simple_nn_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural network demo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import mnist\n",
    "import simple_nn as nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0958"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The network hasn't been trained yet. There is no reason for it having a high accuracy.\n",
    "nn.accuracy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8752"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We train the neural network. This time the accuracy should be closer to 1.\n",
    "nn.train()\n",
    "nn.accuracy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets take a random image from the test dataset and see if the network recognizes correctly the handwritten digit. The [matplotlib.pyplot](https://matplotlib.org/3.2.1/api/_as_gen/matplotlib.pyplot.html#module-matplotlib.pyplot) module is used here only to visualize the image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dpsEj8v+Q9Pt29FClr3+T9H/Zz7vt7k3Ssxr8WHdCg8c27pU0XtJWSR9Iek1SR4F6+x9JuyS9o8FgTWxTbzdo8CP6O5L6sp/b2v3eJfpqyfvG12WBIDhABwRB2IEgCDsQBGEHgiDsQBCEHQiCsANB/D/nH3fqRTxiyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label = 3\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "idx = np.random.randint(10000) # A random integer between 0 and 9999\n",
    "image = mnist.test_images()[idx]\n",
    "label = mnist.test_labels()[idx]\n",
    "plt.imshow(image, 'Greys')\n",
    "plt.show()\n",
    "print('Label =', label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets see what the output for that image is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output = [0.002 0.    0.002 0.973 0.    0.02  0.    0.    0.002 0.001]\n"
     ]
    }
   ],
   "source": [
    "x, h, ha, y, ya = nn.forward_propagation(image)\n",
    "print('Output =', ya.round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get 10 values (each between 0 and 1) for each digit in ascending order from 0 to 9. The index of the highest value is the __guessed digit__: the digit that the network considers as the most likley to be on the image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Guessed digit = 3\n"
     ]
    }
   ],
   "source": [
    "print('Guessed digit =', ya.argmax())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets build a bar chart to visulalise the output data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(idx)\n",
    "if label == ya.argmax():\n",
    "    plt.suptitle('CORRECT', color='g', fontsize=16, fontweight='bold')\n",
    "else:\n",
    "    plt.suptitle('INCORRECT', color='r', fontsize=16, fontweight='bold')\n",
    "plt.subplot(121)\n",
    "plt.imshow(image, 'Greys')\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.title('Label = ' + str(label))\n",
    "plt.subplot(122)\n",
    "plt.bar(range(10), ya)\n",
    "plt.xticks(range(10), range(10))\n",
    "plt.ylim(0, 1)\n",
    "plt.xlim(-.5, 9.5)\n",
    "plt.grid(axis='y')\n",
    "plt.xlabel('output values')\n",
    "plt.title('Guessed digit = ' + str(ya.argmax()))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward propagation\n",
    "For a given input $\\mathbf{x}$ (flattened and normalized image of 784 unicolor pixels) the output $\\mathbf{y_a}$ (10 estimations of probability for each digit) is obtained as follows:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&\\mathbf{h} = \\mathbf{x} \\cdot \\mathbf{W_1} + \\mathbf{b_1}&& (1)\n",
    "\\\\\n",
    "&\\mathbf{h_a} = S(\\mathbf{h}) = {1 \\over 1 + e^{\\mathbf{-h}}}&& (2)\n",
    "\\\\\n",
    "&\\mathbf{y} = \\mathbf{h_a} \\cdot \\mathbf{W_2} + \\mathbf{b_2}&& (3)\n",
    "\\\\\n",
    "&\\mathbf{y_a} = \\sigma(\\mathbf{y}) = {e^{\\mathbf{y}} \\over \\sum_{i=0}^{9} e^{(\\mathbf{y})_i}}&& (4)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Where\n",
    "- $\\mathbf{x} \\in [0, 1]^{784}$ is the value of the input layer (composed of 784 neurons).\n",
    "- $\\mathbf{h} \\in \\mathbb{R}^{16}$ and $\\mathbf{h_a} \\in ]0, 1[^{16}$ are the values the hidden layer (16 neurons) before and after activation by the sigmoid function $S$.\n",
    "- $\\mathbf{y} \\in \\mathbb{R}^{10}$ and $\\mathbf{y_a} \\in ]0, 1[^{10}$ are the values of the output layer (10 neurons) before and after activation by the sofmax function $\\sigma$.\n",
    "- $\\mathbf{W_1} \\in \\mathcal{M}_{784, 16}(\\mathbb{R})$ and $\\mathbf{W_2} \\in \\mathcal{M}_{16, 10}(\\mathbb{R})$ are the weight matrices.\n",
    "- $\\mathbf{b_1} \\in \\mathbb{R}^{16}$  and $\\mathbf{b_2} \\in \\mathbb{R}^{10}$ are the bias terms.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loss function\n",
    "The cross entropy loss function $L$ is used to update the weights and biases of the network. It is calculated using the output $\\mathbf{y_a}$ and the target $\\mathbf{t}$ (a one hot vector obtained from the $label \\in \\left\\{0,1,...,9 \\right\\}$ of the input image).\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "L(\\mathbf{t},\\mathbf{y_a}) &= -\\sum_{i=0}^9 (\\mathbf{t})_i \\cdot \\log (\\mathbf{y_a})_i&& \n",
