Copy_of_04_AIT_MLP_CIFAR10_exercise.ipynb

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  "metadata": {
    "anaconda-cloud": {},
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.6"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/cedenoorlando991/deeplearningassessment3/blob/main/Copy_of_04_AIT_MLP_CIFAR10_exercise.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cW-EyI5Lxpqi"
      },
      "source": [
        "# Copyright\n",
        "\n",
        "<PRE>\n",
        "Copyright (c) 2023 Bálint Gyires-Tóth - All Rights Reserved\n",
        "You may use and modify this code for research and development purpuses.\n",
        "Using this code for educational purposes (self-paced or instructor led) without the permission of the author is prohibited.\n",
        "</PRE>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Example of data exploration, modeling, regulartion and prediction\n",
        "Our exercise today involves loading a standard dataset using TensorFlow Keras API, exploring the data, building a simple neural network, and evaluating the effects of basic methods (activation functions, regularization, weight initialization, etc.). We then perform predictions on the test set and inspect the results. "
      ],
      "metadata": {
        "id": "3EX4cCa4WKJu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1. Data\n",
        "The dataset we will use is the well-known CIFAR10 (Canadian Institute For Advanced Research). Explore the details on the Keras website first: https://keras.io/api/datasets/cifar10/\n",
        "\n",
        "After you explored the basic features of the data, let's load it into the memory and explore the shapes:"
      ],
      "metadata": {
        "id": "yY9fztIeWIKt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from tensorflow.keras.datasets import cifar10\n",
        "from tensorflow.keras.utils import to_categorical\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "giRZKTjzX_7l"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ECFFhr4ewB6l"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "(X_train, Y_train), (X_test, Y_test) = cifar10.load_data()"
      ],
      "metadata": {
        "id": "bez7q0eiWQCK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7398239-5f2e-47e0-e0c8-7edc0bbf843f"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading data from https://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz\n",
            "170498071/170498071 [==============================] - 6s 0us/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(X_train.shape)\n",
        "print(X_test.shape)\n",
        "print(Y_train.shape)\n",
        "print(Y_test.shape)"
      ],
      "metadata": {
        "id": "2tJoRq5wXywi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "67bf4dc9-0ea8-46fa-b24d-a9166de76aeb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(50000, 32, 32, 3)\n",
            "(10000, 32, 32, 3)\n",
            "(50000, 1)\n",
            "(10000, 1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.1. Exercise \n",
        "Display the first ten images of the training data. Hints:\n",
        "* Axis 0 refers to the separate images, e.g. X_train[0]\n",
        "* You can use the [Matplotlib Pyplot imshow function](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html) for displaying the image. Just don't forget to import Plotly first!\n",
        "* A corresponding example, but you have to modify the code for your purpose: https://stackoverflow.com/questions/46615554/how-to-display-multiple-images-in-one-figure-correctly"
      ],
      "metadata": {
        "id": "zTCSGFyDlNvf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "for i in range(0,9):\n",
        "  plt.imshow(X_train[i])\n",
        "  plt.show()\n",
        "# <TODO>"
      ],
      "metadata": {
        "id": "hIQhHTppmBdO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "c80c4677-d11c-4783-9de2-4a6abcebea81"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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3MP5Vd9/Z/LdooAshVpZFg93dnwLA80WFEL8XXM3f7J81s71m9rCZ8WRjIcR1wZUG+9cBbAawE8AkgC+zXzSzB8xsj5ntmZvnyf1CiOXlioLd3afdvebudQDfALA78rsPufsud9/V3cU3HIQQy8sVBbuZXZ5V8TEA+67NcoQQy8VSrLfvAHgfgGEzOwngCwDeZ2Y7ATiAowD+ZCkH6+zswDtveUdQu+k2br0VdoRttK4+nnXFK50BbtxaSUUsksGucB2xSPen6LtpnbQmAuK1xBCxeEqlcPunzTesp3M6ctwCLMzzjD5PRV4+FtY8Ut+t7lyrRZ6zWMujciF8Pmp1/phTmcjrI/KMzp7nFuyxIyeodtfdtwXHFyq8HmInsQcjTu/iwe7unwwMf3OxeUKI6wt9g06IhKBgFyIhKNiFSAgKdiESgoJdiITQ0oKTqVQKHSTTq7udt1Dq6iTLjBTXixU2tJj1FrN4PGyV1SvcQovZSRYpeliNmIcxe8VJwczufp4hWK3xY9XqkSqQpMUTADhqwfFUbPE1rtUy3BJ1RJ5sUuDU6uH1AUBb5DFna/w56yryeT4dtgAB4Ozh6eD4um286Oi5VPjbqLHTqyu7EAlBwS5EQlCwC5EQFOxCJAQFuxAJQcEuREJoqfWWTqfR0xe2gDySbbZQCtsnXuI9uUpkDgDMz81TrVzh80qlcLZZtcqtq0okQ60SOdZCpG/YwjzPhqqSTLqewT46p6evn2r9PcNUa8+F+7kBQI317rNIXzZwraeHF+A8f4afx2IhbFHV67y4koE/rnqNv+Z6e7h9vGH9KNUKC+HXo0eKc/b1hC3sdMTO1ZVdiISgYBciISjYhUgICnYhEoKCXYiE0NLd+JmZPP76sb8JarXsL+m8ixfDiQJzl87ROalIbkRsp356OnwsAKiR7JrBSDupgeEhqrWl+emfvzBDtYOvHaBafi68+zy+kbd4Sme5E9Lbw9e/cSOva7duPFyvb+OmtXTOYBvP4uhp52usR2oRIh1OTqnU+E53OtLiKR1Z4+hExLno5Tv1FQ8n5aS5KYDBwfBjzkSSw3RlFyIhKNiFSAgKdiESgoJdiISgYBciISjYhUgIS2n/NA7gWwBG0Wj39JC7f83MBgF8F8AEGi2gPu7uF2P3lZ+dw+NP/jqo9a/bRud5LWwnPf/rJ+mcDet4/a7hIW4nnTo5RbUqqVvWOdhP55RTPElm+iRvCfT+3XdSbectN1FtoVQMjqey/Kk+cvwY1Q6+9jrVXtr3PNX6+8JNPP/wjz5G59x101aq5SI9ttaNjVOtTKw3ixRri9UNrJDaegCQykTq2vXzRJ4OkrxST3OLmBmRkRKKS7qyVwH8qbvfCOAOAJ8xsxsBPAjgCXffAuCJ5s9CiOuURYPd3Sfd/XfN27MADgBYC+A+AI80f+0RAB9dpjUKIa4Bb+tvdjObAHAbgGcAjLr7ZFOaQuNjvhDiOmXJwW5m3QC+D+Bz7p6/XHN3B8LFu83sATPbY2Z7ymWe+C+EWF6WFOxmlkUj0L/t7j9oDk+b2VhTHwNwJjTX3R9y913uviuX498PFkIsL4sGuzXap3wTwAF3/8pl0mMA7m/evh/Aj6798oQQ14qlZL3dBeBTAF4ysxeaY58H8CUA3zOzTwM4BuDji93RwOAQ/tUn/3VQaxvZQuctzIbtsNdeepHOGVvN7ZhUpE5XRzvPoCrXwy18tu7gax8Y4xlxC8O8DtpHPvTPqdbZ00G1eWK9RTo1oUraWgFAsRq+PwA4c+YC1Y4dOR0c7+zk53fq5HmqHd3/GtVSRb7Gw1PBD5zY/cFddM6GiTVUi2XLpdojaWpZbssZqzVnfE7Ows9ZzHpbNNjd/VcA2F28f7H5QojrA32DToiEoGAXIiEo2IVICAp2IRKCgl2IhNDSgpNmQFsu/P5y8JV9dF7+Uth681h2UplnDM1F2j9ZxLtobwvnGlUWeDumS2f5GqeP86y3v/nbcGFOALg4Gzne3KXgeE8vt7z6BsItuQCgK1Io8eTJsL0GACPD4cKS7b3civzlT/hjvvDaXqrVyrzF1qGpcAHRk5EWWlu2cyu1r7eTawO8xVZHJ8966+sKv66y7bx4ZGdn+Hlx569fXdmFSAgKdiESgoJdiISgYBciISjYhUgICnYhEkJLrbd6tYLZ82Eb7ec/+gmdd2LqZHA8VQlnoQHA3r15qsVSg6pVntUEkmn0+I9/Tqfksty62nnb7VQr53qoli8tUO3w8XCW1/nzvD9cuciz3k5PHaXakaP8Pnfd9s7g+L/9zL+nc559+jdUq17iGXH5Ei+KUgjXVMHhPdz2/OVzk1TrynCbL5vjVlm6jb8Oeoj1tm7DBJ1z3x9+IjhervLrt67sQiQEBbsQCUHBLkRCULALkRAU7EIkhJbuxmezOYyNjgW1LRMb6TxHeLc4E2mtlI7suKfS/D3O6zxxJdfeFRayPMlhzZpwQggAvO+ee6jW0xlJuGjntete3heuy3fwEG/jtHrtBNWKkbZL6Q6+xn0HXwmOv3zwIJ3TObGdaqdP88c80M+1kVy4LlxnN6/jd2GKt8M6f+oQ1c6eCyfdAECxFknaIgUCJ2d4eL77/eE5VV62Tld2IZKCgl2IhKBgFyIhKNiFSAgKdiESgoJdiISwqPVmZuMAvoVGS2YH8JC7f83MvgjgjwGcbf7q5939p7H7qlaruHA23DLojn/ybjrv3e99b3C8rY0nHmQi9lqs/VM90gopjfDxKmXudxTKPGnl/MkjVLtQ5AkXF87xtkuHicV2+kw4AQkAukd4uyO0cVvRctx6K1fDySmP/+JXdM6GzTdTbXyQW5jtKf4y7iSJSKUir0F3OL+fat09vJZfzXkS1dTFOaoND08Exxcq/LX48188GxyfneX1FZfis1cB/Km7/87MegA8Z2aPN7Wvuvt/XcJ9CCFWmKX0epsEMNm8PWtmBwDwt1khxHXJ2/qb3cwmANwG4Jnm0GfNbK+ZPWxm/GtMQogVZ8nBbmbdAL4P4HPungfwdQCbAexE48r/ZTLvATPbY2Z7Zuf430lCiOVlScFuZlk0Av3b7v4DAHD3aXevuXsdwDcA7A7NdfeH3H2Xu+/q6ebVV4QQy8uiwW6NFinfBHDA3b9y2fjlGS0fA8BbugghVpyl7MbfBeBTAF4ysxeaY58H8Ekz24mGHXcUwJ8sdkeplKGLtK05ny/Sec/vfS44PjLCtwlGR4apVqlwW+vixRmqoRheY6bO72/tRm5rjQ/wTzqnDvI6aPNzvObayOjq4HjnUD+dk27ndtJCgT8vY2PrqTZ1Olw38Nz5cHsqABhbE2nLFWn1NVfi5x+Z8OutUud2aVsHyW4E0BbJpiyfP0s1pMJ15gBglGQdlku8hRk7HfwsLW03/lcAQo8w6qkLIa4v9A06IRKCgl2IhKBgFyIhKNiFSAgKdiESQksLTqYMaMuGM3lKxRk679e/fiI47hVuC/V28oKClQrPTioWeEupDHlv3DAxTufsuONGqm1ez225mRNh6woApi6eo1quI2w1bR4KW3IAcPYsz8i6edsOqt108zaqPfq/vhUczyBcABIAKvP8+SyXueaxKovt4ec61o5pYuMmqp058So/VopnYXZ08eNt3741OF5c4M/L+NhIcPwXOW7x6couREJQsAuREBTsQiQEBbsQCUHBLkRCULALkRBaar3V63UsFEgBxkgRyHs+9JHw/ZV5llQ6Yq/Va7yQn6e5fZLOhG2j9i5eeHFqhlt5szO879mFAl+/tfMikK++cDg4fv43PCNr00Zuob3rhi1UK0cy4jpyYavJIxmHsQy7VJq/VEmrNABAoU76BNb4+d2wjltvxbnzVLuxl2fLPfvc81Q7fSxs5xXm+evbFy4Gx8slnhGpK7sQCUHBLkRCULALkRAU7EIkBAW7EAlBwS5EQmht1lvK0NUdtq/6IpXyelaFs4JKEZuhPfI+ljOeeeUdPFuurTM8r17k2Umzs3mqpTt5oceRzf1U29zJs95eOxLu9QbjlmKWFAEFgFOTx6k2NMwLfjKtXOB2UqnEi1HORzLiSpHssEopbPVm2rldOrpmFdWOTU5Tbfo4OfcAinP8sb2+/4Xg+NAQX4cPDIbHI4U5dWUXIiEo2IVICAp2IRKCgl2IhKBgFyIhLLobb2btAJ4C0Nb8/b9y9y+Y2UYAjwIYAvAcgE+5O+9XA6BeL2JhliR/1Pn7Tta6g+PT03yH87WXj1KtPcN33HN9/VQbJu2m1gz30TmZSILPUN8Q1SK5OigWwkkQADAyEt7hX7smvHsLAJNTU1Q7ePAA1SbKG6nGnJLZWf6cLSzwne78Je5qxHbja+VwIlK6jSet7N/HW4fFWjKNjIxSbe0tvJbfyKrwvOFVvG5gO1n/E//wJJ2zlCt7CcAfuPutaLRnvtfM7gDw5wC+6u43ALgI4NNLuC8hxAqxaLB7gzfeOrPNfw7gDwD8VXP8EQAfXY4FCiGuDUvtz55udnA9A+BxAK8DmHH3N5KCTwJYuywrFEJcE5YU7O5ec/edANYB2A3gHUs9gJk9YGZ7zGzP7CwpXCGEWHbe1m68u88AeBLAnQD6zeyNDb51AE6ROQ+5+y5339XTw7+iKIRYXhYNdjNbZWb9zdsdAD4A4AAaQf9HzV+7H8CPlmmNQohrwFISYcYAPGJmaTTeHL7n7j82s5cBPGpm/xnA8wC+ueg91R110sYnFXnfyVTCSRy9pJUUADz39C+oNjXNE0ksy5NCdu9+Z3D87jt30TmXLnGrae/vnqHafJEnfhw8foJqh48eDY4XFvifUO68iFt7L0/GyOdnqTZLWlTN57ltGCklh0yaq32RT4xrNobtwYGhMTpnZA23vNbcdjPVBiM16HKx2oZMiyQvwcPxkoq0oFo02N19L4DbAuOH0fj7XQjxe4C+QSdEQlCwC5EQFOxCJAQFuxAJQcEuREKwWM2qa34ws7MAjjV/HAbAPbDWoXW8Ga3jzfy+rWODuwf90pYG+5sObLbH3blBrXVoHVrHNV2HPsYLkRAU7EIkhJUM9odW8NiXo3W8Ga3jzfyjWceK/c0uhGgt+hgvREJYkWA3s3vN7FUzO2RmD67EGprrOGpmL5nZC2a2p4XHfdjMzpjZvsvGBs3scTN7rfk/7620vOv4opmdap6TF8zswy1Yx7iZPWlmL5vZfjP7d83xlp6TyDpaek7MrN3MnjWzF5vr+E/N8Y1m9kwzbr5rFuljFsLdW/oPQBqNslabAOQAvAjgxlavo7mWowCGV+C47wFwO4B9l439FwAPNm8/CODPV2gdXwTwH1p8PsYA3N683QPgIIAbW31OIuto6TlBI9u3u3k7C+AZAHcA+B6ATzTH/weAf/N27nclruy7ARxy98PeKD39KID7VmAdK4a7PwXgwluG70OjcCfQogKeZB0tx90n3f13zduzaBRHWYsWn5PIOlqKN7jmRV5XItjXAri8+sJKFqt0AD8zs+fM7IEVWsMbjLr7ZPP2FABehHz5+ayZ7W1+zF/2Pycux8wm0Kif8AxW8Jy8ZR1Ai8/JchR5TfoG3d3ufjuADwH4jJm9Z6UXBDTe2dF4I1oJvg5gMxo9AiYBfLlVBzazbgDfB/A5d39TV4hWnpPAOlp+TvwqirwyViLYTwEYv+xnWqxyuXH3U83/zwD4IVa28s60mY0BQPP/MyuxCHefbr7Q6gC+gRadEzPLohFg33b3HzSHW35OQutYqXPSPPYM3maRV8ZKBPtvAWxp7izmAHwCwGOtXoSZdZlZzxu3AXwQwL74rGXlMTQKdwIrWMDzjeBq8jG04JyYmaFRw/CAu3/lMqml54Sto9XnZNmKvLZqh/Etu40fRmOn83UAf7ZCa9iEhhPwIoD9rVwHgO+g8XGwgsbfXp9Go2feEwBeA/B3AAZXaB1/CeAlAHvRCLaxFqzjbjQ+ou8F8ELz34dbfU4i62jpOQFwCxpFXPei8cbyHy97zT4L4BCA/wOg7e3cr75BJ0RCSPoGnRCJQcEuREJQsAuREBTsQiQEBbsQCUHBLkRCULALkRAU7EIkhP8HgqiJJe0C+/AAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Print the corresponding labels of the displayed images from the target variable (Y_train):"
