marcospgp/backpropagation-from-scratch.ipynb

## backpropagation-from-scratch.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "backpropagation-from-scratch.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyOKZgNOYvWf6UcwNMEXHseB",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/marcospgp/backpropagation-from-scratch/blob/master/backpropagation-from-scratch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CKRRjmhbFcx7",
        "colab_type": "text"
      },
      "source": [
        "# Loading MNIST dataset from Keras\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kjvPSnDA4J_w",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "f0d75622-d005-4b0d-f4e1-560d5d2d9f34"
      },
      "source": [
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data(path=\"mnist.npz\")\n",
        "\n",
        "plt.imshow(x_train[0],cmap='gray');"
      ],
      "execution_count": 178,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Klx9qPmxF9jI",
        "colab_type": "text"
      },
      "source": [
        "# Utility functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sdyvaUKoF7ux",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "def sigmoid(x):\n",
        "  # Numerically stable sigmoid function based on\n",
        "  # http://timvieira.github.io/blog/post/2014/02/11/exp-normalize-trick/\n",
        "  \n",
        "  x = np.clip(x, -500, 500) # We get an overflow warning without this\n",
        "  \n",
        "  return np.where(\n",
        "    x >= 0,\n",
        "    1 / (1 + np.exp(-x)),\n",
        "    np.exp(x) / (1 + np.exp(x))\n",
        "  )\n",
        "\n",
        "def dsigmoid(x): # Derivative of sigmoid\n",
        "  return sigmoid(x) * (1 - sigmoid(x))\n",
        "\n",
        "def softmax(x):\n",
        "  # Numerically stable softmax based on (same source as sigmoid)\n",
        "  # http://timvieira.github.io/blog/post/2014/02/11/exp-normalize-trick/\n",
        "  b = x.max()\n",
        "  y = np.exp(x - b)\n",
        "  return y / y.sum()\n",
        "\n",
        "def cross_entropy_loss(y, yHat):\n",
        "  return -np.sum(y * np.log(yHat))\n",
        "\n",
        "def integer_to_one_hot(x, max):\n",
        "  # x: integer to convert to one hot encoding\n",
        "  # max: the size of the one hot encoded array\n",
        "  result = np.zeros(10)\n",
        "  result[x] = 1\n",
        "  return result"
      ],
      "execution_count": 179,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_xIZEupTHyNM",
        "colab_type": "text"
      },
      "source": [
        "# Initialize architecture, weights, and biases"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zBeGvbu6FaM_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 865
        },
        "outputId": "af98eda1-651f-4d66-ebad-4f4885cd0c8d"
      },
      "source": [
        "import math\n",
        "\n",
        "# Initialize weights of each layer with a normal distribution of mean 0 and\n",
        "# standard deviation 1/sqrt(n), where n is the number of inputs.\n",
        "# This means the weighted input will be a random variable itself with mean\n",
        "# 0 and standard deviation close to 1 (if biases are initialized as 0, standard\n",
        "# deviation will be exactly 1)\n",
        "\n",
        "from numpy.random import default_rng\n",
        "\n",
        "rng = default_rng(80085)\n",
        "\n",
        "# Neural network layer sizes: 784 -> 32 -> 32 -> 10\n",
        "\n",
        "weights = [\n",
        "  rng.normal(0, 1/math.sqrt(784), (32, 784)),\n",
        "  rng.normal(0, 1/math.sqrt(32), (32, 32)),\n",
        "  rng.normal(0, 1/math.sqrt(32), (10, 32))\n",
        "]\n",
        "\n",
        "biases = [np.zeros(32), np.zeros(32), np.zeros(10)]\n",
        "\n",
        "# Plot histogram of layer weights to check probability distribution\n",
