04.2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/udlbook/udlbook/blob/main/Notebooks/Chap04/4_2_Clipping_functions.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MaKn8CFlzN8E"
   },
   "source": [
    "#Notebook 4.2 -- Clipping functions\n",
    "\n",
    "The purpose of this notebook is to understand how a neural network with two hidden layers build more complicated functions by clipping and recombining the representations at the intermediate hidden variables.\n",
    "\n",
    "Work through the cells below, running each cell in turn. In various places you will see the words \"TO DO\". Follow the instructions at these places and make predictions about what is going to happen or write code to complete the functions.\n",
    "\n",
    "Contact me at udlbookmail@gmail.com if you find any mistakes or have any suggestions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "8ClURpZQzI6L"
   },
   "outputs": [],
   "source": [
    "# Imports math library\n",
    "import numpy as np\n",
    "# Imports plotting library\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "YdmveeAUz4YG"
   },
   "outputs": [],
   "source": [
    "# Define the Rectified Linear Unit (ReLU) function\n",
    "def ReLU(preactivation):\n",
    "  activation = preactivation.clip(0.0)\n",
    "  return activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "ximCLwIfz8kj"
   },
   "outputs": [],
   "source": [
    "# Define a deep neural network with, one input, one output, two hidden layers and three hidden units (eqns 4.7-4.9)\n",
    "# To make this easier, we store the parameters in ndarrays, so phi_0 = phi[0] and psi_3,3 = psi[3,3] etc.\n",
    "def shallow_1_1_3_3(x, activation_fn, phi, psi, theta):\n",
    "\n",
    "  # TODO -- You write this function\n",
    "  # Replace the skeleton code below.\n",
    "\n",
    "  # ANSWER\n",
    "  # Preactivations at layer 1 (terms in brackets in equation 4.7)\n",
    "  layer1_pre_1 = theta[1,0] + theta[1,1] * x\n",
    "  layer1_pre_2 = theta[2,0] + theta[2,1] * x\n",
    "  layer1_pre_3 = theta[3,0] + theta[3,1] * x\n",
    "\n",
    "  # Activation functions (rest of equation 4.7)\n",
    "  h1 = activation_fn(layer1_pre_1)\n",
    "  h2 = activation_fn(layer1_pre_2)\n",
    "  h3 = activation_fn(layer1_pre_3)\n",
    "\n",
    "  # Preactivations at layer 2 (terms in brackets in equation 4.8)\n",
    "  layer2_pre_1 = psi[1,0] + psi[1,1]*h1 + psi[1,2]*h2 + psi[1,3]*h3\n",
    "  layer2_pre_2 = psi[2,0] + psi[2,1]*h1 + psi[2,2]*h2 + psi[2,3]*h3\n",
    "  layer2_pre_3 = psi[3,0] + psi[3,1]*h1 + psi[3,2]*h2 + psi[3,3]*h3\n",
    "\n",
    "  # Activation functions (rest of equation 4.8)\n",
    "  h1_prime = activation_fn(layer2_pre_1)\n",
    "  h2_prime = activation_fn(layer2_pre_2)\n",
    "  h3_prime = activation_fn(layer2_pre_3)\n",
    "\n",
    "  # Weighted outputs by phi (three last terms of equation 4.9)\n",
    "  phi1_h1_prime = phi[1]*h1_prime \n",
    "  phi2_h2_prime = phi[2]*h2_prime \n",
    "  phi3_h3_prime = phi[3]*h3_prime \n",
    "\n",
    "  # Combine weighted activation and add y offset (summing terms of equation 4.9)\n",
    "  y = phi[0] + phi1_h1_prime + phi2_h2_prime + phi3_h3_prime\n",
    "\n",
    "\n",
    "  # Return everything we have calculated\n",
    "  return y, layer2_pre_1, layer2_pre_2, layer2_pre_3, h1_prime, h2_prime, h3_prime, phi1_h1_prime, phi2_h2_prime, phi3_h3_prime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "ZB2HTalOE40X"
   },
   "outputs": [],
   "source": [
    "# # Plot two layer neural network as in figure 4.5\n",
    "def plot_neural_two_layers(x, y, layer2_pre_1, layer2_pre_2, layer2_pre_3, h1_prime, h2_prime, h3_prime, phi1_h1_prime, phi2_h2_prime, phi3_h3_prime):\n",