      ],
      "metadata": {
        "id": "FAQkUWlmm-bc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(Y_train[:10])"
      ],
      "metadata": {
        "id": "AkOrWzghnJ78",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "75c5398c-704f-4af9-89ea-777b3236e9b8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[6]\n",
            " [9]\n",
            " [9]\n",
            " [4]\n",
            " [1]\n",
            " [1]\n",
            " [2]\n",
            " [7]\n",
            " [8]\n",
            " [3]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.2. Exercise\n",
        "We will train a Multi-Layer Perceptron (MLP), which requires a 2 dimensional input: 0th axis refers to the datapoints (i.e. images), the 1th dimens to the input. As images are 3 dimensional (width, height, color channels), you have to reshape the images into vectors. We also call this flattening. \n",
        "\n",
        "In order to do so, calculate the size of the equivalent 1D vector of the image:"
      ],
      "metadata": {
        "id": "VX24g5FstsRU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "flattened_dim = 3072 \n",
        "X_train.shape"
      ],
      "metadata": {
        "id": "hdoMyxHzuXZG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "35981b51-5d27-4a1f-d8b0-2d9752546703"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(50000, 32, 32, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "After you calculated it, we can reshape the images, and covert the integer arrays into float arrays -- which are needed for the neural networks as input. Hint:\n",
        "* in the [reshape() function of Numpy](https://www.w3schools.com/python/numpy/numpy_array_reshape.asp) you can use -1 for one axis, to automatically calculate that value."
      ],
      "metadata": {
        "id": "WbqXJUSFubeC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# reshape 3D tensors to 2D tensors\n",
        "X_train = X_train.reshape(-1,flattened_dim)\n",
        "X_test = X_test.reshape(-1,flattened_dim)\n",
        "\n",
        "# it is in int8 format, the neural network requires float32\n",
        "X_train = X_train.astype(np.float32)\n",
        "X_test = X_test.astype(np.float32)"
      ],
      "metadata": {
        "id": "vukOcBM0XzSj"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.3. Exercise\n",
        "As the next step, let's split the training data into training and validation data. 80% of the original training data should be the final training data, and 20% the validation.\n",
        "You should use Numpy indexing to select the first 80% of X_train as final X_train, and the last 20% as X_valid. Hints: \n",
        "* https://datascienceparichay.com/article/numpy-array-first-n-rows/\n",
        "* https://datascienceparichay.com/article/numpy-array-last-n-rows/"
      ],
      "metadata": {
        "id": "DO79AdIdvVfD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "train_ratio  = 0.8\n",
        "train_length = X_train.shape[0] # length of the training data\n",
        "train_split  = int(train_length * train_ratio)\n",
        "# where to split the training and validation data\n",
        "X_valid, Y_valid = X_train[train_split:], Y_train[train_split:]\n",
        "X_train, Y_train = X_train[:train_split], Y_train[:train_split]"
      ],
      "metadata": {
        "id": "mRwuWxxIxLgN"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.4. Exercise\n",
        "As the last step of input data preparation, the data should be standardized. Calculate the mean and variance of the training data (elementvise -- so for each value of the flattened image you should get a mean and variance for the training data along 0th axis). Hint: \n",
        "* https://stackoverflow.com/questions/70626231/how-to-calculate-mean-variance-standard-deviation-per-index-of-array"
      ],
      "metadata": {
        "id": "z05y_QWDxWER"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mean = np.mean(X_train,axis=0)\n",
        "std  = np.std(X_train,axis=0)"
      ],
      "metadata": {
        "id": "TSZbvWCBx8Ea"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, use the resulting values to standardize the training, validation and test data by substracting the mean and dividing the result with the standard deviation."
      ],
      "metadata": {
        "id": "6WRHKkkjyN1S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X_train = (X_train - mean) / std\n",
        "X_valid = (X_valid - mean) / std\n",
        "X_test  = (X_test - mean) / std"
      ],
      "metadata": {
        "id": "2ESLP1EIyB2J"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.5. Exercise\n",
        "And as the last step, convert the dense representation of the classes (i.e. 0,1,2,3...9) to one-hot encoding (0 = [1 0 0 0 0 0 0 0 0 0], 1 = [0 1 0 0 0 0 0 0 0 0] ... 9 = [0 0 0 0 0 0 0 0 0 1]). To do this, first, calculate the number of unique elements in the target training data. Hints:\n",
        "* use the [unique() function](https://numpy.org/doc/stable/reference/generated/numpy.unique.html) of Numpy to list the unique elements\n",
        "* you can count the number of elements in a list with the [len() function](https://www.w3schools.com/python/ref_func_len.asp)"
      ],
      "metadata": {
        "id": "ooHCnUin7r4o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "nb_classes =  len(np.unique(Y_train))"
      ],
      "metadata": {
        "id": "i0LAO9cs8KEE"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Doublecheck, if the same number of classes exists in the validation and test target data:"
      ],
      "metadata": {
        "id": "BvM6XhGe8JU9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Validation data has the same number of classes, as the training data:\", nb_classes == len(np.unique(Y_valid)))\n",
        "print(\"Test data has the same number of classes, as the training data:\", nb_classes == len(np.unique(Y_test)))"
      ],
      "metadata": {
        "id": "eZFNSsyx_Py2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "29fd76b6-23de-49f5-99bc-3ce1a52a36d5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Validation data has the same number of classes, as the training data: True\n",
            "Test data has the same number of classes, as the training data: True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "And convert the dense representation into one-hot encoding. Hint:\n",
        "* use the [to_categorical function](https://www.tensorflow.org/api_docs/python/tf/keras/utils/to_categorical) with the calculated nb_classes\n"
      ],
      "metadata": {
        "id": "mJM-iBmR8dLe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Y_train = to_categorical(Y_train, num_classes=nb_classes)\n",
        "Y_valid = to_categorical(Y_valid, num_classes=nb_classes)\n",
        "Y_test  = to_categorical(Y_test, num_classes=nb_classes)"
      ],
      "metadata": {
        "id": "xwZ4OJ6I8lba"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Final check of data preparation\n",
        "Now, lets check the shapes and mean and standard deviation of the training, validation and test data."
      ],
      "metadata": {
        "id": "LshN2OSsv3TZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Shapes of the training, validation and test input data:\", X_train.shape, X_valid.shape, X_test.shape)\n",
        "print(\"Shapes of the training, validation and test output data:\", Y_train.shape, Y_valid.shape, Y_test.shape)\n",
        "print(\"Mean values of the training, validation and test input data:\", X_train.mean(), X_valid.mean(), X_test.mean())\n",
        "print(\"Standard deviation of the training, validation and test input data:\", X_train.std(), X_valid.std(), X_test.std())"
      ],
      "metadata": {
        "id": "O_jdJVcvX0vi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "562d0032-5d69-4f7b-8385-8644b02bb3f6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shapes of the training, validation and test input data: (25600, 3072) (6400, 3072) (10000, 3072)\n",
            "Shapes of the training, validation and test output data: (25600, 10) (6400, 10) (10000, 10)\n",
            "Mean values of the training, validation and test input data: 1.8859283e-09 -0.0034694616 0.011806925\n",
            "Standard deviation of the training, validation and test input data: 1.0000013 1.0014856 0.9965314\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Don't worry, if the mean and standard deviation of the validation and test data are not exactly 0 and 1, but these might be very mear to it (e.g. 0.01 mean, 0.99 variance)."
