZg36+/tx9uzZUBxSg24s01WtVkOtVqOgoADr16/HggULFDlMhiHhTN3e3l6YzWYcOHBA7IL8Npbp2tfXh7Nnz47HGDDyIXgmaDabAQCrV68WtZhAFRYWwmKxwMXBmpGYYLMpNdOVkZZgsyk105WRllOzKTnTlZGWU7MpOdOVkZZTsyk505WRllOzKTnTlZGW4DkbEJpM1ytXrqCnpwcPHjwI+rbHuMt0ZaTlNKkbykxXMQJS3GW6MtJyOrIpOdOVkZZTsyk505WRllOzKTnTlZGWU7MpOdOVkZb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"text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('graph1.png')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "R1JCZQ80OC7A" }, "outputs": [], "source": [ "def initialize_weight():\n", " '''Initializes all weights based on standard normal distribution'''\n", " size = ()\n", " weight = None\n", " return weight" ] }, { "cell_type": "markdown", "metadata": { "id": "a2MjgI5kObcP" }, "source": [ "Activation Function" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "TubnJJzsX-R0" }, "outputs": [], "source": [ "def sigmoid(x):\n", " # implement sigmoid function\n", " pass" ] }, { "cell_type": "markdown", "metadata": { "id": "YwxBeQk7OdHi" }, "source": [ "Metrics for evaluating model" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "7R2BxDRPXs-q" }, "outputs": [], "source": [ "def cross_entropy_loss(y_pred, y_true):\n", " # implement cross_entropy_loss function\n", " pass\n", "\n", "def accuracy(y_pred, y_true):\n", " # implement accuracy function\n", " pass" ] }, { "cell_type": "markdown", "metadata": { "id": "BLPtI-goOf9e" }, "source": [ "Forward Pass. To make your code computationally fast try to use dot product (vectorization) instead of for loops. Also don't forget to use activation function." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "F5V-KiAj5yba" }, "outputs": [], "source": [ "def forward_pass(weight, Xs):\n", " # implement forward pass function \n", " '''Executes the feed forward algorithm. \"Xs\" is the input to the network.\n", " Returns \"layer_activations\", which is a list of all layer outputs'''\n", "\n", " layer_activations = []\n", "\n", " return layer_activations" ] }, { "cell_type": "markdown", "metadata": { "id": "7VMVsoGCRHl7" }, "source": [ "Backward Pass. This is the most important step in learning process where you update your weights so that thel model fits your data." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "BYUdKJjXRF1Y" }, "outputs": [], "source": [ "def backward_pass(layer_activations, Ys,weight):\n", " # implement backward pass function \n", "\n", " '''Executes the backpropogation algorithm. \"Ys\" is the ground truth/labels, \n", " \"layer_activations\" are the return value of the forward pass step.\n", " Returns \"deltas\", which is a list containing weight update values for all layers''' \n", "\n", " deltas = []\n", "\n", " return deltas" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "UXroKJmDT5iA" }, "outputs": [], "source": [ "def weight_update(weight, deltas, lr):\n", " '''After executing the gradient descent algorithm \"deltas\" is return value of the backward pass step\n", " \"lr\" is the learning rate\n", " Update the weights of the model and return updated weights\n", " '''\n", "\n", " return weight\n" ] }, { "cell_type": "markdown", "metadata": { "id": "-Nj2XaiBXYS3" }, "source": [ "Predict function is similar to forward propagation except you need to now return numpy array containing binary class labels 0 and 1 because there are two classes in the dataset. Set a threshold for this classification." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "ypkGA2_dXT7s" }, "outputs": [], "source": [ "def predict(Xs, weight):\n", " '''Returns the model predictions (output of the last layer) for the given \"Xs\".'''\n", " \n", " return predictions" ] }, { "cell_type": "markdown", "metadata": { "id": "Qih_fyVzUwwl" }, "source": [ "Implement the fit funciton. You need to use all above functions to fit and train the model in following steps.