chapter02_mathematical-building-blocks.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bertramwooster/deep-learning-with-python-notebooks/blob/master/chapter02_mathematical-building-blocks.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xoXMjXCVDFyh"
      },
      "source": [
        "This is a companion notebook for the book [Deep Learning with Python, Second Edition](https://www.manning.com/books/deep-learning-with-python-second-edition?a_aid=keras&a_bid=76564dff). For readability, it only contains runnable code blocks and section titles, and omits everything else in the book: text paragraphs, figures, and pseudocode.\n",
        "\n",
        "**If you want to be able to follow what's going on, I recommend reading the notebook side by side with your copy of the book.**\n",
        "\n",
        "This notebook was generated for TensorFlow 2.6."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-uhOFIkMDFyp"
      },
      "source": [
        "# The mathematical building blocks of neural networks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6YC-FJT8DFyr"
      },
      "source": [
        "## A first look at a neural network"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AVVcZ2p0DFyr"
      },
      "source": [
        "**Loading the MNIST dataset in Keras**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "DlQ9PRpmnkFX",
        "outputId": "791c1b6a-473f-4f29-cb62-561cc1503228",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tried again on VSC\n",
            "hell yea on colab\n"
          ]
        }
      ],
      "source": [
        "# now testing with VS Code\n",
        "# and Colab too\n",
        "print('tried again on VSC')\n",
        "print('hell yea on colab')\n",
        "# tried again on colab"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5ksxb6aSwSw6",
        "outputId": "c703081b-a49c-476f-feea-ed140752256b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Num GPUs Available:  1\n"
          ]
        }
      ],
      "source": [
        "import tensorflow as tf\n",
        "print(\"Num GPUs Available: \", len(tf.config.list_physical_devices('GPU')))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hifhmmRMDFys",
        "outputId": "4a82e3c1-bdb6-445f-cbe1-39d35171e307"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "\u001b[1m11490434/11490434\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 0us/step\n"
          ]
        }
      ],
      "source": [
        "# I am testing GitHub with Colab\n",
        "#vnow with VS Code\n",
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "lIb_4Mo7DFyu",
        "outputId": "726c82a3-bf33-4f7e-c485-95cc67c71f1d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "train_images.shape\n",
        "# pplot\n",
        "xx = train_images.reshape(-1)# converts to 1D\n",
        "from matplotlib import pyplot as plt\n",
        "plt.hist([k for k in xx if (k>25 and k<200)], histtype='stepfilled');\n",
        "#xx.max#()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 501
        },
        "id": "ylQn7sQBDFyv",
        "outputId": "10c37ee7-d23d-491a-ba36-a56d53957a4b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.10968519, 0.12485185, 0.11033333, 0.11353704, 0.10818519,\n",
              "        0.10038889, 0.10959259, 0.11601852, 0.10835185, 0.11016667]),\n",
              " array([0. , 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3, 7.2, 8.1, 9. ]),\n",
              " <BarContainer object of 10 artists>)"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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qPh0dHUHrJamoqCiw3ufz6eWXX9Y3vvENFRUVafbs2crLy9POnTvPOcfQ0JC8Xm/QAwAATF4hBcvAwIBGRkZktVqDtlutVrlcrlH3cblc513f19enTz75RBs3btStt96qv/zlL7rzzjv1ve99T/v27Rv1mA6HQxaLJfBITk4O5TQAAMAEE/Z3Cfl8PknSd7/7XT344IPKzMxUVVWVbr/99sBLRv9fdXW1PB5P4NHb23spRwYAAJfYtFAWJyQkKCoqSm63O2i72+1WYmLiqPskJiaed31CQoKmTZumhQsXBq25/vrr9eabb456zJiYGMXExIQyOgAAmMBCusISHR2trKwsOZ3OwDafzyen06n8/PxR98nPzw9aL0nt7e2B9dHR0crJydGxY8eC1hw/flxXX311KOMBAIBJKqQrLJJkt9tVXl6u7Oxs5ebmqq6uToODg6qoqJAklZWVac6cOXI4HJKkyspKFRYWavPmzSouLlZLS4sOHTqkpqamwDHXrl2r0tJSLV26VN/61rfU1taml156SXv37h2fswQAABNayMFSWlqq/v5+1dTUyOVyKTMzU21tbYEba3t6ehQZ+cWFm4KCAjU3N2v9+vVat26dFixYoJ07dyotLS2w5s4771RjY6McDoceeOABXXfddXrhhRd08803j8MpAgCAiS7kz2ExEZ/DAgDAxTWhPocFAAAgHAgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPHGFCwNDQ1KSUlRbGys8vLy1NnZed7127dvV2pqqmJjY5Wenq49e/acc+3999+viIgI1dXVjWU0AAAwCYUcLK2trbLb7aqtrVV3d7cyMjJUVFSkvr6+Udfv379fy5cv14oVK3T48GGVlJSopKRER48ePWvtjh07dODAASUlJYV+JgAAYNIKOVi2bNmi++67TxUVFVq4cKEaGxt12WWX6emnnx51/VNPPaVbb71Va9eu1fXXX69HHnlEN910k+rr64PWnTx5UqtXr9bzzz+v6dOnj+1sAADApBRSsAwPD6urq0s2m+2LA0RGymazqaOjY9R9Ojo6gtZLUlFRUdB6n8+ne++9V2vXrtUNN9wQykgAAGAKmBbK4oGBAY2MjMhqtQZtt1qtev/990fdx+Vyjbre5XIFvn7iiSc0bdo0PfDAAxc0x9DQkIaGhgJfe73eCz0FAAAwAYX9XUJdXV166qmn9OyzzyoiIuKC9nE4HLJYLIFHcnLyRZ4SAACEU0jBkpCQoKioKLnd7qDtbrdbiYmJo+6TmJh43vVvvPGG+vr6NG/ePE2bNk3Tpk3TiRMn9NBDDyklJWXUY1ZXV8vj8QQevb29oZwGAACYYEIKlujoaGVlZcnpdAa2+Xw+OZ1O5efnj7pPfn5+0HpJam9vD6y/99579fbbb+vIkSOBR1JSktauXas///nPox4zJiZG8fHxQQ8AADB5hXQPiyTZ7XaVl5crOztbubm5qqur0+DgoCoqKiRJZWVlmjNnjhwOhySpsrJShYWF2rx5s4qLi9XS0qJDhw6pqalJkjRr1izNmjUr6GdMnz5diYmJuu66677q+QEAgEkg5GApLS1Vf3+/ampq5HK5lJmZqba2tsCNtT09PYqM/OLCTUFBgZqbm7V+/XqtW7dOCxYs0M6dO5WWljZ+ZwEAACa1CL/f7w/3EF+V1+uVxWKRx+O5KC8PpVS9PO7HBABgIvlwY/G4HzOU399hf5cQAADAlyFYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPHGFCwNDQ1KSUlRbGys8vLy1NnZed7127dvV2pqqmJjY5Wenq49e/YEvnfmzBk9/PDDSk9P14wZM5SUlKSysjKdOnVqLKMBAIBJKORgaW1tld1uV21trbq7u5WRkaGioiL19fWNun7//v1avny5VqxYocOHD6ukpEQlJSU6evSoJOn06dPq7u7Whg0b1N3drT/+8Y86duyY7rjjjq92ZgAAYNKI8Pv9/lB2yMvLU05Ojurr6yVJPp9PycnJWr16taqqqs5aX1paqsHBQe3evTuwbfHixcrMzFRjY+OoP+PgwYPKzc3ViRMnNG/evC+dyev1ymKxyOPxKD4+PpTTuSApVS+P+zEBAJhIPtxYPO7HDOX3d0hXWIaHh9XV1SWbzfbFASIjZbPZ1NHRMeo+HR0dQeslqaio6JzrJcnj8SgiIkJXXHHFqN8fGhqS1+sNegAAgMkrpGAZGBjQyMiIrFZr0Har1SqXyzXqPi6XK6T1n376qR5++GEtX778nLXlcDhksVgCj+Tk5FBOAwAATDBGvUvozJkzuvvuu+X3+7Vt27ZzrquurpbH4wk8ent7L+GUAADgUpsWyuKEhARFRUXJ7XYHbXe73UpMTBx1n8TExAta/3msnDhxQq+++up5X8uKiYlRTExMKKMDAIAJLKQrLNHR0crKypLT6Qxs8/l8cjqdys/PH3Wf/Pz8oPWS1N7eHrT+81j54IMP9Morr2jWrFmhjAUAACa5kK6wSJLdbld5ebmys7OVm5ururo6DQ4OqqKiQpJUVlamOXPmyOFwSJIqKytVWFiozZs3q7i4WC0tLTp06JCampokfRYr3//+99Xd3a3du3drZGQkcH/LlVdeqejo6PE6VwAAMEGFHCylpaXq7+9XTU2NXC6XMjMz1dbWFrixtqenR5GRX1y4KSgoUHNzs9avX69169ZpwYIF2rlzp9LS0iRJJ0+e1K5duyRJmZmZQT/rtdde0ze/+c0xnhoAAJgsQv4cFhPxOSwAAFxcE+pzWAAAAMKBYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYj2ABAADGI1gAAIDxCBYAAGA8ggUAABiPYAEAAMYjWAAAgPEIFgAAYDyCBQAAGI9gAQAAxiNYAACA8QgWAABgPIIFAAAYb0zB0tDQoJSUFMXGxiovL0+dnZ3nXb99+3alpqYqNjZW6enp2rNnT9D3/X6/ampqdNVVVykuLk42m00ffPDBWEYDAACTUMjB0traKrvdrtraWnV3dysjI0NFRUXq6+sbdf3+/fu1fPlyrVixQocPH1ZJSYlKSkp09OjRwJonn3xSv/zlL9XY2Ki33npLM2bMUFFRkT799NOxnxkAAJg0Ivx+vz+UHfLy8pSTk6P6+npJks/nU3JyslavXq2qqqqz1peWlmpwcFC7d+8ObFu8eLEyMzPV2Ngov9+vpKQkPfTQQ/rpT38qSfJ4PLJarXr22We1bNmyL53J6/XKYrHI4/EoPj4+lNO5IClVL4/7MQEAmEg+3Fg87scM5ff3tFAOPDw8rK6uLlVXVwe2RUZGymazqaOjY9R9Ojo6ZLfbg7YVFRVp586dkqR//etfcrlcstlsge9bLBbl5eWpo6Nj1GAZGhrS0NBQ4GuPxyPpsxO/GHxDpy/KcQEAmCguxu/Yz495IddOQgqWgYEBjYyMyGq1Bm23Wq16//33R93H5XKNut7lcgW+//m2c635/xwOh/7nf/7nrO3JyckXdiIAACAklrqLd+yPP/5YFovlvGtCChZTVFdXB1218fl8+uijjzRr1ixFRESM68/yer1KTk5Wb2/vRXm5CaHh+TALz4d5eE7MwvNxfn6/Xx9//LGSkpK+dG1IwZKQkKCoqCi53e6g7W63W4mJiaPuk5iYeN71n/+n2+3WVVddFbQmMzNz1GPGxMQoJiYmaNsVV1wRyqmELD4+nn/ZDMLzYRaeD/PwnJiF5+PcvuzKyudCepdQdHS0srKy5HQ6A9t8Pp+cTqfy8/NH3Sc/Pz9ovSS1t7cH1s+fP1+JiYlBa7xer956661zHhMAAEwtIb8kZLfbVV5eruzsbOXm5qqurk6Dg4OqqKiQJJWVlWnOnDlyOBySpMrKShUWFmrz5s0qLi5WS0uLDh06pKamJklSRESE1qxZo0cffVQLFizQ/PnztWHDBiUlJamkpGT8zhQAAExYIQdLaWmp+vv7VVNTI5fLpczMTLW1tQVumu3p6VFk5BcXbgoKCtTc3Kz169dr3bp1WrBggXbu3Km0tLTAmp/97GcaHBzUT37yE/3nP//RzTffrLa2NsXGxo7DKX41MTExqq2tPeslKIQHz4dZeD7Mw3NiFp6P8RPy57AAAABcavwtIQAAYDyCBQAAGI9gAQAAxiNYAACA8QiWL9HQ0KCUlBTFxsYqLy9PnZ2d4R5pSnI4HMrJydHMmTM1e/ZslZSU6NixY+EeC/9n48aNgY8oQHicPHlSP/zhDzVr1izFxcUpPT1dhw4dCvdYU9LIyIg2bNig+fPnKy4uTl//+tf1yCOPXNDfy8G5ESzn0draKrvdrtraWnV3dysjI0NFRUXq6+sL92hTzr59+7Ry5UodOHBA7e3tOnPmjG655RYNDg6Ge7Qp7+DBg/r1r3+tG2+8MdyjTFn//ve/tWTJEk2fPl1/+tOf9O6772rz5s362te+Fu7RpqQnnnhC27ZtU319vd577z098cQTevLJJ7V169Zwjzah8bbm88jLy1NOTo7q6+slffapvsnJyVq9erWqqqrCPN3U1t/fr9mzZ2vfvn1aunRpuMeZsj755BPddNNN+tWvfqVHH31UmZmZqqurC/dYU05VVZX++te/6o033gj3KJB0++23y2q16re//W1g21133aW4uDg999xzYZxsYuMKyzkMDw+rq6tLNpstsC0yMlI2m00dHR1hnAyS5PF4JElXXnllmCeZ2lauXKni4uKg/57g0tu1a5eys7P1gx/8QLNnz9aiRYv0m9/8JtxjTVkFBQVyOp06fvy4JOlvf/ub3nzzTd12221hnmxim5B/rflSGBgY0MjISOATfD9ntVr1/vvvh2kqSJ9d6VqzZo2WLFkS9InJuLRaWlrU3d2tgwcPhnuUKe+f//yntm3bJrvdrnXr1ungwYN64IEHFB0drfLy8nCPN+VUVVXJ6/UqNTVVUVFRGhkZ0WOPPaZ77rkn3KNNaAQLJpyVK1fq6NGjevPNN8M9ypTV29uryspKtbe3G/EnNKY6n8+n7OxsPf7445KkRYsW6ejRo2psbCRYwuAPf/iDnn/+eTU3N+uGG27QkSNHtGbNGiUlJfF8fAUEyzkkJCQoKipKbrc7aLvb7VZiYmKYpsKqVau0e/duvf7665o7d264x5myurq61NfXp5tuuimwbWRkRK+//rrq6+s1NDSkqKioME44tVx11VVauHBh0Lbrr79eL7zwQpgmmtrWrl2rqqoqLVu2TJKUnp6uEydOyOFwECxfAfewnEN0dLSysrLkdDoD23w+n5xOp/Lz88M42dTk9/u1atUq7dixQ6+++qrmz58f7pGmtG9/+9v6+9//riNHjgQe2dnZuueee3TkyBFi5RJbsmTJWW/zP378uK6++uowTTS1nT59OuiPAEtSVFSUfD5fmCaaHLjCch52u13l5eXKzs5Wbm6u6urqNDg4qIqKinCPNuWsXLlSzc3NevHFFzVz5ky5XC5JksViUVxcXJinm3pmzpx51v1DM2bM0KxZs7ivKAwefPBBFRQU6PHHH9fdd9+tzs5ONTU1qampKdyjTUnf+c539Nhjj2nevHm64YYbdPjwYW3ZskU//vGPwz3axObHeW3dutU/b948f3R0tD83N9d/4MCBcI80JUka9fHMM8+EezT8n8LCQn9lZWW4x5iyXnrpJX9aWpo/JibGn5qa6m9qagr3SFOW1+v1V1ZW+ufNm+ePjY31X3PNNf6f//zn/qGhoXCPNqHxOSwAAMB43MMCAACMR7AAAADjESwAAMB4BAsAADAewQIAAIxHsAAAAOMRLAAAwHgECwAAMB7BAgAAjEewAAAA4xEsAADAeAQLAAAw3v8COk3+Vxw7QGsAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "len(train_labels)\n",
        "#from matplotlib import pyplot as plt\n",
        "plt.hist(train_labels, density = True, bins = 10, histtype='barstacked')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "zitMnpF_DFyv",
        "outputId": "691211fc-46eb-4df2-c6d7-2b926e842d30",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5, 0, 4, ..., 5, 6, 8], dtype=uint8)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "train_labels"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "YbrHBi21DFyw",
