practice(3_13).ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMaB09fpLfJ70PR8onRxBUw",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/JDVVd/Class_DeeplearningforAI/blob/main/practice(3_13).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SXrzWeWPGThH"
      },
      "source": [
        "# The mathematical building blocks of neural networks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vsB1pTYrGThI"
      },
      "source": [
        "## A first look at a neural network"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b2fj3VT-GThJ",
        "outputId": "42b2bb32-dc4f-4b74-fcf5-72dec6562465",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11490434/11490434 [==============================] - 2s 0us/step\n"
          ]
        }
      ],
      "source": [
        "from tensorflow.keras.datasets import mnist\n",
        "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VuQcYfqYGThK",
        "outputId": "96670c11-45e9-446b-94b7-7f3b6789f247",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "train_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "urD006yMGThK",
        "outputId": "6f286e65-dd5a-4a04-b0c6-77a19f26e31a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "60000"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "len(train_labels)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GQTA_WCsGThL",
        "outputId": "0b04da71-3ad3-4806-c8fa-ed2fe324048b",
        "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": 4
        }
      ],
      "source": [
        "train_labels"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yCBTduo7GThL",
        "outputId": "a0187462-4e48-4c60-eba9-85f52227d1d3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "test_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rV9ykCYcGThL",
        "outputId": "f5811d48-0818-4894-a10c-b618f14127a9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10000"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "len(test_labels)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gEMtCEiZGThM",
        "outputId": "934626c3-f60f-49a5-c5eb-0f0d0ebe1684",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([7, 2, 1, ..., 4, 5, 6], dtype=uint8)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "test_labels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5bc1Bs5VGThM"
      },
      "source": [
        "**The network architecture**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0x9CHGczGThM"
      },
      "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": "eaIWZ8E3GThM"
      },
      "source": [
        "**The compilation step**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "t1cnEknzGThM"
      },
      "outputs": [],
      "source": [
        "model.compile(optimizer=\"rmsprop\",\n",
        "              loss=\"sparse_categorical_crossentropy\",\n",
        "              metrics=[\"accuracy\"])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kMKds2iZGThN"
      },
      "source": [
        "**Preparing the image data**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MG-2z_3qGThN"
      },
      "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": "PeulxJGDGThN"
      },
      "source": [
        "**\"Fitting\" the model**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "104fKwL_GThN",
        "outputId": "73176873-d64b-42fd-86bb-91edb4d51697",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/5\n",
            "469/469 [==============================] - 2s 5ms/step - loss: 0.2037 - accuracy: 0.9421\n",
            "Epoch 2/5\n",
            "469/469 [==============================] - 1s 3ms/step - loss: 0.2000 - accuracy: 0.9430\n",
            "Epoch 3/5\n",
            "469/469 [==============================] - 1s 3ms/step - loss: 0.1958 - accuracy: 0.9448\n",
            "Epoch 4/5\n",
            "469/469 [==============================] - 1s 3ms/step - loss: 0.1927 - accuracy: 0.9452\n",
            "Epoch 5/5\n",
            "469/469 [==============================] - 1s 3ms/step - loss: 0.1891 - accuracy: 0.9466\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.src.callbacks.History at 0x7e46d9f1ef20>"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "model.fit(train_images, train_labels, epochs=5, batch_size=128)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rgDFv_kFGThN"
      },
      "source": [
        "**Using the model to make predictions**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AmmpEdxFGThN",
        "outputId": "d31afc8f-e4c8-433e-c75d-0fbeab9ee9ea",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 62ms/step\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([9.3130993e-08, 6.5835920e-11, 1.8033670e-06, 1.4988375e-05,\n",
              "       2.3064159e-12, 6.3885849e-08, 4.1788074e-13, 9.9998260e-01,\n",
              "       3.8530498e-08, 2.8894760e-07], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "test_digits = test_images[0:10]\n",
        "predictions = model.predict(test_digits)\n",
        "predictions[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Fl84k1LTGThN",
        "outputId": "b6115798-03a5-4280-94b9-ba34a4a8aea5",
        "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": null,
      "metadata": {
        "id": "XSWu3ChXGThN",
        "outputId": "9b987397-742a-4518-9d80-fee2abd0d108",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9999826"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "predictions[0][7]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ExTwfatWGThN",
        "outputId": "89b2a74d-927d-4077-b8a5-fcba9a895f3a",
        "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": "LRGzYfu6GThN"
      },
      "source": [
        "**Evaluating the model on new data**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wzUtQxKCGThN",