      ],
      "metadata": {
        "id": "5GtAOOoezmZY"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cJ14oyZExpqj"
      },
      "source": [
        "# 2. Training "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s4ZXYRMBxpql"
      },
      "source": [
        "Let us begin with a simple example of creating a small neural network without regularization and training it with actual data. The purpose of this is to provide you with an example as to how to proceed with the next exercise. "
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# imports \n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from tensorflow.keras.models import Sequential\n",
        "from tensorflow.keras.layers import Dense, Embedding, Flatten, Dropout\n",
        "from tensorflow.keras.initializers import HeNormal\n",
        "from tensorflow.keras.initializers    import LecunUniform\n",
        "from tensorflow.keras.callbacks import EarlyStopping"
      ],
      "metadata": {
        "id": "6-8Q6ll7ZDgq"
      },
      "execution_count": 40,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# model definition\n",
        "model = Sequential()\n",
        "model.add(Dense(128, activation='tanh', input_shape=(flattened_dim,)))\n",
        "model.add(Dense(128, activation='tanh'))\n",
        "model.add(Dense(nb_classes, activation='softmax'))\n",
        "\n",
        "# loss function and optimizer\n",
        "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
      ],
      "metadata": {
        "id": "pke6w3CD8DHp"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CZbOR76QxprC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "de4fca8f-310e-4773-a2bc-9b1c896896f4"
      },
      "source": [
        "# training\n",
        "network_history = model.fit(X_train, Y_train, \n",
        "                            validation_data=(X_valid,Y_valid),\n",
        "                            batch_size=128,                             \n",
        "                            epochs=40, \n",
        "                            verbose=1)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/40\n",
            "313/313 [==============================] - 6s 6ms/step - loss: 1.8148 - accuracy: 0.3663 - val_loss: 1.7515 - val_accuracy: 0.3898\n",
            "Epoch 2/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.6984 - accuracy: 0.4079 - val_loss: 1.7306 - val_accuracy: 0.3961\n",
            "Epoch 3/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6410 - accuracy: 0.4320 - val_loss: 1.7050 - val_accuracy: 0.4050\n",
            "Epoch 4/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6027 - accuracy: 0.4442 - val_loss: 1.6970 - val_accuracy: 0.4117\n",
            "Epoch 5/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.5746 - accuracy: 0.4528 - val_loss: 1.6748 - val_accuracy: 0.4198\n",
            "Epoch 6/40\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 1.5446 - accuracy: 0.4656 - val_loss: 1.6721 - val_accuracy: 0.4280\n",
            "Epoch 7/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5116 - accuracy: 0.4780 - val_loss: 1.6611 - val_accuracy: 0.4269\n",
            "Epoch 8/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.4782 - accuracy: 0.4893 - val_loss: 1.6648 - val_accuracy: 0.4239\n",
            "Epoch 9/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.4565 - accuracy: 0.4989 - val_loss: 1.6495 - val_accuracy: 0.4288\n",
            "Epoch 10/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.4351 - accuracy: 0.5054 - val_loss: 1.6453 - val_accuracy: 0.4326\n",
            "Epoch 11/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.4136 - accuracy: 0.5112 - val_loss: 1.6298 - val_accuracy: 0.4462\n",
            "Epoch 12/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3939 - accuracy: 0.5190 - val_loss: 1.6289 - val_accuracy: 0.4452\n",
            "Epoch 13/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3719 - accuracy: 0.5253 - val_loss: 1.6419 - val_accuracy: 0.4410\n",
            "Epoch 14/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.3561 - accuracy: 0.5319 - val_loss: 1.6391 - val_accuracy: 0.4397\n",
            "Epoch 15/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.3294 - accuracy: 0.5413 - val_loss: 1.6437 - val_accuracy: 0.4408\n",
            "Epoch 16/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.3030 - accuracy: 0.5504 - val_loss: 1.6316 - val_accuracy: 0.4408\n",
            "Epoch 17/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.2948 - accuracy: 0.5556 - val_loss: 1.6424 - val_accuracy: 0.4486\n",
            "Epoch 18/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.2657 - accuracy: 0.5630 - val_loss: 1.6448 - val_accuracy: 0.4428\n",
            "Epoch 19/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2428 - accuracy: 0.5712 - val_loss: 1.6499 - val_accuracy: 0.4445\n",
            "Epoch 20/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.2261 - accuracy: 0.5770 - val_loss: 1.6457 - val_accuracy: 0.4482\n",
            "Epoch 21/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.2134 - accuracy: 0.5796 - val_loss: 1.6471 - val_accuracy: 0.4475\n",
            "Epoch 22/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1923 - accuracy: 0.5894 - val_loss: 1.6636 - val_accuracy: 0.4456\n",
            "Epoch 23/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.1771 - accuracy: 0.5958 - val_loss: 1.6508 - val_accuracy: 0.4497\n",
            "Epoch 24/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1616 - accuracy: 0.5992 - val_loss: 1.6531 - val_accuracy: 0.4533\n",
            "Epoch 25/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.1360 - accuracy: 0.6063 - val_loss: 1.6671 - val_accuracy: 0.4474\n",
            "Epoch 26/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.1226 - accuracy: 0.6127 - val_loss: 1.6759 - val_accuracy: 0.4478\n",
            "Epoch 27/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.1043 - accuracy: 0.6194 - val_loss: 1.6789 - val_accuracy: 0.4515\n",
            "Epoch 28/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.0865 - accuracy: 0.6284 - val_loss: 1.6768 - val_accuracy: 0.4525\n",
            "Epoch 29/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.0633 - accuracy: 0.6351 - val_loss: 1.6976 - val_accuracy: 0.4483\n",
            "Epoch 30/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0488 - accuracy: 0.6395 - val_loss: 1.7150 - val_accuracy: 0.4462\n",
            "Epoch 31/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.0293 - accuracy: 0.6494 - val_loss: 1.7238 - val_accuracy: 0.4440\n",
            "Epoch 32/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.0215 - accuracy: 0.6492 - val_loss: 1.7368 - val_accuracy: 0.4490\n",
            "Epoch 33/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.0014 - accuracy: 0.6569 - val_loss: 1.7432 - val_accuracy: 0.4448\n",
            "Epoch 34/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.9844 - accuracy: 0.6612 - val_loss: 1.7454 - val_accuracy: 0.4506\n",
            "Epoch 35/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.9726 - accuracy: 0.6656 - val_loss: 1.7654 - val_accuracy: 0.4456\n",
            "Epoch 36/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9549 - accuracy: 0.6732 - val_loss: 1.7724 - val_accuracy: 0.4504\n",
            "Epoch 37/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.9497 - accuracy: 0.6730 - val_loss: 1.7997 - val_accuracy: 0.4404\n",
            "Epoch 38/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.9292 - accuracy: 0.6823 - val_loss: 1.8182 - val_accuracy: 0.4458\n",
            "Epoch 39/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9243 - accuracy: 0.6853 - val_loss: 1.8142 - val_accuracy: 0.4425\n",
            "Epoch 40/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9051 - accuracy: 0.6912 - val_loss: 1.8139 - val_accuracy: 0.4473\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uFqhzV85xprJ"
      },
      "source": [
        "Let's plot the training and validation loss and accuracy curves:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BYmXGkLCxprK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "outputId": "9d56ee45-1816-4218-fb13-b867d585815d"
      },
      "source": [
        "def plot_history(network_history):\n",
        "    plt.figure()\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Loss')\n",
        "    plt.plot(network_history.history['loss'])\n",
        "    plt.plot(network_history.history['val_loss'])\n",
        "    plt.legend(['Training', 'Validation'])\n",
        "\n",
        "    plt.figure()\n",
        "    plt.xlabel('Epochs')\n",