        "outputId": "dd79767b-816b-4c76-917a-bc38ebd63c0c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "test_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "5C6P_dQ5DFyw",
        "outputId": "52a7097d-fa0d-4e06-bf43-83e0c10bf334",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10000"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "len(test_labels)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "GnGkVegnDFyx",
        "outputId": "176c2b9f-bf27-4b75-ecda-484a9f34bef1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000,)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "test_labels.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "afJnkITuDFyx"
      },
      "source": [
        "**The network architecture**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "l-8UeitUDFyy"
      },
      "outputs": [],
      "source": [
        "from tensorflow import keras\n",
        "from tensorflow.keras import layers\n",
        "model = keras.Sequential([\n",
        "    layers.Dense(512, activation=\"relu\"),\n",
        "    layers.Dense(10, activation=\"softmax\")\n",
        "])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E_-YANATDFyy"
      },
      "source": [
        "**The compilation step**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "D7MQLJ3FDFyz"
      },
      "outputs": [],
      "source": [
        "model.compile(optimizer=\"rmsprop\",\n",
        "              loss=\"sparse_categorical_crossentropy\",\n",
        "              metrics=[\"accuracy\"])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PsKQHllJDFyz"
      },
      "source": [
        "**Preparing the image data**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "jGQo4DTzDFyz"
      },
      "outputs": [],
      "source": [
        "train_images = train_images.reshape((60000, 28 * 28))\n",
        "train_images = train_images.astype(\"float32\") / 255\n",
        "test_images = test_images.reshape((10000, 28 * 28))\n",
        "test_images = test_images.astype(\"float32\") / 255"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JK8yw6y1DFy0"
      },
      "source": [
        "**\"Fitting\" the model**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "-1bondUpDFy0",
        "outputId": "1a1c3c7c-a471-41a7-9d2b-bf99a0bf8cf2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/5\n",
            "\u001b[1m469/469\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m4s\u001b[0m 3ms/step - accuracy: 0.8739 - loss: 0.4384\n",
            "Epoch 2/5\n",
            "\u001b[1m469/469\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step - accuracy: 0.9655 - loss: 0.1181\n",
            "Epoch 3/5\n",
            "\u001b[1m469/469\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step - accuracy: 0.9784 - loss: 0.0716\n",
            "Epoch 4/5\n",
            "\u001b[1m469/469\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step - accuracy: 0.9842 - loss: 0.0519\n",
            "Epoch 5/5\n",
            "\u001b[1m469/469\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step - accuracy: 0.9891 - loss: 0.0373\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.history.History at 0x7b93263d2b10>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "model.fit(train_images, train_labels, epochs=5, batch_size=128)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tKayd5RSDFy1"
      },
      "source": [
        "**Using the model to make predictions**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "L787LHCDDFy1",
        "outputId": "80050a5d-82d4-41d3-f6be-e45bf3ddff17",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[1m1/1\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m0s\u001b[0m 30ms/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3.6169126e-08, 2.2906368e-08, 1.8479921e-06, 7.0953279e-06,\n",
              "        9.4371013e-12, 1.4099594e-07, 3.8487659e-12, 9.9998796e-01,\n",
              "        2.9172688e-07, 2.5682436e-06],\n",
              "       [5.4667371e-08, 4.3045540e-05, 9.9994779e-01, 7.4438426e-06,\n",
              "        1.3786186e-12, 3.2416085e-07, 4.7508718e-07, 8.6268124e-13,\n",
              "        8.2685540e-07, 1.0719750e-12]], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "test_digits = test_images[0:10]\n",
        "predictions = model.predict(test_digits)\n",
        "predictions[0:2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "Ve2igzo-DFy1",
        "outputId": "36d0e50f-16eb-42e9-f6cc-3f99648a918d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "predictions[0].argmax()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "uzY3pIwODFy2",
        "outputId": "e1909d32-65a8-4d1c-e5d0-c20e3d6debc9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.99998796"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "predictions[0][7]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "xezgIKlNDFy2",
        "outputId": "3e1ec671-0e81-484f-9247-ded087d2ad7d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "test_labels[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-XHYYjG1DFy3"
      },