        "outputId": "387a15a5-a750-41bd-8921-6a9993b05635",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 2ms/step - loss: 0.1861 - accuracy: 0.9459\n",
            "test_acc: 0.945900022983551\n"
          ]
        }
      ],
      "source": [
        "test_loss, test_acc = model.evaluate(test_images, test_labels)\n",
        "print(f\"test_acc: {test_acc}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AyOYeU5sGThN"
      },
      "source": [
        "## Data representations for neural networks"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xiN8LOaqGThO"
      },
      "source": [
        "### Scalars (rank-0 tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UDJcyFKNGThO",
        "outputId": "f123bb9c-e9f3-40a4-eab9-05f40191b363",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(12)"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "import numpy as np\n",
        "x = np.array(12)\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LHvxgIRlGThO",
        "outputId": "3fdec621-bf65-45cb-bd25-6df8267b452d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ],
      "source": [
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vdg_HtnhGThO"
      },
      "source": [
        "### Vectors (rank-1 tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gsVQPE6GGThO",
        "outputId": "781ac8fd-8300-44a3-aaab-ca4b458bfacb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([12,  3,  6, 14,  7])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "x = np.array([12, 3, 6, 14, 7])\n",
        "x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A_NZhZAwGThO",
        "outputId": "f579d157-3cf7-4fcd-b6be-899771784a98",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "x.ndim"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ksUm1hEDGThO"
      },
      "source": [
        "### Matrices (rank-2 tensors)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jySYTqDfGThO",
        "outputId": "55613eb9-6da1-45e3-e5cc-5cf7e4697d32",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "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": "zP5P8ei9GThO"
      },
      "source": [
        "### Rank-3 and higher-rank tensors"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "o34YOhvtGThO",
        "outputId": "e653f191-d60e-4d5c-96f2-92842d377806",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "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": "2V5IPR2GGThO"
      },
      "source": [
        "### Key attributes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-1A67NSLGThO"
      },
      "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": null,
      "metadata": {
        "id": "7whm-qA2GThc",
        "outputId": "926a3e81-8ed4-487f-81c0-3fcfe6bfa5d8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "train_images.ndim"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WwLIhVmkGThc",
        "outputId": "1ff48ae7-3762-4898-ec7a-29ab6cac754d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "train_images.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "V7B0Npw4GThc",
        "outputId": "928a6426-300f-43d6-c9b0-c74e6628300a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dtype('uint8')"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "train_images.dtype"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kxtb8HaDGThc"
      },
      "source": [
        "**Displaying the fourth digit**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_v_re-MIGThc",
        "outputId": "cbc93332-5803-4413-da79-af698aa1f0ce",
        "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[4]\n",
        "plt.imshow(digit, cmap=plt.cm.binary)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JYhH05mlGThd"
      },
      "source": [
        "### Manipulating tensors in NumPy"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train_images.shape"
      ],
      "metadata": {
        "id": "PvTGQ3sPP-sO",
        "outputId": "faf8dd7e-dd77-484b-9fbe-df13ec0c69d2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FMgi35N3GThd",
        "outputId": "1279710f-6b78-4963-d83d-521f238a551f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "my_slice = train_images[10:100]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vudP8zd-GThd",
        "outputId": "6467df7e-b39a-4c98-da6c-cfcbb391a906",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ],
      "source": [
        "my_slice = train_images[10:100, :, :]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rbZ-j4BvGThd",
        "outputId": "ca1b2250-a91c-40c0-a158-29bc80070e56",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(90, 28, 28)"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "my_slice = train_images[10:100, 0:28, 0:28]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cMXS83mwGThd"
      },
      "outputs": [],
      "source": [
        "my_slice = train_images[:, 14:, 14:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MLvA5DERGThd",
        "outputId": "573448de-56f9-4cfd-91e7-337e870ed5af",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60000, 14, 14)"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "my_slice = train_images[:, 7:-7, 7:-7]\n",
        "my_slice.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "61EKojLlGThd"
      },
      "source": [
        "### The notion of data batches"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "c_nqk6-aGThd"
      },
      "outputs": [],
      "source": [
        "batch = train_images[:128]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Lu4nr_v_GThd"
      },
      "outputs": [],
      "source": [
        "batch = train_images[128:256]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jAhJKb8yGThd"
      },
      "outputs": [],
      "source": [
        "n = 3\n",
        "batch = train_images[128 * n:128 * (n + 1)]"
      ]
    }
  ]
}