        "    plt.ylabel('Accuracy')\n",
        "    plt.plot(network_history.history['accuracy'])\n",
        "    plt.plot(network_history.history['val_accuracy'])\n",
        "    plt.legend(['Training', 'Validation'], loc='lower right')\n",
        "    plt.show()\n",
        "\n",
        "plot_history(network_history)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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4C/0SSrni2IkSZv60jxmr9pGZX0yXliG8fkc8o+Lb6DhByqO5so9gFHA30Al4HxhgjEkXkSbAdqDKIBARb+BN4CogDVgrIvOMMdsrzBMLPAMMMcYcFxEduEXVuj0Z+bz3414+W59GUamDK+IimXhZR4Z0aq4tAKVwrUVwC/C6MWZZxYnGmAIRufccrxsA7DbGpACIyBxgNFZ4nDQReNMYc9z5nukXUrxS1ckvLmPF7kw+STzA4h3p+Pl4cVPvNtx7WYweCqpUJa4EwWTg8MkHIhIItDDGpBpjlpzjdW2AAxUepwEDK80T53zPFVjdR5ONMQtdqEmpMxhj2J2ezw8701m6M4O1qccoLTeEB/nx6ytjuXNQeyJD/O0uU6l6yZUg+AQYXOFxuXNa/1r6/FhgGBANLBORnsaY7IozicgkYBJAu3btauFjVWNQ7jD8kJR+auV/MLsQgM4tQrhnaAzD4qJI6NAMX28vmytVqn5zJQh8jDElJx8YY0pExM+F1x0E2lZ4HO2cVlEasNoYUwrsFZFkrGBYW3EmY8w7wDsACQkJxoXPVo1cYUk5D81az/dJ6QT5eTOkUwQPDe/EsM6RtG4aaHd5SjUorgRBhoiMMsbMAxCR0UCmC69bC8SKSAxWAIwBKh8RNBfrsNRpIhKB1VWU4mLtykMdP1HCPTPWsulANpN/1o2xA9vh7+Ntd1lKNViuBMH9wEwR+TcgWP3+d53vRcaYMhF5GFiE1f//njFmm4i8CCQ6g2URcLWIbMfqcnrKGJNVw++iPMDB7ELumrqaA8cLeesX/bi2R0u7S1KqwRNjXOtpEZFgAGNMvlsrOo+EhASTmJhoZwnKJklHchn/3hoKSsp5964EvTiMUhdARNYZYxKqes6lE8pE5AagOxBw8rhrY8yLtVahUuexOiWLX72fSBM/bz65/1K6tNQhoZWqLa6cUPYfoAkwHHgXuBVY4+a6lDpl4dYjPDpnA22bBTLjngFEN2tid0lKNSquHFc32BhzF3DcGPNH4FKcx/8r5W4zV+/jwZnr6N46lE/vH6whoJQbuNI1VOT8WSAirYEsoJX7SlLK8tbS3fx14U5GdInizXF9CfTTI4OUcgdXguArEWkK/A1YjzU43BR3FqU8mzGGv3+XzL++383o3q159bZ4PSlMKTc6ZxCIiBewxHmm72ci8jUQYIzJqYvilOcxxvCn+TuY+uNexvRvy59v6qkjgyrlZufczHJelezNCo+LNQSUuzgchj/M3crUH/cyYXAH/nKzhoBSdcGV9vYSEblFdLxe5UZl5Q6e/GQTs1bv58Fhl/DCz7rpENFK1RFX9hHcBzwBlIlIEdbZxcYYowdyq1pRUubgsY82sGDLEZ68Oo6HR8TaXZJSHsWVS1Xq4O3KbYpKy3lwpjV43HM3duPeoTF2l6SUx3HlhLLLq5pe+UI1Sl2InMJSvk86yvur9rHxQDb/d1NPxg3UIcaVsoMrXUNPVbgfgHXlsXXACLdUpBqt9NwiFm0/yrfbjrBqTxZlDkOLUH/euKM3o3u3sbs8pTyWK11DP6v4WETaAm+4qyDVuKQdL2D+5sMs2naEDQeyMQZiIoK497IYru3ekvjopnjpkUFK2cqlQecqSQO61nYhqnHZkpbDf5ftYcGWwzgM9GgTyhMj47imR0tio4L1iCCl6hFX9hH8C+tsYrAON+2NdYaxUmcwxrB8Vyb/XbaHFbuzCPb3YeJlHblzUHvahusYQUrVV660CCoO/l8GzDbGrHBTPaoBKi13sGDLYf7zvxR2HM4lKsSfZ67rwtiB7QgN8LW7PKXUebgSBJ8CRcaYcgAR8RaRJsaYAveWphqCuRsO8rdFOzmYXUinqGD+emsvRvdurZeOVKoBcSUIlgAjgZNXJgsEvgUGu6soVf/lF5fx3NytfLHhIPHRYfxxVHdGdInSHb9KNUCuBEFAxctTGmPyRUQ7fD3Y1oM5PDxrPfuPFfDYyFgeGRGrYwIp1YC5EgQnRKSvMWY9gIj0AwrdW5aqj4wxvLcilZe/2UHzIH9mTxyk1w1WqhFwJQgeAz4RkUNY4wy1BO5wZ1Gq/snKL+apTzfzfVI6I7tG8bdb42kW5Gd3WUqpWuDKCWVrRaQL0Nk5aacxptS9Zan6ZOWeTB6bs5HsglIm/6wb4wd30PMAlGpEXDmP4CFgpjFmq/NxMxEZa4x5y+3VKVul5xbxxpJdzF6zn5iIIKbd3Z/urcPsLkspVctc6RqaaIypeHGa4yIyEdAgaKRyi0p5538pTP1xL2UOB+Mv7cBT13QmyL8mJ6Irpeo7V/6zvUVEjDEGrPMIAO0cboSKy8r5YNU+3vxhN8cLShkV35rfXB1H++ZBdpemlHIjV4JgIfCRiPzX+fg+4Bv3laTqWrnD8OXGg7z2bTIHswu5LDaC313bhR5ttBtIKU/gShD8DpgE3O98vBnryCHVCGw9mMOTn2wi6UgePduE8cotvRgaG2F3WUqpOuTKUUMOEVkNXALcDkQAn7m7MOVexhg++Gkff/p6B+FBfvx7XB+u79FKzwxWygNVGwQiEgeMdd4ygY8AjDHD66Y05S45haU8/dlmvtl6hOGdI3nt9t6E6zkBSnmsc7UIkoDlwI3GmN0AIvJ4nVSl3GbjgWwenrWeIzlF/OH6rtw7NEZbAUp5uHMFwc3AGOAHEVkIzME6s1g1QMYYpv64l5e/SaJFaAAf338pfds1s7sspVQ9UG0QGGPmAnNFJAgYjTXURJSIvA18YYz5tk4qVBft+IkSnvxkE0uS0rm6Wwv+dms8YU30OgFKKYsrO4tPALOAWSLSDLgN60giDYIG4Puko/z+860cO1Giw0Mopap0QaeKGmOOA+84b6oey8ov5sWvt/PlxkPEtQhmyl0J9IzW8wKUUmfTMQMaGWMM8zYd4o9fbSevqJTHRsby4LBO+Pl42V2aUqqe0iBoRA7nFPLsF1tZkpRO77ZN+eutvYhrEWJ3WUqpek6DoBFwOAyz1uzn5W+SKHcYnruxGxMGd9CrhimlXOLW/gIRuVZEdorIbhF5uornJ4hIhohsdN5+5c56GqOcwlLGT1vDs3O30rttU759/HLuHRqjIaCUcpnbWgTOUUrfBK4C0oC1IjLPGLO90qwfGWMedlcdjdmh7ELunraWlMx8/u+mnowd0FaPCFJKXTB3dg0NAHYbY1IARGQO1vkIlYNA1UDSkVwmvLeWE8VlTL97AEM66UBxSqmacWfXUBvgQIXHac5pld0iIptF5FMRaevGehqNlbszue3tVQB8fP+lGgJKqYti9zGFXwEdjDG9gO+AGVXNJCKTRCRRRBIzMjLqtMD65suNBxk/bQ2tmgbw+YOD6doq1O6SlFINnDuD4CBQcQs/2jntFGNMljGm2PnwXaBfVW9kjHnHGJNgjEmIjIx0S7H1nTGG//xvD7+es5F+7Zvxyf2Dad000O6ylFKNgDv3EawFYkUkBisAxgDjKs4gIq2MMYedD0cBO9xYT4NV7jD88attvL9qHz+Lb82rt/XC38fb7rKUUo2E24LAGFMmIg8DiwBv4D1jzDYReRFINMbMAx4VkVFAGXAMmOCuehqqA8cKeObzLfy4O5P7Lu/I767tosNGK6VqlTivSd9gJCQkmMTERLvLcDuHw7qC2CsLkxDguRu7MWZAO7vLUko1UCKyzhiTUNVzemZxPZSSkc/vPtvM2tTjXB4XyV9u7kkb3R+glHITDYJ6pKzcwbs/7uX175Lx9/Hi1dviuaVvGz1JTCnlVhoE9UTSkVx+++lmNqflcE33Frw0ugdRoQF2l6WU8gAaBDY7eQnJVxYmERrgy5vj+nJ9z5baClBK1RkNAhsVlpTzzOebmbvxENd0b8Ffbu5FeJCf3WUppTyMBoFNDhwr4L4P1rHjSC5PXdOZB4ddoq0ApZQtNAhssHJ3Jg/NWk+Zw/De+P4M7xJld0lKKQ+mQVCHTu4P+L8FO7gkMph37kogJiLI7rKUUh5Og6COVN4f8NrtvQn218WvlLKfronqwMHsQia9n8j2w7k8eXUcDw7rpMNEKKXqDQ0CN9t4IJtfzUikuLScqeMTGNGlhd0lKaXUGTQI3OjrzYf4zcebiAr1Z/bEgcS2CLG7JKWUOosGgRsYY/jX97v5+3fJJLRvxn9/2Y/mwf52l6WUUlXSIKhlRaXlPP2ZtVP45j5t+MstPfXaAUqpek2DoBZl5hcz6f1E1u/P1pPElFINhgZBLdl5JI97Z6wlM7+Yt37Rl+t7trK7JKWUcokGQS1Yv/8446euIdDPm4/vu5Re0U3tLkkppVymQXCR1u07zvj31hAR7MesiYP0gvJKqQZHg+AirNt3jLumriEqNIDZEwfRMkyvH6CUani87C6goUpM1RBQSjUOGgQ1sDb1GOPfW0OL0ADmTNIQUEo1bBoEF6hiCMyeNIgWejlJpVQDp/sILsCavceYMG0NLcMCmDNxkF5TWCnVKGiLwEWrU7KYMG0NrTQElFKNjLYIXJB8NI97ZyTSKszqDooK0RBQSjUe2iI4j6z8Yu6ZvpZAP28+/NVADQGlVKOjQXAORaXlTPpgHRl5xbx7VwKtwvRkMaVU46NBUA1jDM98voV1+47z2u3xxLdtandJ7lOUC8bYXYVSyia6j6Aaby3dwxcbDvLEVXHc2Ku13eW4R8ZO+P4l2PEVNImAtgOh7QDrZ+s+4OvB3WAp/4PFL0CbfjDiWQhsZndFSrmNBkEVFmw5zN8W7WR079Y8MqKT3eXUvuwDsPRl2DQLfIPg0oeh8Djs/wl2zrfm8fKF1r2tUGjRA0SgvBQcZdbt1P1SK0Q6Xw/BkbVTnzGQmQz7VsLhjdZnVcc3EGIuh47DISD04j87PwO+/QNs/ghCWkHie7BtLlz9J4gfYy0HV+rfvwoOroP4cRDU/OLrUsqNxDSwLoGEhASTmJjotvffnJbN7f9dRbdWocyaOIgA30Z0UZkTmbD8NVj7LiDQ/1dw2RMQFHHmPAdWO29r4OB6KC8+/3uLF7QfAt1GQ5cbIfQChuEuL4XDm2H/SiuM9q+CgizrucBm4Bdc/WsLs6Ekzwqu9pdC7NUQew1ExLq20j7J4YAN78N3L0DJCRjya7j8ScjcBfOfgLS11ve74TWI6lr1e5QVw7Yv4Ke34PAma1pAUxj5AvQdD14u/C0ZA8mL4H+vWPVf8TvrO+l1LdRFEpF1xpiEKp/TIDjtcE4ho/+9Al9vL+Y+NITIkEZyecmiXFj1Jqz6N5QWQO9fwLCnISz6/K8tK4bs/daK3tvXWuF6+YC3j/XTyxeydsOOebD9S8hIAgTaDbJCoevPrC3rExmQexByD515yzlgrTRLC6zPaxYD7Qdbr283GJpfcu6VYHmpFVi7FkHyt5Cxw/k+HawVaMdh1oq7afvqV8RHt8HXj1vh134I3Pg6RHY+/fwZIZFvtaCu+C34BVnP52fAumlWwOYfhYjOMOgBq0X17XOQutzqarvhNaurqTr7VsLiP8KBnyC8IxgHHE+F6AFw5XNWy6culBZBUTaEtKybz1N1QoPABQUlZdz2n1WkZp7gswcH06VlLXQz2C3vCKyZAolTra6fbqNh+LMQGee+z0xPOh0KR7da07x8rG6kirz9rIAIbQMte1pb8+0uvfiVT/Z+2PWtFQp7l0FZoTXdJ8BqJUR2sVbykV2geSfYNNsKSf9Qq/un97jqg+dEprXfYMOHENbW2lo/8BNs/sRqNXW6ygqAS0acfg9jYOtnsOgPVkj0mwBXPg9Nwk+/7+HNsORF2P2dtUyu+B30udN6bsOH8L+/Qt4hiLnCem10lf/LtSP1R/jyYSukR/3T6g5TjYIGgQsmz9vG+6tSeXd8AiO6tKj196e8DPKPOLeEK24ZO++XFVtbr52vg+j+rnUjVOfIVmvltuUTawXc5Qa47DfQpm+tfR2XZO6GpK+gKMda4Ye2gdDW1s8mzcHLzQetlRbCkS3WTvGMJOfPnZCz/8z5+twJI190vS9/3yqruyh9O/g2gfixMPD+cwdsUa61X2b1fyAgDEZOtlofS//PCoqAplY33YBJ1n6PM75HkbWvYvlrUJAJcdfBiD9Y+26Kc62QLzhm/Tx5K8m3WkQturv2nYrzYPFkq1XTrIMVSPtXweBHrVov5u+xrhgD2fusrsSK3Z0K0CA4L2MMg/6yhL7tmvH2nedoutdE9n748XXYMPPsvnafQAhzrhwdDmvr0lFmrSRjr4a4a62tS1d2ghoDuxdb3T8pS60VVJ87rS3U8I61+50auuJ8a2d0xk6rlVCTLezyUmvruVX8mVv353N0G8x/0tofAtbvadCDMPgRCGx6/rpXvw0r/gXFOSDeYMrP/ZqOw6z373RV9cG7ewl89WvISbP+XkY8a7XYFj5tBUOnq+DWqVaA1bLS0lLS0tIoKiq6sBcah/U7KC+1DlgoL7HuGwcgVredf4jVnXkxjLH+b8uKrUB2lFpB7RsEPv71ct9NQEAA0dHR+Pqe+d01CM5j55E8rnljGS/f3JMxA9rVzpse2ws//h02zgLEamK36Vdhq7i1tSO04h9SYTbsWQI7F1rdG0XZVh98h6HWa6vbKnOUQdJ8a6s3pBUMvM/qgtBDHusnY2DLp3BsD/S7G0IusAVaeBzWTbdaGU3CITDc+l1XvA+w4QOrazDvEIRfYq3k48eCv3Pne2E2fPusNV/zWBj9JrQbeOZnrZ0K3/zW2nczdg5E1O5RdHv37iUkJITmYcFIWZHVlVdWbC0jYwDnzVT46Sg/c6NKvK1DnX0CrZV0aaHVQsJhdfkFR1mtBFeP+CottA5AKM6D4hPW+8DplX9RjhXA3n6nl7lP/difaIwhKyuLvLw8YmJiznjOtiAQkWuBfwDewLvGmJerme8W4FOgvzHmnGt5dwTBlGUp/HnBDlY+PaL6S02WFlnN7SbNz/0HlbUHlv/d6nv28oF+460jUFzZMVtReZm18zL5GysYsnade/5W8TDoIeh+E/j4XdhnqcarvNTaX/PTW9bhrP5h0O8uaNkLvnse8tNhyKNwxdPVnzeS+iN89Etr5XfrNOh0pWuf7XBAWZF1Ky2w/ofKCq0VbMZOOLqVHZE30iU6HDm5sgVrBStegIDg/Cmnf1Ze8Xv7nf0/WV4GBRnWfh1HmdXyCo6yuuBEnIFS6qypwq206HQryyfAalX4hYB/kPX/fPJ7FWVbYVOSZ03zC7FCIaCp+7s8z8MYQ1JSEl27nnl0my1BICLeQDJwFZAGrAXGGmO2V5ovBJgP+AEP2xEEv5y6msM5RSx+4oqqZ8hIhhk/s/r4fYOgaTto1t46EuXk/cBwWP8+bPnY+sPsd7cVABdyGKVS7nRgrRUI27+0VnZR3WH0v13bd3Q8FWaPs47KuvrPVuuirAiOpVgbP8f2WEePZaVY04qyrefPxT+UHSM/oGvsJc7ulkBr5Vub+yMcDig8ZgVeebH1v+nla9VWsVvtVLgEWK0H/2Br3vMpK7bev+CY1T2FWN1R3n7OW8X7flZInGrtOE7fNw6s1s95+AS41PrYsWPHBQWBO08oGwDsNsakOIuYA4wGtlea7yXgFeApN9ZSrcKSclbvPcadA9tXPUNGMky/wbp/9Z+sHbvH91k7pVJXnN4igAr9vY9eeHNfKXdr2x/aTrP2BRzaaO2HcrX12KwD3PstfHEfLHrG2u91Iv3MeYKirCOxYkdaLWefQGvl6tvEWoGdXNn7BlrzNW0PSUnQtG1tf9PTvLysHcdNmltdOicyrOmBzcA3gKycE1x5/WhAOHLkCN7e3kRGWidGrlmzBj+/6pdPYmIi77//Pv/85z8huKXVY1Cc59xfUWI9Li9h8KgJrJw3vXa+T1g0+NTSiZsVuDMI2gAHKjxOA87ogBSRvkBbY8x8EbElCFbvzaKkzMHlcVUcZZCRDDNutO5P+PrMY8vBSvLC41Yo5B62jvaprbNrlXKXsOgL76oEayv59g+sVsWRLdY5HuEdrZV6eMfaObPbXUSsnfGVdsg3D4pk40br5L/JkycTHBzMk08+eer5srIyfHyqXk0mJCSQkJBw+v39Q6xbRcaw8qe1p8PBOCp0c3lVcf88XGml1IBtQ0yIiBfwd2CCC/NOAiYBtGtXSztznZYlZ+Ln48XAmEqHDmbuskLAOGB8FSFgFWb1CzYJt04YUqqx8/KCwQ/bXYVbTZgwgYCAADZs2MCQIUMYM2YMv/71rykqKiIwMJBp06bRuXNnli5dyquvvsrXX3/N5MmT2b9/PykpKezfv5/HHnuMRx99FEQIbhpOfn4+S5cuZfLkyURERLB161b69evHhx9+iIiwYMECnnjiCYKCghgyZAgpKSl8/fXXdfad3RkEB4GKbb5o57STQoAewFKxkrAlME9ERlXeT2CMeQd4B6x9BLVZ5PJdGQyMCSfQr0K/ZOYumF4hBKK61OZHKqWq8MevtrH9UG6tvme31qG88DMXz6WoIC0tjZUrV+Lt7U1ubi7Lly/Hx8eHxYsX8/vf/57PPvvsrNckJSXxww8/kJeXR+fOnXnggQfOOoRzw4YNbNu2jdatWzNkyBBWrFhBQkIC9913H8uWLSMmJoaxY8fW+PvWlDuDYC0QKyIxWAEwBhh38kljTA5wqj9GRJYCT55vZ3FtOpRdyK70fG5PqJBXp0KgXENAKQ9122234e1tbRzm5OQwfvx4du3ahYhQWlr1IIg33HAD/v7++Pv7ExUVxdGjR4mOPrMLbsCAAaem9e7dm9TUVIKDg+nYseOpwz3Hjh3LO++848Zvdza3BYExpkxEHgYWYR0++p4xZpuIvAgkGmPmueuzXbV8l7Xj6PI4Z79+5m4rBBxl1j4BDQGl6kxNttzdJSgo6NT95557juHDh/PFF1+QmprKsGHDqnyNv//po3m8vb0pKyur0Tx2cOs+AmPMAmBBpWnPVzPvMHfWUpVlyZm0DA0gLsLPOgLos3srhEA1I0wqpTxKTk4Obdq0AWD69Om1/v6dO3cmJSWF1NRUOnTowEcffVTrn3E+nneFMmMg+wCOLZ8zaNerzPF+DvlLW5h+vXXyzfivNASUUqf89re/5ZlnnqFPnz5u2YIPDAzkrbfe4tprr6Vfv36EhIQQFlb7w3mci+cMMbHrO+u0/LRE68QwoMj4ciKiF807D7YO/exw2YWNG6OUuihVnfjkifLz8wkODsYYw0MPPURsbCyPP/54jd+vPp1QVr/kHrRGi+x4BUT3Z9ahKF5YDWvuuQ6CdEgGpZR9pkyZwowZMygpKaFPnz7cd999dfr5nhMEfcdbA7E5ffrWCrq1MTTTEFBK2ezxxx+/qBbAxfKcfQQVztrLKShl44Hs00cLKaWUB/OcIKhgxZ5MHAYNAqWUwkODYPmuDEL8fejdtqndpSillO08LgiMMSxLzmRwp+b4envc11dKqbN43JpwT8YJDmYXareQUorhw4ezaNGiM6a98cYbPPDAA1XOP2zYME4evn799deTnZ191jyTJ0/m1VdfPefnzp07l+3bT4/I//zzz7N48eILrL72eFwQLEt2DisRq0GglKcbO3Ysc+bMOWPanDlzXBr4bcGCBTRt2rRGn1s5CF588UVGjhxZo/eqDZ4XBLsy6BgRRNvwJnaXopSy2a233sr8+fMpKSkBIDU1lUOHDjF79mwSEhLo3r07L7zwQpWv7dChA5mZmQD8+c9/Ji4ujqFDh7Jz585T80yZMoX+/fsTHx/PLbfcQkFBAStXrmTevHk89dRT9O7dmz179jBhwgQ+/fRTAJYsWUKfPn3o2bMn99xzD8XFxac+74UXXqBv37707NmTpKSkWlsOnnMeAVBUWs5PKVmM6V+71zRQStWCb562LnhTm1r2hOuqvFQ6AOHh4QwYMIBvvvmG0aNHM2fOHG6//XZ+//vfEx4eTnl5OVdeeSWbN2+mV69eVb7HunXrmDNnDhs3bqSsrIy+ffvSr18/AG6++WYmTpwIwLPPPsvUqVN55JFHGDVqFDfeeCO33nrrGe9VVFTEhAkTWLJkCXFxcdx11128/fbbPPbYYwBERESwfv163nrrLV599VXefffdWlhIHtYiSEw9TlGpg8tiq7gamVLKI1XsHjrZLfTxxx/Tt29f+vTpw7Zt287oxqls+fLl3HTTTTRp0oTQ0FBGjRp16rmtW7dy2WWX0bNnT2bOnMm2bdvOWcvOnTuJiYkhLi4OgPHjx7Ns2bJTz998880A9OvXj9TU1Jp+5bN4VItg2a4MfL2FQR2bn39mpVTdOseWuzuNHj2axx9/nPXr11NQUEB4eDivvvoqa9eupVmzZkyYMIGioqIavfeECROYO3cu8fHxTJ8+naVLl15UrSeHsa7tIaw9qkWwLDmDhPbhBPl7VP4ppc4hODiY4cOHc8899zB27Fhyc3MJCgoiLCyMo0eP8s0335zz9Zdffjlz586lsLCQvLw8vvrqq1PP5eXl0apVK0pLS5k5c+ap6SEhIeTl5Z31Xp07dyY1NZXdu3cD8MEHH3DFFVfU0jetnscEwdHcIpKO5Olho0qps4wdO5ZNmzYxduxY4uPj6dOnD126dGHcuHEMGTLknK/t27cvd9xxB/Hx8Vx33XX079//1HMvvfQSAwcOZMiQIXTpcvpCV2PGjOFvf/sbffr0Yc+ePaemBwQEMG3aNG677TZ69uyJl5cX999/f+1/4Uo8ZhjqT9el8eQnm5j/6FC6t67bsb6VUlXTYajd40KHofaYFkFYoC9XdWtB15ahdpeilFL1isd0ll/VrQVXdWthdxlKKVXveEyLQCmlVNU0CJRStmpo+ynru5osTw0CpZRtAgICyMrK0jCoJcYYsrKyCAgIuKDXecw+AqVU/RMdHU1aWhoZGRl2l9JoBAQEEB0dfUGv0SBQStnG19eXmJgYu8vweNo1pJRSHk6DQCmlPJwGgVJKebgGN8SEiGQA+2r48gggsxbLqU1aW81obTWjtdVMQ66tvTGmysHWGlwQXAwRSaxurA27aW01o7XVjNZWM421Nu0aUkopD6dBoJRSHs7TguAduws4B62tZrS2mtHaaqZR1uZR+wiUUkqdzdNaBEoppSrxmCAQkWtFZKeI7BaRp+2upyIRSRWRLSKyUUQu/PJrtVvLeyKSLiJbK0wLF5HvRGSX82ezelTbZBE56Fx2G0XkeptqaysiP4jIdhHZJiK/dk63fdmdozbbl52IBIjIGhHZ5Kztj87pMSKy2vn/+pGI+NWj2qaLyN4Ky613XddWoUZvEdkgIl87H9dsuRljGv0N8Ab2AB0BP2AT0M3uuirUlwpE2F2Hs5bLgb7A1grT/go87bz/NPBKPaptMvBkPVhurYC+zvshQDLQrT4su3PUZvuyAwQIdt73BVYDg4CPgTHO6f8BHqhHtU0HbrX7b85Z1xPALOBr5+MaLTdPaREMAHYbY1KMMSXAHGC0zTXVS8aYZcCxSpNHAzOc92cAP6/Lmk6qprZ6wRhz2Biz3nk/D9gBtKEeLLtz1GY7Y8l3PvR13gwwAvjUOd2u5VZdbfWCiEQDNwDvOh8LNVxunhIEbYADFR6nUU/+EZwM8K2IrBORSXYXU4UWxpjDzvtHgPp2zc+HRWSzs+vIlm6rikSkA9AHawuyXi27SrVBPVh2zu6NjUA68B1W6z3bGFPmnMW2/9fKtRljTi63PzuX2+si4m9HbcAbwG8Bh/Nxc2q43DwlCOq7ocaYvsB1wEMicrndBVXHWG3OerNVBLwNXAL0Bg4Dr9lZjIgEA58Bjxljcis+Z/eyq6K2erHsjDHlxpjeQDRW672LHXVUpXJtItIDeAarxv5AOPC7uq5LRG4E0o0x62rj/TwlCA4CbSs8jnZOqxeMMQedP9OBL7D+GeqToyLSCsD5M93mek4xxhx1/rM6gCnYuOxExBdrRTvTGPO5c3K9WHZV1Vaflp2znmzgB+BSoKmInLxeiu3/rxVqu9bZ1WaMMcXANOxZbkOAUSKSitXVPQL4BzVcbp4SBGuBWOcedT9gDDDP5poAEJEgEQk5eR+4Gth67lfVuXnAeOf98cCXNtZyhpMrWaebsGnZOftnpwI7jDF/r/CU7cuuutrqw7ITkUgRaeq8HwhchbUP4wfgVudsdi23qmpLqhDsgtUHX+fLzRjzjDEm2hjTAWt99r0x5hfUdLnZvde7rm7A9VhHS+wB/mB3PRXq6oh1FNMmYJvdtQGzsboJSrH6GO/F6ntcAuwCFgPh9ai2D4AtwGaslW4rm2obitXtsxnY6LxdXx+W3Tlqs33ZAb2ADc4atgLPO6d3BNYAu4FPAP96VNv3zuW2FfgQ55FFdt2AYZw+aqhGy03PLFZKKQ/nKV1DSimlqqFBoJRSHk6DQCmlPJwGgVJKeTgNAqWU8nAaBEo5iUh5hRElN0otjlIrIh0qjpqqVH3ic/5ZlPIYhcYaTkApj6ItAqXOQ6zrRfxVrGtGrBGRTs7pHUTke+fgY0tEpJ1zegsR+cI5jv0mERnsfCtvEZniHNv+W+fZqojIo85rBWwWkTk2fU3lwTQIlDotsFLX0B0VnssxxvQE/o016iPAv4AZxphewEzgn87p/wT+Z4yJx7p+wjbn9FjgTWNMdyAbuMU5/Wmgj/N97nfPV1OqenpmsVJOIpJvjAmuYnoqMMIYk+IcvO2IMaa5iGRiDctQ6px+2BgTISIZQLSxBiU7+R4dsIYxjnU+/h3ga4z5k4gsBPKBucBcc3oMfKXqhLYIlHKNqeb+hSiucL+c0/vobgDexGo9rK0weqRSdUKDQCnX3FHh5yrn/ZVYIz8C/AJY7ry/BHgATl3YJKy6NxURL6CtMeYHrHHtw4CzWiVKuZNueSh1WqDzalQnLTTGnDyEtJmIbMbaqh/rnPYIME1EngIygLud038NvCMi92Jt+T+ANWpqVbyBD51hIcA/jTX2vVJ1RvcRKHUezn0ECcaYTLtrUcodtGtIKaU8nLYIlFLKw2mLQCmlPJwGgVJKeTgNAqWU8nAaBEop5eE0CJRSysNpECillIf7f1WZ8KU07fPWAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "What do you think? Does it overfit? "
      ],
      "metadata": {
        "id": "tgG7QeXF-dx6"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Q9rIeBBxprO"
      },
      "source": [
        "# Inspecting the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6r2AmmoMxprP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7f3e2d78-dfb6-42e1-d37f-279066f357bb"
      },
      "source": [
        "model.summary()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model: \"sequential\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense (Dense)               (None, 128)               393344    \n",
            "                                                                 \n",
            " dense_1 (Dense)             (None, 128)               16512     \n",
            "                                                                 \n",
            " dense_2 (Dense)             (None, 10)                1290      \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 411,146\n",
            "Trainable params: 411,146\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D3-bVDVuxprS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9e19a9fe-250f-4882-d925-5feace20dc02"
      },
      "source": [
        "print('Input: ', model.input)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Input:  KerasTensor(type_spec=TensorSpec(shape=(None, 3072), dtype=tf.float32, name='dense_input'), name='dense_input', description=\"created by layer 'dense_input'\")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Da2OJ3DmxprX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "47978ac9-2560-4ccd-9209-926b98aa6589"
      },
      "source": [
        "print('Layers:\\n')\n",
        "for layer in model.layers:\n",
        "    print(\"Layer's name: \", layer.name, ', trainable: ', layer.trainable)\n",
        "    print(layer.get_config(),'\\n')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Layers:\n",
            "\n",
            "Layer's name:  dense , trainable:  True\n",
            "{'name': 'dense', 'trainable': True, 'dtype': 'float32', 'batch_input_shape': (None, 3072), 'units': 128, 'activation': 'tanh', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None} \n",
            "\n",
            "Layer's name:  dense_1 , trainable:  True\n",
            "{'name': 'dense_1', 'trainable': True, 'dtype': 'float32', 'units': 128, 'activation': 'tanh', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None} \n",
            "\n",
            "Layer's name:  dense_2 , trainable:  True\n",
            "{'name': 'dense_2', 'trainable': True, 'dtype': 'float32', 'units': 10, 'activation': 'softmax', 'use_bias': True, 'kernel_initializer': {'class_name': 'GlorotUniform', 'config': {'seed': None}}, 'bias_initializer': {'class_name': 'Zeros', 'config': {}}, 'kernel_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None} \n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AtVX3M3lxprc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2287f7c5-4ab3-4f3e-ef9d-e823000f5172"
      },
      "source": [
        "print('Output: ', model.output)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Output:  KerasTensor(type_spec=TensorSpec(shape=(None, 10), dtype=tf.float32, name=None), name='dense_2/Softmax:0', description=\"created by layer 'dense_2'\")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 2.1. Exercise\n",
        "Introduce [early stopping](https://www.tensorflow.org/api_docs/python/tf/keras/callbacks/EarlyStopping) and [dropout](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dropout) with a rate between 0.1..0.5. Tips:\n",
        "\n",
        "* Insert the dropout layer between the two Dense layers. \n",
        "* Set the patience of early stopping to 5.\n",
        "* Set the number of epochs to a very high number.\n",
        "* Don't forget to restore best weights after early stopping. \n",