      "source": [
        "**Evaluating the model on new data**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "xNdZononDFy3",
        "outputId": "980097ff-2194-4650-d67f-37770502d104",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 3ms/step - accuracy: 0.9765 - loss: 0.0742\n",
            "test_acc: 0.9797000288963318\n"
          ]
        }
      ],
      "source": [
        "test_loss, test_acc = model.evaluate(test_images, test_labels)\n",
        "print(f\"test_acc: {test_acc}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mDdr5Cp0DFy4"
      },
      "source": [
        "## Data representations for neural networks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-jIIy4TgDFy4"
      },
      "source": [
        "### Scalars (rank-0 tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "fzKLZrvWDFy4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "14734878-3d66-4c0a-ac4e-bf8819e648a4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(12)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "import numpy as np\n",
        "x = np.array(12)\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EfpsVC_vDFy5"
      },
      "outputs": [],
      "source": [
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P-apJulkDFy5"
      },
      "source": [
        "### Vectors (rank-1 tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "j9BnhConDFy5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7b34338c-de04-460c-d6b6-b5010ad082ab"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([12,  3,  6, 14,  7])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "x = np.array([12, 3, 6, 14, 7])\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "OpUa9q74DFy6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1c130aeb-9cb0-4482-bdcd-ada98252ee11"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zpAovEYwDFy6"
      },
      "source": [
        "### Matrices (rank-2 tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "ssUJ866HDFy7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca86f246-081a-497b-e54e-37797c67a1d8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "x = np.array([[5, 78, 2, 34, 0],\n",
        "              [6, 79, 3, 35, 1],\n",
        "              [7, 80, 4, 36, 2]])\n",
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UowMYDrlDFy7"
      },
      "source": [
        "### Rank-3 and higher-rank tensors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "lJVsrgnJDFy7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bb232d8d-bf49-438f-f117-230390f1103e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "x = np.array([[[5, 78, 2, 34, 0],\n",
        "               [6, 79, 3, 35, 1],\n",
        "               [7, 80, 4, 36, 2]],\n",
        "              [[5, 78, 2, 34, 0],\n",
        "               [6, 79, 3, 35, 1],\n",
        "               [7, 80, 4, 36, 2]],\n",
        "              [[5, 78, 2, 34, 0],\n",
        "               [6, 79, 3, 35, 1],\n",
        "               [7, 80, 4, 36, 2]]])\n",
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tmHM-8HeDFy8"
      },
      "source": [
        "### Key attributes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "C4DCJgN6DFy8"
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "1OIRZyteDFy_",
        "outputId": "e95e579e-c0aa-4fe0-81c1-1d42484f8ce4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "train_images.ndim"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "_5uP7MgUDFy_",
        "outputId": "947c494d-f233-471a-d7ba-656fdefe2138",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "train_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "YH_Xf3uRDFy_",
        "outputId": "e38eeabb-2c82-4b7c-ad53-e7ef73b9e759",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dtype('uint8')"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "train_images.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MrGERzVFDFzA"
      },
      "source": [
        "**Displaying the fourth digit**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "DiFhrW_bDFzA",
        "outputId": "32424140-3fd8-45f6-8b66-7fcb83874993",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "digit = train_images[400]\n",
        "plt.imshow(digit, cmap=plt.cm.binary)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "WuoELPUNDFzA",
        "outputId": "64f945e7-a96b-49e4-f434-8ed5853809cf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "train_labels[400]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A7JBMa8iDFzA"
      },
      "source": [
        "### Manipulating tensors in NumPy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "wN2vtRbJDFzA",
        "outputId": "b3ec99b8-e9fd-462d-9e18-9ce2889569cb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "my_slice = train_images[10:100]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "id": "XCvk9MuZDFzB",
        "outputId": "ad5552e8-7599-44cb-e709-7c005da147ff",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "my_slice = train_images[10:100, :, :]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "Qaw6KssLDFzB",