        "\n",
        "print(\"Weight distribution per layer:\")\n",
        "for index, layer in enumerate(weights):\n",
        "  plt.figure()\n",
        "  plt.suptitle(\n",
        "    \"Layer \" + str(index + 1) + \" with \" + str(layer.shape[0]) +\n",
        "    \" neurons, \" + str(layer.shape[1]) + \" inputs each (\" + str(layer.size) +\n",
        "    \" weights in total)\"\n",
        "  )\n",
        "  plt.hist(layer.flatten(), bins=100);\n"
      ],
      "execution_count": 180,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Weight distribution per layer:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IafUGD_VGeLh",
        "colab_type": "text"
      },
      "source": [
        "# Feed forward\n",
        "\n",
        "Feed forward once before training to check accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cd6jGroQGdOF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 134
        },
        "outputId": "c059fa47-5c37-442c-8207-9412d7be7eca"
      },
      "source": [
        "def feed_forward_sample(sample, y):\n",
        "  \"\"\" Feeds a sample forward through the neural network.\n",
        "    Parameters:\n",
        "      sample: 1D numpy array. The input sample (an MNIST digit).\n",
        "      label: An integer from 0 to 9.\n",
        "\n",
        "    Returns: The cross entropy loss.\n",
        "  \"\"\"\n",
        "  a = sample.flatten()\n",
        "\n",
        "  for index, w in enumerate(weights):\n",
        "    z = np.matmul(w, a) + biases[index]\n",
        "    if index < len(weights) - 1:\n",
        "      a = sigmoid(z)\n",
        "    else:\n",
        "      a = softmax(z)\n",
        "\n",
        "  # Calculate loss\n",
        "  one_hot_y = integer_to_one_hot(y, 10)\n",
        "  loss = cross_entropy_loss(one_hot_y, a)\n",
        "\n",
        "  # Convert activations to one hot encoded guess\n",
        "  one_hot_guess = np.zeros_like(a)\n",
        "  one_hot_guess[np.argmax(a)] = 1\n",
        "  \n",
        "  return loss, one_hot_guess\n",
        "\n",
        "\n",
        "# Feedforward all training samples\n",
        "def feed_forward_dataset(x, y):\n",
        "  losses = np.empty(x.shape[0])\n",
        "  one_hot_guesses = np.empty((x.shape[0], 10))\n",
        "\n",
        "  for i in range(x.shape[0]):\n",
        "    if i == 0 or ((i + 1) % 10000 == 0):\n",
        "      print(i + 1, \"/\", x.shape[0], \"(\", format(((i + 1) / x.shape[0]) * 100, \".2f\"), \"%)\")\n",
        "    losses[i], one_hot_guesses[i] = feed_forward(x[i], y[i])\n",
        "\n",
        "  print(\"\\nAverage loss:\", np.round(np.average(losses), decimals=2))\n",
        "\n",
        "  y_one_hot = np.zeros((y.size, 10))\n",
        "  y_one_hot[np.arange(y.size), y] = 1\n",
        "\n",
        "  # Expected correct guesses 6 000/60 000, assuming perfect randomness\n",
        "  correct_guesses = np.sum(y_one_hot * one_hot_guesses)\n",
        "  correct_guess_percent = format((correct_guesses / y.shape[0]) * 100, \".2f\")\n",
        "  print(\"Accuracy (# of correct guesses):\", correct_guesses, \"/\", y.shape[0], \"(\", correct_guess_percent, \"%)\")\n",
        "\n",
        "def feed_forward_training_data():\n",
        "  print(\"Feeding forward all training data...\")\n",
        "  feed_forward_dataset(x_train, y_train)\n",
        "  print(\"\")\n",
        "\n",
        "def feed_forward_test_data():\n",
        "  print(\"Feeding forward all test data...\")\n",
        "  feed_forward_dataset(x_test, y_test)\n",
        "  print(\"\")\n",
        "\n",
        "feed_forward_test_data()"
      ],
      "execution_count": 181,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Feeding forward all test data...\n",
            "1 / 10000 ( 0.01 %)\n",
            "10000 / 10000 ( 100.00 %)\n",