        "* And also set early stopping to monitor validation accuracy (the default value is validation loss -- which is categorical crossentropy now).\n",
        "\n",
        "Compile and train the model. Attempt to increase the validation accuracy as much as possible by making changes to the dropout rate. Inspect the effects of the modifications."
      ],
      "metadata": {
        "id": "E-hHfs9qA_iO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "es = EarlyStopping(monitor='val_accuracy',patience = 5,restore_best_weights=True)"
      ],
      "metadata": {
        "id": "NwXrPzOgEBG-"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# model definition with dropout\n",
        "model = Sequential()\n",
        "model.add(Dense(128, activation='tanh', input_shape=(flattened_dim,)))\n",
        "model.add(Dropout(.5,input_shape=(flattened_dim,)))\n",
        "model.add(Dense(128, activation='tanh'))\n",
        "model.add(Dense(nb_classes, activation='softmax'))\n",
        "\n",
        "# loss function and optimizer\n",
        "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
      ],
      "metadata": {
        "id": "7hZEGzj8GFwP"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# training with early stopping\n",
        "network_history = model.fit(X_train, Y_train, \n",
        "                            validation_data=(X_valid,Y_valid),\n",
        "                            batch_size=128,                             \n",
        "                            epochs=100, \n",
        "                            verbose=1, \n",
        "                            callbacks=[es])"
      ],
      "metadata": {
        "id": "GCG54R-vGGWj",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0f06b8c0-a399-4afe-a689-d5c8118b5303"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "313/313 [==============================] - 4s 6ms/step - loss: 1.9554 - accuracy: 0.3083 - val_loss: 1.8055 - val_accuracy: 0.3631\n",
            "Epoch 2/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.8549 - accuracy: 0.3430 - val_loss: 1.7645 - val_accuracy: 0.3859\n",
            "Epoch 3/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.8134 - accuracy: 0.3580 - val_loss: 1.7490 - val_accuracy: 0.3949\n",
            "Epoch 4/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.7815 - accuracy: 0.3724 - val_loss: 1.7250 - val_accuracy: 0.4021\n",
            "Epoch 5/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.7584 - accuracy: 0.3817 - val_loss: 1.7082 - val_accuracy: 0.4064\n",
            "Epoch 6/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.7447 - accuracy: 0.3854 - val_loss: 1.7014 - val_accuracy: 0.4108\n",
            "Epoch 7/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.7296 - accuracy: 0.3950 - val_loss: 1.6755 - val_accuracy: 0.4207\n",
            "Epoch 8/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.7095 - accuracy: 0.4003 - val_loss: 1.6688 - val_accuracy: 0.4190\n",
            "Epoch 9/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6964 - accuracy: 0.4049 - val_loss: 1.6577 - val_accuracy: 0.4229\n",
            "Epoch 10/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6909 - accuracy: 0.4047 - val_loss: 1.6528 - val_accuracy: 0.4254\n",
            "Epoch 11/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.6792 - accuracy: 0.4119 - val_loss: 1.6420 - val_accuracy: 0.4259\n",
            "Epoch 12/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6671 - accuracy: 0.4167 - val_loss: 1.6344 - val_accuracy: 0.4283\n",
            "Epoch 13/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.6558 - accuracy: 0.4163 - val_loss: 1.6480 - val_accuracy: 0.4246\n",
            "Epoch 14/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.6486 - accuracy: 0.4207 - val_loss: 1.6218 - val_accuracy: 0.4329\n",
            "Epoch 15/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.6353 - accuracy: 0.4245 - val_loss: 1.6199 - val_accuracy: 0.4326\n",
            "Epoch 16/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.6270 - accuracy: 0.4272 - val_loss: 1.6181 - val_accuracy: 0.4345\n",
            "Epoch 17/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.6197 - accuracy: 0.4296 - val_loss: 1.6014 - val_accuracy: 0.4408\n",
            "Epoch 18/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.6122 - accuracy: 0.4304 - val_loss: 1.5938 - val_accuracy: 0.4395\n",
            "Epoch 19/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6043 - accuracy: 0.4319 - val_loss: 1.5900 - val_accuracy: 0.4460\n",
            "Epoch 20/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.6001 - accuracy: 0.4316 - val_loss: 1.5833 - val_accuracy: 0.4411\n",
            "Epoch 21/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5961 - accuracy: 0.4353 - val_loss: 1.5751 - val_accuracy: 0.4463\n",
            "Epoch 22/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5858 - accuracy: 0.4386 - val_loss: 1.5717 - val_accuracy: 0.4453\n",
            "Epoch 23/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5827 - accuracy: 0.4409 - val_loss: 1.5684 - val_accuracy: 0.4469\n",
            "Epoch 24/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5775 - accuracy: 0.4416 - val_loss: 1.5588 - val_accuracy: 0.4527\n",
            "Epoch 25/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.5685 - accuracy: 0.4459 - val_loss: 1.5579 - val_accuracy: 0.4515\n",
            "Epoch 26/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5653 - accuracy: 0.4496 - val_loss: 1.5523 - val_accuracy: 0.4543\n",
            "Epoch 27/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5595 - accuracy: 0.4488 - val_loss: 1.5481 - val_accuracy: 0.4512\n",
            "Epoch 28/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5575 - accuracy: 0.4484 - val_loss: 1.5529 - val_accuracy: 0.4535\n",
            "Epoch 29/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5528 - accuracy: 0.4521 - val_loss: 1.5368 - val_accuracy: 0.4609\n",
            "Epoch 30/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5511 - accuracy: 0.4508 - val_loss: 1.5322 - val_accuracy: 0.4596\n",
            "Epoch 31/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5449 - accuracy: 0.4516 - val_loss: 1.5316 - val_accuracy: 0.4613\n",
            "Epoch 32/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5428 - accuracy: 0.4558 - val_loss: 1.5331 - val_accuracy: 0.4593\n",
            "Epoch 33/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.5402 - accuracy: 0.4543 - val_loss: 1.5231 - val_accuracy: 0.4635\n",
            "Epoch 34/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5357 - accuracy: 0.4575 - val_loss: 1.5273 - val_accuracy: 0.4644\n",
            "Epoch 35/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5326 - accuracy: 0.4579 - val_loss: 1.5242 - val_accuracy: 0.4687\n",
            "Epoch 36/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5292 - accuracy: 0.4581 - val_loss: 1.5180 - val_accuracy: 0.4643\n",
            "Epoch 37/100\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5202 - accuracy: 0.4626 - val_loss: 1.5207 - val_accuracy: 0.4642\n",
            "Epoch 38/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5291 - accuracy: 0.4578 - val_loss: 1.5145 - val_accuracy: 0.4687\n",
            "Epoch 39/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5237 - accuracy: 0.4598 - val_loss: 1.5105 - val_accuracy: 0.4716\n",
            "Epoch 40/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5189 - accuracy: 0.4627 - val_loss: 1.5207 - val_accuracy: 0.4636\n",
            "Epoch 41/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.5068 - accuracy: 0.4651 - val_loss: 1.5125 - val_accuracy: 0.4672\n",
            "Epoch 42/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5067 - accuracy: 0.4684 - val_loss: 1.5070 - val_accuracy: 0.4709\n",
            "Epoch 43/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5080 - accuracy: 0.4651 - val_loss: 1.5158 - val_accuracy: 0.4688\n",
            "Epoch 44/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.5039 - accuracy: 0.4688 - val_loss: 1.5081 - val_accuracy: 0.4654\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 2.2 Exercise\n",
        "Change the [activation function of the dense layers (except the last one)](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Dense) to rectified linear unit (ReLU) and the [weight initialization](https://www.tensorflow.org/api_docs/python/tf/keras/initializers) to the theoretically best one. Use the original model's code.\n",
        "\n",
        "Compile and train the model. Inspect the effects of the modifications."