        "outputId": "8f3110e4-d4eb-429d-9f0f-99bfe916d337",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "my_slice = train_images[10:100, 0:28, 0:28]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "nAtgTNVFDFzB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ee353984-4f36-432c-90e8-1d82e0f6973c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 18, 14)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "my_slice = train_images[:, 10:, 14:]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3WKOMJ8bDFzB"
      },
      "outputs": [],
      "source": [
        "my_slice = train_images[:, 7:-7, 7:-7]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AiI7oSm2DFzC"
      },
      "source": [
        "### The notion of data batches"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "JBtAIaUgDFzC"
      },
      "outputs": [],
      "source": [
        "batch = train_images[:128]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JtTMcZLsDFzC"
      },
      "outputs": [],
      "source": [
        "batch = train_images[128:256]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xN7HEar9DFzC"
      },
      "outputs": [],
      "source": [
        "n = 3\n",
        "batch = train_images[128 * n:128 * (n + 1)]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1KSbSnWZDFzD"
      },
      "source": [
        "### Real-world examples of data tensors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L0Q_EBefDFzD"
      },
      "source": [
        "### Vector data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JKk6R4DnDFzE"
      },
      "source": [
        "### Timeseries data or sequence data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TuFK1PdaDFzE"
      },
      "source": [
        "### Image data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NTpg8Kw4DFzE"
      },
      "source": [
        "### Video data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3It5fcA8DFzF"
      },
      "source": [
        "## The gears of neural networks: tensor operations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mloPWX7VDFzF"
      },
      "source": [
        "### Element-wise operations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "CbWX9Tn3DFzF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "819e22dc-4581-4a00-9a48-edb9943b5eee"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original is:\n",
            " [[ 0.81896526 -0.21497121 -2.03072919  0.22681229]\n",
            " [-0.82806113 -0.94971965  0.09748025  1.13071035]\n",
            " [-0.503177   -1.6146684  -0.51143783  1.30857567]\n",
            " [-0.60106271 -1.04358358 -0.77787108 -0.03621124]] \n",
            " \t and \t \n",
            " relu is:\n",
            " [[0.81896526 0.         0.         0.22681229]\n",
            " [0.         0.         0.09748025 1.13071035]\n",
            " [0.         0.         0.         1.30857567]\n",
            " [0.         0.         0.         0.        ]]\n"
          ]
        }
      ],
      "source": [
        "def naive_relu(x):\n",
        "    assert len(x.shape) == 2\n",
        "    x = x.copy()\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            x[i, j] = max(x[i, j], 0)\n",
        "    return x\n",
        "import numpy as np\n",
        "rng = np.random.default_rng(1303)\n",
        "x = rng.standard_normal((4,4))\n",
        "print(f'Original is:\\n {x} \\n \\t and \\t \\n relu is:\\n {naive_relu(x)}')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "Ltol1XKKDFzG"
      },
      "outputs": [],
      "source": [
        "def naive_add(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert x.shape == y.shape\n",
        "    x = x.copy()\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            x[i, j] += y[i, j]\n",
        "    return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "5xhZkmtDDFzG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b6cc2da0-864a-4630-b7b1-c94a516b5c9b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Took: 0.006878 s\n"
          ]
        }
      ],
      "source": [
        "import time\n",
        "rng = np.random.default_rng(1303)\n",
        "x = rng.standard_normal((20,100))\n",
        "rng = np.random.default_rng(1303)\n",
        "y = rng.standard_normal((20,100))\n",
        "\n",
        "t0 = time.time()\n",
        "for _ in range(1000):\n",
        "    z = x + y\n",
        "    z = np.maximum(z, 0.)\n",
        "print(\"Took: {0:.6f} s\".format(time.time() - t0))# very slow"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "bHyOoziADFzG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a5094740-dda0-4ff8-baaa-90527935fd98"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Took: 1.57 s\n"
          ]
        }
      ],
      "source": [
        "t0 = time.time()\n",
        "for _ in range(1000):\n",
        "    z = naive_add(x, y)\n",
        "    z = naive_relu(z)\n",
        "print(\"Took: {0:.2f} s\".format(time.time() - t0))# very fast"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0pP5l8qEDFzG"