            "\n",
            "Average loss: 2.36\n",
            "Accuracy (# of correct guesses): 994.0 / 10000 ( 9.94 %)\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sSrlc2VLOi8L",
        "colab_type": "text"
      },
      "source": [
        "# Training\n",
        "\n",
        "1.   Feedforward one sample, storing layer activations\n",
        "2.   Calculate gradient\n",
        "3.   Update weights & biases according to learning rate\n",
        "4.   Repeat\n",
        "\n",
        "More details about this implementation [here](https://www.mathcha.io/editor/vrmV3C1KFnvu2Dx3ewh7rgr54fBOvJL2TzoNWNe)\n",
        "\n",
        "The maximum accuracy reached was ~85%, after training for a few epochs. The network then starts to overfit.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BLLEsVdcOgzi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 991
        },
        "outputId": "4dd03490-34a4-4646-8a16-733f72601816"
      },
      "source": [
        "def train_one_sample(sample, y, learning_rate=0.003):\n",
        "  a = sample.flatten()\n",
        "\n",
        "  # We will store each layer's activations to calculate gradient\n",
        "  activations = []\n",
        "\n",
        "  # Feedforward\n",
        "  for i, w in enumerate(weights): # Each w is a layer's 2D weight matrix\n",
        "    z = np.matmul(w, a) + biases[i]\n",
        "    if (i < len(weights) - 1):\n",
        "      a = sigmoid(z)\n",
        "    else:  \n",
        "      a = softmax(z) # softmax on last layer\n",
        "    activations.append(a)\n",
        "\n",
        "  # Calculate loss\n",
        "  one_hot_y = integer_to_one_hot(y, 10)\n",
        "  loss = cross_entropy_loss(one_hot_y, a)\n",
        "\n",
        "  # Convert last layer's activations to one hot encoded guess\n",
        "  one_hot_guess = np.zeros_like(a)\n",
        "  one_hot_guess[np.argmax(a)] = 1\n",
        "\n",
        "  # Check whether guess was correct\n",
        "  correct_guess = (np.sum(one_hot_y * one_hot_guess) == 1)\n",
        "\n",
        "  weight_gradients = [None] * len(weights)\n",
        "  bias_gradients = [None] * len(weights)\n",
        "  activation_gradients = [None] * (len(weights) - 1)\n",
        "  \n",
        "  # Backpropagation\n",
        "  for i in range(len(weights) - 1, -1, -1): # Traverse layers in reverse\n",
        "    last_layer = i == len(weights) - 1\n",
        "    second_to_last_layer = i == len(weights) - 2\n",
        "\n",
        "    if last_layer:\n",
        "      # Gather all needed variables, making vectors vertical\n",
        "      y = one_hot_y[:, np.newaxis]\n",
        "      a = activations[i][:, np.newaxis]\n",
        "      a_prev = activations[i-1][:, np.newaxis]\n",
        "\n",
        "      weight_gradients[i] = np.matmul((a - y), a_prev.T)\n",
        "      bias_gradients[i] = a - y\n",
        "\n",
        "    else:\n",
        "      # Gather all needed variables, making vectors vertical\n",
        "      w_next = weights[i+1]\n",
        "      a_next = activations[i + 1][:, np.newaxis]\n",
        "      y = one_hot_y[:, np.newaxis]\n",
        "      a = activations[i][:, np.newaxis]\n",
        "      if i > 0:\n",
        "        a_prev = activations[i-1][:, np.newaxis]\n",
        "      else:\n",
        "        # Previous activation is the sample itself\n",
        "        a_prev = sample.flatten()[:, np.newaxis]\n",
        "\n",
        "      # Activation gradient\n",
        "      if second_to_last_layer:\n",
        "        dCda = np.matmul(w_next.T, (a_next - y))\n",
        "        activation_gradients[i] = dCda\n",
        "      else:\n",
        "        dCda_next = activation_gradients[i+1]\n",
        "        dCda = np.matmul(w_next.T, (dsigmoid(a_next) * dCda_next))\n",