      ],
      "metadata": {
        "id": "zQCDM1o1BBtF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# model definition with relu\n",
        "model = Sequential()\n",
        "model.add(Dense(128, activation='relu', kernel_initializer=HeNormal(), input_shape=(flattened_dim,)))\n",
        "model.add(Dense(128, activation='relu', kernel_initializer=HeNormal()))\n",
        "model.add(Dense(nb_classes, activation='softmax'))\n",
        "\n",
        "# loss function and optimizer\n",
        "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
      ],
      "metadata": {
        "id": "YjHAAh-wGu9O"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# training\n",
        "network_history = model.fit(X_train, Y_train, \n",
        "                            validation_data=(X_valid,Y_valid),\n",
        "                            batch_size=128,                             \n",
        "                            epochs=40, \n",
        "                            verbose=1)"
      ],
      "metadata": {
        "id": "rarwKM1wGxMz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e2a58626-451e-487e-ca72-ef0b578dca94"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/40\n",
            "313/313 [==============================] - 3s 6ms/step - loss: 1.8406 - accuracy: 0.3749 - val_loss: 1.6835 - val_accuracy: 0.4113\n",
            "Epoch 2/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.5427 - accuracy: 0.4611 - val_loss: 1.5983 - val_accuracy: 0.4440\n",
            "Epoch 3/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.4216 - accuracy: 0.5035 - val_loss: 1.5491 - val_accuracy: 0.4634\n",
            "Epoch 4/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.3330 - accuracy: 0.5333 - val_loss: 1.5189 - val_accuracy: 0.4769\n",
            "Epoch 5/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.2594 - accuracy: 0.5580 - val_loss: 1.5222 - val_accuracy: 0.4739\n",
            "Epoch 6/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2040 - accuracy: 0.5796 - val_loss: 1.5190 - val_accuracy: 0.4837\n",
            "Epoch 7/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1543 - accuracy: 0.5958 - val_loss: 1.5215 - val_accuracy: 0.4916\n",
            "Epoch 8/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.0991 - accuracy: 0.6159 - val_loss: 1.5304 - val_accuracy: 0.4868\n",
            "Epoch 9/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.0469 - accuracy: 0.6308 - val_loss: 1.5659 - val_accuracy: 0.4934\n",
            "Epoch 10/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 1.0017 - accuracy: 0.6471 - val_loss: 1.5793 - val_accuracy: 0.4932\n",
            "Epoch 11/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9707 - accuracy: 0.6594 - val_loss: 1.6006 - val_accuracy: 0.4962\n",
            "Epoch 12/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.9213 - accuracy: 0.6775 - val_loss: 1.6358 - val_accuracy: 0.4961\n",
            "Epoch 13/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.8826 - accuracy: 0.6885 - val_loss: 1.6588 - val_accuracy: 0.4997\n",
            "Epoch 14/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.8491 - accuracy: 0.7024 - val_loss: 1.7106 - val_accuracy: 0.4944\n",
            "Epoch 15/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.8170 - accuracy: 0.7125 - val_loss: 1.7583 - val_accuracy: 0.4915\n",
            "Epoch 16/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.7747 - accuracy: 0.7261 - val_loss: 1.7657 - val_accuracy: 0.4952\n",
            "Epoch 17/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.7439 - accuracy: 0.7400 - val_loss: 1.7942 - val_accuracy: 0.4920\n",
            "Epoch 18/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.7078 - accuracy: 0.7487 - val_loss: 1.8782 - val_accuracy: 0.4961\n",
            "Epoch 19/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.6876 - accuracy: 0.7579 - val_loss: 1.9050 - val_accuracy: 0.4880\n",
            "Epoch 20/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.6533 - accuracy: 0.7705 - val_loss: 1.9553 - val_accuracy: 0.4902\n",
            "Epoch 21/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.6220 - accuracy: 0.7814 - val_loss: 2.0034 - val_accuracy: 0.4919\n",
            "Epoch 22/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.6083 - accuracy: 0.7843 - val_loss: 2.0917 - val_accuracy: 0.4913\n",
            "Epoch 23/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.5830 - accuracy: 0.7957 - val_loss: 2.0809 - val_accuracy: 0.4960\n",
            "Epoch 24/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.5526 - accuracy: 0.8067 - val_loss: 2.1871 - val_accuracy: 0.4884\n",
            "Epoch 25/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.5260 - accuracy: 0.8157 - val_loss: 2.2494 - val_accuracy: 0.4801\n",
            "Epoch 26/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.5175 - accuracy: 0.8181 - val_loss: 2.2838 - val_accuracy: 0.4896\n",
            "Epoch 27/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.4908 - accuracy: 0.8262 - val_loss: 2.3754 - val_accuracy: 0.4864\n",
            "Epoch 28/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.4821 - accuracy: 0.8326 - val_loss: 2.4257 - val_accuracy: 0.4885\n",
            "Epoch 29/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.4458 - accuracy: 0.8443 - val_loss: 2.4466 - val_accuracy: 0.4867\n",
            "Epoch 30/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.4360 - accuracy: 0.8480 - val_loss: 2.5607 - val_accuracy: 0.4810\n",
            "Epoch 31/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.4277 - accuracy: 0.8490 - val_loss: 2.6085 - val_accuracy: 0.4793\n",
            "Epoch 32/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.3993 - accuracy: 0.8592 - val_loss: 2.7081 - val_accuracy: 0.4764\n",
            "Epoch 33/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.3975 - accuracy: 0.8601 - val_loss: 2.7196 - val_accuracy: 0.4888\n",
            "Epoch 34/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.3781 - accuracy: 0.8671 - val_loss: 2.8458 - val_accuracy: 0.4799\n",
            "Epoch 35/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.3786 - accuracy: 0.8685 - val_loss: 2.8414 - val_accuracy: 0.4804\n",
            "Epoch 36/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.3551 - accuracy: 0.8757 - val_loss: 2.9239 - val_accuracy: 0.4782\n",
            "Epoch 37/40\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.3580 - accuracy: 0.8740 - val_loss: 3.0325 - val_accuracy: 0.4788\n",
            "Epoch 38/40\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.3451 - accuracy: 0.8786 - val_loss: 3.1020 - val_accuracy: 0.4765\n",
            "Epoch 39/40\n",
            "313/313 [==============================] - 1s 4ms/step - loss: 0.3160 - accuracy: 0.8899 - val_loss: 3.0915 - val_accuracy: 0.4828\n",
            "Epoch 40/40\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.3081 - accuracy: 0.8938 - val_loss: 3.2148 - val_accuracy: 0.4762\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2.3. Exercise\n",
        "Based on the modifications above, and by any further modifications (e.g. more layers, less layers, more neurons/layer, etc.) to the model design, find a combination that is able to achieve **validation accuracy, that is higher than 53%**.\n"
      ],
      "metadata": {
        "id": "j1tGVPdD-pp3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "es = EarlyStopping(monitor='val_accuracy',patience = 5,restore_best_weights=True)"
      ],
      "metadata": {
        "id": "5dBQxJHIHrbd"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# model definition with relu\n",
        "model = Sequential()\n",
        "initiliazer = LecunUniform()\n",
        "model.add(Dense(128, activation='relu', kernel_initializer=initiliazer, input_shape=(flattened_dim,)))\n",
        "model.add(Dropout(.35,input_shape=(flattened_dim,)))\n",
        "model.add(Dense(128, activation='relu', kernel_initializer=initiliazer))\n",
        "model.add(Dense(128, activation='relu', kernel_initializer=initiliazer))\n",
        "model.add(Dense(128, activation='relu', kernel_initializer=initiliazer))\n",
        "model.add(Dense(nb_classes, activation='softmax'))\n",
        "\n",
        "# loss function and optimizer\n",
        "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
      ],
      "metadata": {
        "id": "PuxHOqLt-3Nd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b1f7e4d1-f2df-459c-d3b6-4f4e6b272145"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/keras/initializers/initializers_v2.py:120: UserWarning: The initializer LecunUniform is unseeded and being called multiple times, which will return identical values  each time (even if the initializer is unseeded). Please update your code to provide a seed to the initializer, or avoid using the same initalizer instance more than once.\n",
            "  warnings.warn(\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# training\n",
        "network_history = model.fit(X_train, Y_train, \n",
        "                            validation_data=(X_valid,Y_valid),\n",
        "                            batch_size=128,                             \n",
        "                            epochs=100, \n",
        "                            verbose=1)"
      ],
      "metadata": {
        "id": "u8tFNCNVHyt9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3b4d20b9-dda1-4568-ed2d-0145dd12c4d7"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/100\n",
            "313/313 [==============================] - 3s 6ms/step - loss: 1.8629 - accuracy: 0.3306 - val_loss: 1.6912 - val_accuracy: 0.3991\n",
            "Epoch 2/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 1.6983 - accuracy: 0.3957 - val_loss: 1.5941 - val_accuracy: 0.4339\n",
            "Epoch 3/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.6187 - accuracy: 0.4245 - val_loss: 1.5514 - val_accuracy: 0.4455\n",
            "Epoch 4/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5726 - accuracy: 0.4408 - val_loss: 1.5181 - val_accuracy: 0.4644\n",
            "Epoch 5/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5388 - accuracy: 0.4505 - val_loss: 1.5078 - val_accuracy: 0.4710\n",
            "Epoch 6/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.5038 - accuracy: 0.4653 - val_loss: 1.4690 - val_accuracy: 0.4852\n",
            "Epoch 7/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.4769 - accuracy: 0.4759 - val_loss: 1.4689 - val_accuracy: 0.4865\n",
            "Epoch 8/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.4515 - accuracy: 0.4823 - val_loss: 1.4550 - val_accuracy: 0.4896\n",
            "Epoch 9/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.4290 - accuracy: 0.4902 - val_loss: 1.4373 - val_accuracy: 0.4922\n",
            "Epoch 10/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.4136 - accuracy: 0.4965 - val_loss: 1.4255 - val_accuracy: 0.4990\n",
            "Epoch 11/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3909 - accuracy: 0.5029 - val_loss: 1.4171 - val_accuracy: 0.5048\n",
            "Epoch 12/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3697 - accuracy: 0.5095 - val_loss: 1.4023 - val_accuracy: 0.5022\n",
            "Epoch 13/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3598 - accuracy: 0.5148 - val_loss: 1.4076 - val_accuracy: 0.5026\n",
            "Epoch 14/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.3428 - accuracy: 0.5199 - val_loss: 1.3951 - val_accuracy: 0.5114\n",
            "Epoch 15/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3421 - accuracy: 0.5214 - val_loss: 1.3809 - val_accuracy: 0.5142\n",
            "Epoch 16/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.3191 - accuracy: 0.5282 - val_loss: 1.3771 - val_accuracy: 0.5187\n",
            "Epoch 17/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.3084 - accuracy: 0.5337 - val_loss: 1.3829 - val_accuracy: 0.5060\n",
            "Epoch 18/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.2985 - accuracy: 0.5365 - val_loss: 1.3914 - val_accuracy: 0.5084\n",
            "Epoch 19/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2852 - accuracy: 0.5405 - val_loss: 1.3750 - val_accuracy: 0.5157\n",
            "Epoch 20/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2766 - accuracy: 0.5423 - val_loss: 1.3736 - val_accuracy: 0.5205\n",
            "Epoch 21/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2636 - accuracy: 0.5460 - val_loss: 1.3655 - val_accuracy: 0.5205\n",
            "Epoch 22/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2582 - accuracy: 0.5503 - val_loss: 1.3699 - val_accuracy: 0.5183\n",
            "Epoch 23/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2467 - accuracy: 0.5522 - val_loss: 1.3567 - val_accuracy: 0.5179\n",
            "Epoch 24/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.2441 - accuracy: 0.5559 - val_loss: 1.3649 - val_accuracy: 0.5189\n",
            "Epoch 25/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.2312 - accuracy: 0.5602 - val_loss: 1.3504 - val_accuracy: 0.5271\n",
            "Epoch 26/100\n",
            "313/313 [==============================] - 2s 8ms/step - loss: 1.2225 - accuracy: 0.5645 - val_loss: 1.3499 - val_accuracy: 0.5245\n",
            "Epoch 27/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 1.2127 - accuracy: 0.5659 - val_loss: 1.3572 - val_accuracy: 0.5262\n",
            "Epoch 28/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.2046 - accuracy: 0.5671 - val_loss: 1.3661 - val_accuracy: 0.5193\n",