      },
      "source": [
        "### Broadcasting"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rHCRRrbPDFzG"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "X = np.random.random((32, 10))\n",
        "y = np.random.random((10,))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YHnXt5tnDFzH"
      },
      "outputs": [],
      "source": [
        "y = np.expand_dims(y, axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vyT9NpfJDFzH"
      },
      "outputs": [],
      "source": [
        "Y = np.concatenate([y] * 32, axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "72v5xoXCDFzH"
      },
      "outputs": [],
      "source": [
        "def naive_add_matrix_and_vector(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert len(y.shape) == 1\n",
        "    assert x.shape[1] == y.shape[0]\n",
        "    x = x.copy()\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            x[i, j] += y[j]\n",
        "    return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NKxl7-E9DFzH"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "x = np.random.random((64, 3, 32, 10))\n",
        "y = np.random.random((32, 10))\n",
        "z = np.maximum(x, y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C0TuRVBGDFzI"
      },
      "source": [
        "### Tensor product"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CChVxwULDFzJ"
      },
      "outputs": [],
      "source": [
        "x = np.random.random((32,))\n",
        "y = np.random.random((32,))\n",
        "z = np.dot(x, y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KrpvyUjzDFzJ"
      },
      "outputs": [],
      "source": [
        "def naive_vector_dot(x, y):\n",
        "    assert len(x.shape) == 1\n",
        "    assert len(y.shape) == 1\n",
        "    assert x.shape[0] == y.shape[0]\n",
        "    z = 0.\n",
        "    for i in range(x.shape[0]):\n",
        "        z += x[i] * y[i]\n",
        "    return z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jxCsGBmVDFzJ"
      },
      "outputs": [],
      "source": [
        "def naive_matrix_vector_dot(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert len(y.shape) == 1\n",
        "    assert x.shape[1] == y.shape[0]\n",
        "    z = np.zeros(x.shape[0])\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(x.shape[1]):\n",
        "            z[i] += x[i, j] * y[j]\n",
        "    return z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5UrVaciNDFzK"
      },
      "outputs": [],
      "source": [
        "def naive_matrix_vector_dot(x, y):\n",
        "    z = np.zeros(x.shape[0])\n",
        "    for i in range(x.shape[0]):\n",
        "        z[i] = naive_vector_dot(x[i, :], y)\n",
        "    return z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "s_l2HWs8DFzK"
      },
      "outputs": [],
      "source": [
        "def naive_matrix_dot(x, y):\n",
        "    assert len(x.shape) == 2\n",
        "    assert len(y.shape) == 2\n",
        "    assert x.shape[1] == y.shape[0]\n",
        "    z = np.zeros((x.shape[0], y.shape[1]))\n",
        "    for i in range(x.shape[0]):\n",
        "        for j in range(y.shape[1]):\n",
        "            row_x = x[i, :]\n",
        "            column_y = y[:, j]\n",
        "            z[i, j] = naive_vector_dot(row_x, column_y)\n",
        "    return z"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wOcfLZ13DFzL"
      },
      "source": [
        "### Tensor reshaping"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AyC87ei9DFzL"
      },
      "outputs": [],
      "source": [
        "train_images = train_images.reshape((60000, 28 * 28))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DfyCcsaeDFzM"
      },
      "outputs": [],
      "source": [
        "x = np.array([[0., 1.],\n",
        "             [2., 3.],\n",
        "             [4., 5.]])\n",
        "x.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BAtlidmuDFzM"
      },
      "outputs": [],
      "source": [
        "x = x.reshape((6, 1))\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fBUYYnHZDFzN"
      },
      "outputs": [],
      "source": [
        "x = np.zeros((300, 20))\n",
        "x = np.transpose(x)\n",
        "x.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "21W6eDP6DFzN"
      },
      "source": [
        "### Geometric interpretation of tensor operations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "meOsYaRFDFzN"
      },
      "source": [
        "### A geometric interpretation of deep learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T3PysEFgDFzO"
      },
      "source": [
        "## The engine of neural networks: gradient-based optimization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1oVRhSgsDFzO"
      },
      "source": [
        "### What's a derivative?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BKgCg1cfDFzO"
      },
      "source": [
        "### Derivative of a tensor operation: the gradient"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YT8rmRJRDFzO"