        "        activation_gradients[i] = dCda\n",
        "\n",
        "      # Weights & biases gradients\n",
        "      x = dsigmoid(a) * dCda\n",
        "      weight_gradients[i] = np.matmul(x, a_prev.T)\n",
        "      bias_gradients[i] = x\n",
        "\n",
        "    # Update weights & biases based on gradient\n",
        "    weights[i] -= weight_gradients[i] * learning_rate\n",
        "    biases[i] -= bias_gradients[i].flatten() * learning_rate\n",
        "\n",
        "def train_one_epoch(learning_rate=0.003):\n",
        "  print(\"Training for one epoch over the training dataset...\")\n",
        "  for i in range(x_train.shape[0]):\n",
        "    if i == 0 or ((i + 1) % 10000 == 0):\n",
        "      completion_percent = format(((i + 1) / x_train.shape[0]) * 100, \".2f\")\n",
        "      print(i + 1, \"/\", x_train.shape[0], \"(\", completion_percent, \"%)\")\n",
        "    train_one_sample(x_train[i], y_train[i], learning_rate)\n",
        "  print(\"Finished training.\\n\")\n",
        "\n",
        "# Train and check accuracy before & after each epoch\n",
        "\n",
        "feed_forward_test_data()\n",
        "\n",
        "def test_and_train():\n",
        "  train_one_epoch()\n",
        "  feed_forward_test_data()\n",
        "\n",
        "for i in range(3): # Adjust number of epochs here\n",
        "  test_and_train()"
      ],
      "execution_count": 182,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Feeding forward all test data...\n",
            "1 / 10000 ( 0.01 %)\n",
            "10000 / 10000 ( 100.00 %)\n",
            "\n",
            "Average loss: 2.36\n",
            "Accuracy (# of correct guesses): 994.0 / 10000 ( 9.94 %)\n",
            "\n",
            "Training for one epoch over the training dataset...\n",
            "1 / 60000 ( 0.00 %)\n",
            "10000 / 60000 ( 16.67 %)\n",
            "20000 / 60000 ( 33.33 %)\n",
            "30000 / 60000 ( 50.00 %)\n",
            "40000 / 60000 ( 66.67 %)\n",
            "50000 / 60000 ( 83.33 %)\n",
            "60000 / 60000 ( 100.00 %)\n",
            "Finished training.\n",
            "\n",
            "Feeding forward all test data...\n",
            "1 / 10000 ( 0.01 %)\n",
            "10000 / 10000 ( 100.00 %)\n",
            "\n",
            "Average loss: 0.63\n",
            "Accuracy (# of correct guesses): 8023.0 / 10000 ( 80.23 %)\n",
            "\n",
            "Training for one epoch over the training dataset...\n",
            "1 / 60000 ( 0.00 %)\n",
            "10000 / 60000 ( 16.67 %)\n",
            "20000 / 60000 ( 33.33 %)\n",
            "30000 / 60000 ( 50.00 %)\n",
            "40000 / 60000 ( 66.67 %)\n",
            "50000 / 60000 ( 83.33 %)\n",
            "60000 / 60000 ( 100.00 %)\n",
            "Finished training.\n",
            "\n",
            "Feeding forward all test data...\n",
            "1 / 10000 ( 0.01 %)\n",
            "10000 / 10000 ( 100.00 %)\n",
            "\n",
            "Average loss: 0.51\n",
            "Accuracy (# of correct guesses): 8481.0 / 10000 ( 84.81 %)\n",
            "\n",
            "Training for one epoch over the training dataset...\n",
            "1 / 60000 ( 0.00 %)\n",
            "10000 / 60000 ( 16.67 %)\n",
            "20000 / 60000 ( 33.33 %)\n",
            "30000 / 60000 ( 50.00 %)\n",
            "40000 / 60000 ( 66.67 %)\n",
            "50000 / 60000 ( 83.33 %)\n",
            "60000 / 60000 ( 100.00 %)\n",
            "Finished training.\n",
            "\n",
            "Feeding forward all test data...\n",
            "1 / 10000 ( 0.01 %)\n",
            "10000 / 10000 ( 100.00 %)\n",
            "\n",
            "Average loss: 0.49\n",
            "Accuracy (# of correct guesses): 8563.0 / 10000 ( 85.63 %)\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}