    "\n",
    "    fig, ax = plt.subplots(3,3)\n",
    "    fig.set_size_inches(8.5, 8.5)\n",
    "    fig.tight_layout(pad=3.0)\n",
    "    ax[0,0].plot(x,layer2_pre_1,'r-'); ax[0,0].set_ylabel('$\\psi_{10}+\\psi_{11}h_{1}+\\psi_{12}h_{2}+\\psi_{13}h_3$')\n",
    "    ax[0,1].plot(x,layer2_pre_2,'b-'); ax[0,1].set_ylabel('$\\psi_{20}+\\psi_{21}h_{1}+\\psi_{22}h_{2}+\\psi_{23}h_3$')\n",
    "    ax[0,2].plot(x,layer2_pre_3,'g-'); ax[0,2].set_ylabel('$\\psi_{30}+\\psi_{31}h_{1}+\\psi_{32}h_{2}+\\psi_{33}h_3$')\n",
    "    ax[1,0].plot(x,h1_prime,'r-'); ax[1,0].set_ylabel(\"$h_{1}^{'}$\")\n",
    "    ax[1,1].plot(x,h2_prime,'b-'); ax[1,1].set_ylabel(\"$h_{2}^{'}$\")\n",
    "    ax[1,2].plot(x,h3_prime,'g-'); ax[1,2].set_ylabel(\"$h_{3}^{'}$\")\n",
    "    ax[2,0].plot(x,phi1_h1_prime,'r-'); ax[2,0].set_ylabel(\"$\\phi_1 h_{1}^{'}$\")\n",
    "    ax[2,1].plot(x,phi2_h2_prime,'b-'); ax[2,1].set_ylabel(\"$\\phi_2 h_{2}^{'}$\")\n",
    "    ax[2,2].plot(x,phi3_h3_prime,'g-'); ax[2,2].set_ylabel(\"$\\phi_3 h_{3}^{'}$\")\n",
    "\n",
    "    for plot_y in range(3):\n",
    "      for plot_x in range(3):\n",
    "        ax[plot_y,plot_x].set_xlim([0,1]);ax[plot_x,plot_y].set_ylim([-1,1])\n",
    "        ax[plot_y,plot_x].set_aspect(0.5)\n",
    "      ax[2,plot_y].set_xlabel('Input, $x$');\n",
    "    plt.show()\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x,y)\n",
    "    ax.set_xlabel('Input, $x$'); ax.set_ylabel('Output, $y$')\n",
    "    ax.set_xlim([0,1]);ax.set_ylim([-1,1])\n",
    "    ax.set_aspect(0.5)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LxBJCObC-NTY"
   },
   "source": [
    "Now let's define the parameters and visualize the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "id": "JRebvurv22pT"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 850x850 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define parameters (note first dimension of theta and phi is padded to make indices match\n",
    "# notation in book)\n",
    "theta = np.zeros([4,2])\n",
    "psi = np.zeros([4,4])\n",
    "phi = np.zeros([4,1])\n",
    "\n",
    "theta[1,0] =  0.3 ; theta[1,1] = -1.0\n",
    "theta[2,0]= -1.0  ; theta[2,1] = 2.0\n",
    "theta[3,0] = -0.5  ; theta[3,1] = 0.65\n",
    "psi[1,0] = 0.5;  psi[1,1] = 2.0; psi[1,2] = -1.0; psi[1,3]=7.0\n",
    "psi[2,0] = -0.2;  psi[2,1] = 2.0; psi[2,2] = 1.2; psi[2,3]=-8.0\n",
    "psi[3,0] = 0.3;  psi[3,1] = -2.3; psi[3,2] = -0.8; psi[3,3]=2.0\n",
    "phi[0] = 0.0; phi[1] = 0.5; phi[2] = -1.5; phi [3] = -2.2\n",
    "\n",
    "# Define a range of input values\n",
    "x = np.arange(0,1,0.01)\n",
    "\n",
    "# Run the neural network\n",
    "y, layer2_pre_1, layer2_pre_2, layer2_pre_3, h1_prime, h2_prime, h3_prime, phi1_h1_prime, phi2_h2_prime, phi3_h3_prime \\\n",
    "    = shallow_1_1_3_3(x, ReLU, phi, psi, theta)\n",
    "\n",
    "# And then plot it\n",
    "plot_neural_two_layers(x, y, layer2_pre_1, layer2_pre_2, layer2_pre_3, h1_prime, h2_prime, h3_prime, phi1_h1_prime, phi2_h2_prime, phi3_h3_prime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GcjUUHbXf25D"
   },
   "source": [
    "To do:  To test your understanding of this, consider:\n",
    "\n",
    "1.   What would happen if we increase $\\psi_{1,0}$?\n",
    "2.   What would happen if we multiplied $\\psi_{2,0}, \\psi_{2,1}, \\psi_{2,2},  \\psi_{2,3}$ by -1?\n",
    "3.  What would happen if set $\\phi_{3}$ to -1?\n",
    "\n",
    "You can rerun the code to see if you were correct.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyPkFrjmRAUf0fxN07RC4xMI",
   "include_colab_link": true,
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}