            "Epoch 29/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1994 - accuracy: 0.5713 - val_loss: 1.3532 - val_accuracy: 0.5288\n",
            "Epoch 30/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1882 - accuracy: 0.5750 - val_loss: 1.3675 - val_accuracy: 0.5236\n",
            "Epoch 31/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.1842 - accuracy: 0.5781 - val_loss: 1.3597 - val_accuracy: 0.5214\n",
            "Epoch 32/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 1.1772 - accuracy: 0.5802 - val_loss: 1.3641 - val_accuracy: 0.5243\n",
            "Epoch 33/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1717 - accuracy: 0.5800 - val_loss: 1.3409 - val_accuracy: 0.5312\n",
            "Epoch 34/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1678 - accuracy: 0.5805 - val_loss: 1.3684 - val_accuracy: 0.5248\n",
            "Epoch 35/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1568 - accuracy: 0.5857 - val_loss: 1.3664 - val_accuracy: 0.5267\n",
            "Epoch 36/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1502 - accuracy: 0.5874 - val_loss: 1.3557 - val_accuracy: 0.5243\n",
            "Epoch 37/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1468 - accuracy: 0.5911 - val_loss: 1.3614 - val_accuracy: 0.5272\n",
            "Epoch 38/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1420 - accuracy: 0.5914 - val_loss: 1.3802 - val_accuracy: 0.5117\n",
            "Epoch 39/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.1321 - accuracy: 0.5921 - val_loss: 1.3533 - val_accuracy: 0.5275\n",
            "Epoch 40/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1338 - accuracy: 0.5943 - val_loss: 1.3532 - val_accuracy: 0.5318\n",
            "Epoch 41/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1281 - accuracy: 0.5995 - val_loss: 1.3514 - val_accuracy: 0.5308\n",
            "Epoch 42/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1176 - accuracy: 0.5982 - val_loss: 1.3478 - val_accuracy: 0.5263\n",
            "Epoch 43/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1175 - accuracy: 0.5980 - val_loss: 1.3549 - val_accuracy: 0.5284\n",
            "Epoch 44/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.1068 - accuracy: 0.6019 - val_loss: 1.3683 - val_accuracy: 0.5271\n",
            "Epoch 45/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.1066 - accuracy: 0.6026 - val_loss: 1.3584 - val_accuracy: 0.5276\n",
            "Epoch 46/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0931 - accuracy: 0.6079 - val_loss: 1.3427 - val_accuracy: 0.5298\n",
            "Epoch 47/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 1.1000 - accuracy: 0.6054 - val_loss: 1.3807 - val_accuracy: 0.5268\n",
            "Epoch 48/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0915 - accuracy: 0.6101 - val_loss: 1.3704 - val_accuracy: 0.5236\n",
            "Epoch 49/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.0820 - accuracy: 0.6125 - val_loss: 1.3823 - val_accuracy: 0.5197\n",
            "Epoch 50/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0810 - accuracy: 0.6112 - val_loss: 1.3667 - val_accuracy: 0.5280\n",
            "Epoch 51/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0771 - accuracy: 0.6138 - val_loss: 1.3670 - val_accuracy: 0.5312\n",
            "Epoch 52/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 1.0660 - accuracy: 0.6176 - val_loss: 1.3726 - val_accuracy: 0.5290\n",
            "Epoch 53/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0684 - accuracy: 0.6180 - val_loss: 1.3730 - val_accuracy: 0.5255\n",
            "Epoch 54/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.0648 - accuracy: 0.6183 - val_loss: 1.3802 - val_accuracy: 0.5249\n",
            "Epoch 55/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.0557 - accuracy: 0.6202 - val_loss: 1.3881 - val_accuracy: 0.5212\n",
            "Epoch 56/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0531 - accuracy: 0.6242 - val_loss: 1.3756 - val_accuracy: 0.5272\n",
            "Epoch 57/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0541 - accuracy: 0.6208 - val_loss: 1.3837 - val_accuracy: 0.5222\n",
            "Epoch 58/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0478 - accuracy: 0.6251 - val_loss: 1.3672 - val_accuracy: 0.5283\n",
            "Epoch 59/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0466 - accuracy: 0.6244 - val_loss: 1.3731 - val_accuracy: 0.5331\n",
            "Epoch 60/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0395 - accuracy: 0.6294 - val_loss: 1.3753 - val_accuracy: 0.5251\n",
            "Epoch 61/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0328 - accuracy: 0.6333 - val_loss: 1.3766 - val_accuracy: 0.5265\n",
            "Epoch 62/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 1.0280 - accuracy: 0.6348 - val_loss: 1.3789 - val_accuracy: 0.5252\n",
            "Epoch 63/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0247 - accuracy: 0.6332 - val_loss: 1.3900 - val_accuracy: 0.5279\n",
            "Epoch 64/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0277 - accuracy: 0.6347 - val_loss: 1.3665 - val_accuracy: 0.5350\n",
            "Epoch 65/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0241 - accuracy: 0.6344 - val_loss: 1.3753 - val_accuracy: 0.5310\n",
            "Epoch 66/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0120 - accuracy: 0.6392 - val_loss: 1.3831 - val_accuracy: 0.5275\n",
            "Epoch 67/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0205 - accuracy: 0.6349 - val_loss: 1.3783 - val_accuracy: 0.5327\n",
            "Epoch 68/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0166 - accuracy: 0.6373 - val_loss: 1.3916 - val_accuracy: 0.5270\n",
            "Epoch 69/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.0045 - accuracy: 0.6421 - val_loss: 1.3759 - val_accuracy: 0.5284\n",
            "Epoch 70/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 1.0072 - accuracy: 0.6395 - val_loss: 1.3757 - val_accuracy: 0.5304\n",
            "Epoch 71/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0023 - accuracy: 0.6433 - val_loss: 1.3835 - val_accuracy: 0.5235\n",
            "Epoch 72/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 1.0013 - accuracy: 0.6428 - val_loss: 1.3849 - val_accuracy: 0.5224\n",
            "Epoch 73/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9944 - accuracy: 0.6442 - val_loss: 1.3907 - val_accuracy: 0.5188\n",
            "Epoch 74/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9927 - accuracy: 0.6446 - val_loss: 1.3875 - val_accuracy: 0.5304\n",
            "Epoch 75/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9917 - accuracy: 0.6464 - val_loss: 1.3850 - val_accuracy: 0.5293\n",
            "Epoch 76/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9852 - accuracy: 0.6454 - val_loss: 1.3832 - val_accuracy: 0.5317\n",
            "Epoch 77/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 0.9826 - accuracy: 0.6497 - val_loss: 1.3988 - val_accuracy: 0.5309\n",
            "Epoch 78/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9781 - accuracy: 0.6472 - val_loss: 1.3920 - val_accuracy: 0.5303\n",
            "Epoch 79/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9782 - accuracy: 0.6502 - val_loss: 1.3873 - val_accuracy: 0.5305\n",
            "Epoch 80/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9721 - accuracy: 0.6526 - val_loss: 1.4003 - val_accuracy: 0.5287\n",
            "Epoch 81/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9717 - accuracy: 0.6526 - val_loss: 1.3963 - val_accuracy: 0.5260\n",
            "Epoch 82/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9681 - accuracy: 0.6523 - val_loss: 1.4007 - val_accuracy: 0.5258\n",
            "Epoch 83/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9676 - accuracy: 0.6553 - val_loss: 1.4083 - val_accuracy: 0.5245\n",
            "Epoch 84/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.9541 - accuracy: 0.6606 - val_loss: 1.4184 - val_accuracy: 0.5257\n",
            "Epoch 85/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.9592 - accuracy: 0.6574 - val_loss: 1.4090 - val_accuracy: 0.5307\n",
            "Epoch 86/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9619 - accuracy: 0.6593 - val_loss: 1.3984 - val_accuracy: 0.5330\n",
            "Epoch 87/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9542 - accuracy: 0.6610 - val_loss: 1.3977 - val_accuracy: 0.5277\n",
            "Epoch 88/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9515 - accuracy: 0.6598 - val_loss: 1.4116 - val_accuracy: 0.5204\n",
            "Epoch 89/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9517 - accuracy: 0.6609 - val_loss: 1.4163 - val_accuracy: 0.5191\n",
            "Epoch 90/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9490 - accuracy: 0.6646 - val_loss: 1.4110 - val_accuracy: 0.5265\n",
            "Epoch 91/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9481 - accuracy: 0.6617 - val_loss: 1.4077 - val_accuracy: 0.5302\n",
            "Epoch 92/100\n",
            "313/313 [==============================] - 2s 7ms/step - loss: 0.9359 - accuracy: 0.6682 - val_loss: 1.4124 - val_accuracy: 0.5259\n",
            "Epoch 93/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9383 - accuracy: 0.6647 - val_loss: 1.4102 - val_accuracy: 0.5275\n",
            "Epoch 94/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9414 - accuracy: 0.6649 - val_loss: 1.4052 - val_accuracy: 0.5316\n",
            "Epoch 95/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9397 - accuracy: 0.6638 - val_loss: 1.4107 - val_accuracy: 0.5331\n",
            "Epoch 96/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9313 - accuracy: 0.6677 - val_loss: 1.4252 - val_accuracy: 0.5282\n",
            "Epoch 97/100\n",
            "313/313 [==============================] - 2s 5ms/step - loss: 0.9269 - accuracy: 0.6714 - val_loss: 1.4291 - val_accuracy: 0.5332\n",
            "Epoch 98/100\n",
            "313/313 [==============================] - 1s 5ms/step - loss: 0.9344 - accuracy: 0.6645 - val_loss: 1.4154 - val_accuracy: 0.5305\n",
            "Epoch 99/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.9156 - accuracy: 0.6709 - val_loss: 1.4234 - val_accuracy: 0.5279\n",
            "Epoch 100/100\n",
            "313/313 [==============================] - 2s 6ms/step - loss: 0.9271 - accuracy: 0.6687 - val_loss: 1.4126 - val_accuracy: 0.5297\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 3. Evaluation on test data and inference\n",
        "At this point, we will perform a basic evaluation and inference. With the model.evaluate function, the same metrics are calculated, that were used during training:"
      ],
      "metadata": {
        "id": "2FtKp-a2-A9m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(model.evaluate(X_test, Y_test))"
      ],
      "metadata": {
        "id": "I3_9wgDREUna",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "62cc9259-6944-4e1f-ab62-766b5b9b74d0"
      },
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "313/313 [==============================] - 1s 3ms/step - loss: 1.4130 - accuracy: 0.5406\n",
            "[1.4130007028579712, 0.5406000018119812]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "we would like to see similar values, as in the validation set. If those are close to each other, then the generalization ability of the model is good (in case of an independent test-set)."
      ],
      "metadata": {
        "id": "ECHguBFtGL7f"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 3.1. Exercise\n",
        "Predict the class of the first 10 elements in the test set, and compare the predicted values with the actual, target values in the test set. Hints:\n",
        "* you can use [model.predict](https://www.activestate.com/resources/quick-reads/how-to-use-a-model-to-do-predictions-with-keras/) for prediction\n",
        "* from the output you can select the largest value with the [argmax() function of Numpy](https://stackoverflow.com/questions/62358642/convert-one-hot-encoding-back-to-number-label). As there are multiple values, you have to call it with axis=1 parameter.\n",
        "* it is enought to compare the predictions and the targets by printing the values out and inspecting them."
      ],
      "metadata": {
        "id": "0Io4zYJeHjz6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "preds = model.predict(X_test[:10])\n",
        "preds_dense = np.argmax(preds,axis=1)"
      ],
      "metadata": {
        "id": "XEEyU7exILqF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c5f17e20-f428-42b5-d333-827e1a03992d"
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/1 [==============================] - 0s 26ms/step\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Before comparision, you have to convert back the one-hot encoded target values the same way, as you converted the output of the neural network to class values with argmax() function."
      ],
      "metadata": {
        "id": "seZTEFI-I5cZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Target labels:\", np.argmax(Y_test[:10],axis=1))\n",
        "print(\"Predicted labels:\", preds_dense)"
      ],
      "metadata": {
        "id": "PHLvoMuIIkJ6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fecaefad-942d-4adb-9667-3185db7415bc"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Target labels: [3 8 8 0 6 6 1 6 3 1]\n",
            "Predicted labels: [4 8 0 8 4 6 3 6 5 1]\n"
          ]
        }
      ]
    }
  ]
}