      },
      "source": [
        "### Stochastic gradient descent"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D47gEEEnDFzO"
      },
      "source": [
        "### Chaining derivatives: The Backpropagation algorithm"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YDc4DSLIDFzO"
      },
      "source": [
        "#### The chain rule"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L5Ba8pstDFzP"
      },
      "source": [
        "#### Automatic differentiation with computation graphs"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-wKhhbgeDFzP"
      },
      "source": [
        "#### The gradient tape in TensorFlow"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-TOwIGlvDFzP"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "x = tf.Variable(0.)\n",
        "with tf.GradientTape() as tape:\n",
        "    y = 2 * x + 3\n",
        "grad_of_y_wrt_x = tape.gradient(y, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PT1mKerzDFzP"
      },
      "outputs": [],
      "source": [
        "x = tf.Variable(tf.random.uniform((2, 2)))\n",
        "with tf.GradientTape() as tape:\n",
        "    y = 2 * x + 3\n",
        "grad_of_y_wrt_x = tape.gradient(y, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YSsmcXC4DFzQ"
      },
      "outputs": [],
      "source": [
        "W = tf.Variable(tf.random.uniform((2, 2)))\n",
        "b = tf.Variable(tf.zeros((2,)))\n",
        "x = tf.random.uniform((2, 2))\n",
        "with tf.GradientTape() as tape:\n",
        "    y = tf.matmul(x, W) + b\n",
        "grad_of_y_wrt_W_and_b = tape.gradient(y, [W, b])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P1T5OjTXDFzQ"
      },
      "source": [
        "## Looking back at our first example"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Kwl94rWTDFzQ"
      },
      "outputs": [],
      "source": [
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
        "train_images = train_images.reshape((60000, 28 * 28))\n",
        "train_images = train_images.astype(\"float32\") / 255\n",
        "test_images = test_images.reshape((10000, 28 * 28))\n",
        "test_images = test_images.astype(\"float32\") / 255"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uhY4pj7rDFzR"
      },
      "outputs": [],
      "source": [
        "model = keras.Sequential([\n",
        "    layers.Dense(512, activation=\"relu\"),\n",
        "    layers.Dense(10, activation=\"softmax\")\n",
        "])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ky_GSMoFDFzR"
      },
      "outputs": [],
      "source": [
        "model.compile(optimizer=\"rmsprop\",\n",
        "              loss=\"sparse_categorical_crossentropy\",\n",
        "              metrics=[\"accuracy\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KDhKd68xDFzR"
      },
      "outputs": [],
      "source": [
        "model.fit(train_images, train_labels, epochs=5, batch_size=128)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K-K6wPpFDFzS"
      },
      "source": [
        "### Reimplementing our first example from scratch in TensorFlow"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oyB4eH-CDFzS"
      },
      "source": [
        "#### A simple Dense class"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KlAJ-4yaDFzT"
      },
      "outputs": [],
      "source": [
        "import tensorflow as tf\n",
        "\n",
        "class NaiveDense:\n",
        "    def __init__(self, input_size, output_size, activation):\n",
        "        self.activation = activation\n",
        "\n",
        "        w_shape = (input_size, output_size)\n",
        "        w_initial_value = tf.random.uniform(w_shape, minval=0, maxval=1e-1)\n",
        "        self.W = tf.Variable(w_initial_value)\n",
        "\n",
        "        b_shape = (output_size,)\n",
        "        b_initial_value = tf.zeros(b_shape)\n",
        "        self.b = tf.Variable(b_initial_value)\n",
        "\n",
        "    def __call__(self, inputs):\n",
        "        return self.activation(tf.matmul(inputs, self.W) + self.b)\n",
        "\n",
        "    @property\n",
        "    def weights(self):\n",
        "        return [self.W, self.b]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n0CUFYl1DFzT"
      },
      "source": [
        "#### A simple Sequential class"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "t2bpU0G7DFzT"
      },
      "outputs": [],
      "source": [
        "class NaiveSequential:\n",
        "    def __init__(self, layers):\n",
        "        self.layers = layers\n",
        "\n",
        "    def __call__(self, inputs):\n",
        "        x = inputs\n",
        "        for layer in self.layers:\n",
        "           x = layer(x)\n",
        "        return x\n",
        "\n",
        "    @property\n",
        "    def weights(self):\n",
        "       weights = []\n",
        "       for layer in self.layers:\n",
        "           weights += layer.weights\n",
        "       return weights"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MfADLcFCDFzU"
      },