\n", "\n", "* Weight initialization\n", "* Forward Pass\n", "* Backward Pass\n", "* Weight Update\n", "* Compute Cost, Accuracy and append it to the list\n", "\n", "\n", "You should use the lecture [slides](https://www.zubairkhalid.org/ee514/2022/notes12.pdf) as reference for the equations. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "GvxUDulhSwdU" }, "outputs": [], "source": [ "def fit(Xs, Ys , epochs , lr = 1e-3 ):\n", " losses = []\n", " accuracy = []\n", " weights = None\n", " for epoch in range(epochs):\n", " # ToDo\n", "\n", " losses.append()\n", " accuracy.append()\n", " if epoch%100 == 0:\n", " print(\"epoch \",epoch,\"loss \",cross_entropy_loss() )\n", " \n", " return losses,accuracy\n", "losses, accuracy, weights = fit(X_train,y_train,epochs)" ] }, { "cell_type": "markdown", "metadata": { "id": "c9NtLVBm16kF" }, "source": [ "Expected Loss after training is below 90" ] }, { "cell_type": "markdown", "metadata": { "id": "xQrSRZ4VXGBE" }, "source": [ "Plot the following graphs:\n", "\n", "– Training loss (y-axis) vs no. of epochs (x-axis).\n", "\n", "– Training accuracy (y-axis) vs no. of epochs (x-axis).\n", "\n", "\n", "Predict the labels of test data using the predict function. Skeleton code for this function is already given to you. You may find np.argmax or np.where useful to extract labels.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "Wovq2RwsXE2W" }, "outputs": [], "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "id": "ngzznhLHY62J" }, "source": [ "Once you are done training. Run the following cell to plot the decision boundary." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "KDAAqZdWfmk-" }, "outputs": [], "source": [ "fig, ax = plt.subplots()\n", "x_min, x_max = X_train[:, 0].min() - .5, X_train[:, 0].max() + .5\n", "y_min, y_max = X_train[:, 1].min() - .5, X_train[:, 1].max() + .5\n", "\n", "def plot_decision_boundary(pred_func,weight, x_min, x_max, y_min, y_max, cmap, ax):\n", " h = 0.01\n", " # Generate a grid of points with distance h between them\n", " xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n", " # Predict the function value for the whole gid\n", " Z = pred_func(np.c_[xx.flatten(), yy.flatten()],weight)\n", " Z = Z.reshape(xx.shape)\n", " # Plot the contour\n", " ax.contourf(xx, yy, Z, cmap=cmap, alpha=0.5)\n", "\n", "plot_decision_boundary(predict, weights,\n", " x_min, x_max, y_min, y_max, \n", " plt.cm.Spectral, ax)\n", "ax.scatter(X_train[:,0], X_train[:,1], c=y_train, cmap=plt.cm.Spectral);\n", "ax.set(xlabel='Feature 1', ylabel='Feature 2', title='Neural Network Classifier {}'.format(rollnumber));" ] }, { "cell_type": "markdown", "metadata": { "id": "N3tRWNGEZjwK" }, "source": [ "## Part2\n", "\n", "In part 2 you will add a hidden layer of 10 neurons to your neural network architecure and re-implement all of the functions above. You can copy cells. Comment on the difference between the decision boundary in both parts that you observed." ] }, { "cell_type": "markdown", "metadata": { "id": "bCyoE8hj16kH" }, "source": [ "This is the Neural Network architecture for this part" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "04P8i__916kH", "outputId": "9b02abea-4ce3-4f3b-d229-9d806554a23a" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('graph.png')" ] }, { "cell_type": "markdown", "metadata": { "id": "i_UmaaUE16kH" }, "source": [ "Expected loss after training for this part is less than 20" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "_uak-yB516kH" }, "outputs": [], "source": [ "" ] } ], "metadata": { "accelerator": "GPU", "colab": { "collapsed_sections": [], "name": "PA5.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.9" } }, "nbformat": 4, "nbformat_minor": 0 }