    "\\\\ & = - \\log (\\mathbf{y_a})_{label}&& (5)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backpropagation\n",
    "\n",
    "In order to update each of the learnable parameters (weights and biases) we need to calculate the gradient $\\nabla L$ of the loss function:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\nabla L = \n",
    "\\begin{bmatrix}\n",
    "\\partial L \\over \\partial \\mathbf{b_1}\n",
    "\\\\ \n",
    "\\partial L \\over \\partial \\mathbf{W_1}\n",
    "\\\\\n",
    "\\partial L \\over \\partial \\mathbf{b_2}\n",
    "\\\\ \n",
    "\\partial L \\over \\partial \\mathbf{W_2}\n",
    "\\end{bmatrix}\n",
    "&& (6)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Before we start, here is a quick reminder of the derivative of the sofmax function $\\sigma$:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "{\\partial \\sigma \\over \\partial (\\mathbf{y})_i} (\\mathbf{y})_{label} = \n",
    "\\begin{cases} \n",
    "(\\mathbf{y_a})_{label} \\cdot (1 - (\\mathbf{y_a})_{label}) &\\mbox{if } i = label\n",
    "\\\\ \n",
    "(\\mathbf{y_a})_{label} \\cdot (\\mathbf{y_a})_{i} &\\mbox{else}\n",
    "\\end{cases} && (7)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Let's calculate the derivatives with respect to each learning parameters of the network: $\\partial L \\over \\partial \\mathbf{b_2}$, $\\partial L \\over \\partial \\mathbf{W_2}$, $\\partial L \\over \\partial \\mathbf{b_1}$ and $\\partial L \\over \\partial \\mathbf{W_1}$.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "{\\partial L \\over \\partial \\mathbf{b_2}}\n",
    "&= {\\partial L \\over \\partial \\mathbf{y_a}} \\cdot {\\partial \\mathbf{y_a} \\over \\partial \\mathbf{y}} \\cdot {\\partial \\mathbf{y} \\over \\partial \\mathbf{b_2}}\n",
    "\\\\\n",
    "&= {- 1 \\over (\\mathbf{y_a})_{label}} \\cdot {\\partial \\sigma \\over \\partial \\mathbf{y}}(\\mathbf{y})_{label}\n",
    "\\\\\n",
    "&= \\mathbf{y_a} - \\mathbf{t} && (8)\n",
    "\\\\\n",
    "\\\\\n",
    "{\\partial L \\over \\partial \\mathbf{W_2}} \n",
    "&= {\\partial L \\over \\partial \\mathbf{y}} \\cdot {\\partial \\mathbf{y} \\over \\partial \\mathbf{W_2}}\n",
    "\\\\\n",
    "&= \\mathbf{h_a}^T {\\partial L \\over \\partial \\mathbf{b_2}} && (9)\n",
    "\\\\\n",
    "\\\\\n",
    "{\\partial L \\over \\partial \\mathbf{b_1}} \n",
    "&= {\\partial L \\over \\partial \\mathbf{h_a}} \\cdot {\\partial \\mathbf{h_a} \\over \\partial \\mathbf{b_1}}\n",
    "\\\\\n",
    "&= \\mathbf{W_2} ({\\partial L \\over \\partial \\mathbf{b_2}})^T \\cdot {\\partial S \\over \\partial \\mathbf{h}} (\\mathbf{h})\n",
    "\\\\\n",
    "&= \\mathbf{W_2} ({\\partial L \\over \\partial \\mathbf{b_2}})^T \\cdot \\mathbf{h_a} \\cdot (1 - \\mathbf{h_a}) && (10)\n",
    "\\\\\n",
    "\\\\\n",
    "{\\partial L \\over \\partial \\mathbf{W_1}}\n",
    "&= {\\partial L \\over \\partial \\mathbf{h}} \\cdot {\\partial \\mathbf{h} \\over \\partial \\mathbf{W_1}}\n",
    "\\\\\n",
    "&= \\mathbf{x}^T {\\partial L \\over \\partial \\mathbf{b_1}} &&(11)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Where $^T$ is the transpose operator. In our case for a any vector ${\\mathbf v}^T$ is a column vector.\n",
    "\n",
    "Note that ${\\partial \\mathbf{y} \\over \\partial \\mathbf{b_2}} = \\mathbf{1}_{\\mathbb{R}^{10}}$ \n",
    "and ${\\partial \\mathbf{h} \\over \\partial \\mathbf{b_1}} = \\mathbf{1}_{\\mathbb{R}^{16}}$, \n",
    "so ${\\partial \\mathbf{y_a} \\over \\partial \\mathbf{b_2}} = {\\partial \\mathbf{y_a} \\over \\partial \\mathbf{y}}$ \n",
    "and ${\\partial \\mathbf{h_a} \\over \\partial \\mathbf{b_1}} = {\\partial \\mathbf{h_a} \\over \\partial \\mathbf{h}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n_examples = 10\n",
    "image_ids = np.random.permutation(np.arange(10000))[:n_examples] # Random numbers between 0 and 9999\n",
    "\n",
    "for id in image_ids:\n",
    "    image = nn.test_images[id]\n",
    "    label = nn.test_labels[id]\n",
    "    x, h, ha, y, ya = nn.forward_propagation(image)\n",
    "    plt.figure(id)\n",
    "    if label == ya.argmax():\n",
    "        plt.suptitle('CORRECT', color='g', fontsize=16, fontweight='bold')\n",
    "    else:\n",
    "        plt.suptitle('INCORRECT', color='r', fontsize=16, fontweight='bold')\n",
    "    plt.subplot(121)\n",
    "    plt.imshow(image, 'Greys')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.title('Label = ' + str(label))\n",
    "    plt.subplot(122)\n",
    "    plt.bar(range(10), ya)\n",
    "    plt.xticks(range(10), range(10))\n",
    "    plt.ylim(0, 1)\n",
    "    plt.xlim(-.5, 9.5)\n",
    "    plt.grid(axis='y')\n",
    "    plt.xlabel('output values')\n",
    "    plt.title('Guessed digit = ' + str(ya.argmax()))\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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