      "outputs": [],
      "source": [
        "model = NaiveSequential([\n",
        "    NaiveDense(input_size=28 * 28, output_size=512, activation=tf.nn.relu),\n",
        "    NaiveDense(input_size=512, output_size=10, activation=tf.nn.softmax)\n",
        "])\n",
        "assert len(model.weights) == 4"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YypXAttwDFzU"
      },
      "source": [
        "#### A batch generator"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oJ0J-geXDFzU"
      },
      "outputs": [],
      "source": [
        "import math\n",
        "\n",
        "class BatchGenerator:\n",
        "    def __init__(self, images, labels, batch_size=128):\n",
        "        assert len(images) == len(labels)\n",
        "        self.index = 0\n",
        "        self.images = images\n",
        "        self.labels = labels\n",
        "        self.batch_size = batch_size\n",
        "        self.num_batches = math.ceil(len(images) / batch_size)\n",
        "\n",
        "    def next(self):\n",
        "        images = self.images[self.index : self.index + self.batch_size]\n",
        "        labels = self.labels[self.index : self.index + self.batch_size]\n",
        "        self.index += self.batch_size\n",
        "        return images, labels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QJI9b0bwDFzV"
      },
      "source": [
        "### Running one training step"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "94j1cdYSDFzV"
      },
      "outputs": [],
      "source": [
        "def one_training_step(model, images_batch, labels_batch):\n",
        "    with tf.GradientTape() as tape:\n",
        "        predictions = model(images_batch)\n",
        "        per_sample_losses = tf.keras.losses.sparse_categorical_crossentropy(\n",
        "            labels_batch, predictions)\n",
        "        average_loss = tf.reduce_mean(per_sample_losses)\n",
        "    gradients = tape.gradient(average_loss, model.weights)\n",
        "    update_weights(gradients, model.weights)\n",
        "    return average_loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lXKEnj3TDFzV"
      },
      "outputs": [],
      "source": [
        "learning_rate = 1e-3\n",
        "\n",
        "def update_weights(gradients, weights):\n",
        "    for g, w in zip(gradients, weights):\n",
        "        w.assign_sub(g * learning_rate)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sDRo0zMPDFzV"
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras import optimizers\n",
        "\n",
        "optimizer = optimizers.SGD(learning_rate=1e-3)\n",
        "\n",
        "def update_weights(gradients, weights):\n",
        "    optimizer.apply_gradients(zip(gradients, weights))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MWmniCgUDFzV"
      },
      "source": [
        "### The full training loop"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3serMoiYDFzW"
      },
      "outputs": [],
      "source": [
        "def fit(model, images, labels, epochs, batch_size=128):\n",
        "    for epoch_counter in range(epochs):\n",
        "        print(f\"Epoch {epoch_counter}\")\n",
        "        batch_generator = BatchGenerator(images, labels)\n",
        "        for batch_counter in range(batch_generator.num_batches):\n",
        "            images_batch, labels_batch = batch_generator.next()\n",
        "            loss = one_training_step(model, images_batch, labels_batch)\n",
        "            if batch_counter % 100 == 0:\n",
        "                print(f\"loss at batch {batch_counter}: {loss:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "q5iv5vJzDFzW"
      },
      "outputs": [],
      "source": [
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
        "\n",
        "train_images = train_images.reshape((60000, 28 * 28))\n",
        "train_images = train_images.astype(\"float32\") / 255\n",
        "test_images = test_images.reshape((10000, 28 * 28))\n",
        "test_images = test_images.astype(\"float32\") / 255\n",
        "\n",
        "fit(model, train_images, train_labels, epochs=10, batch_size=128)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FPpMgCDQDFzW"
      },
      "source": [
        "### Evaluating the model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XPeSLjcbDFzX"
      },
      "outputs": [],
      "source": [
        "predictions = model(test_images)\n",
        "predictions = predictions.numpy()\n",
        "predicted_labels = np.argmax(predictions, axis=1)\n",
        "matches = predicted_labels == test_labels\n",
        "print(f\"accuracy: {matches.mean():.2f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u_-C3xHZDFzX"
      },
      "source": [
        "## Summary"
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "gpuType": "T4",
      "name": "chapter02_mathematical-building-blocks.i",
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      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
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