practicals/Intro_ML_French_Prac.ipynb

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        "# **Dive into Machine Learning: Learning by Implementing**\n",
        "\n",
        "<img src=\"https://static.javatpoint.com/tutorial/machine-learning/images/introduction-to-machine-learning.png\" width=\"60%\" />\n",
        "\n",
        "*Avant de commencer*\n",
        "\n",
        "Utilisez ce lien pour accéder au tutoriel et enregistrez une copie.\n",
        "\n",
        "<a href=\"https://colab.research.google.com/github/deep-learning-indaba/indaba-pracs-2023/blob/main/practicals/Intro_ML_French_Prac.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
        "\n",
        "© Deep Learning Indaba 2023. Apache License 2.0.\n",
        "\n",
        "**Auteurs: Espoir Murhabazi, Ulrich A. Mbou Sob**\n",
        "\n",
        "**Réviseurs: Aaron Joel Lontsi**\n",
        "\n",
        "**Introduction:**\n",
        "\n",
        "Dans ce tutoriel, nous explorerons les fondamentaux de l'apprentissage automatique. Nous allons apprendre comment créer et entrainer un classificateur d'apprentissage automatique. Nous allons nous familiariser avec les concepts sur la fonction coût et son optimisation.\n",
        "\n",
        "**Topics:**\n",
        "\n",
        "Sujets: Apprentissage Supervisé, Réseau de Neurones, Calcul Numérique.\n",
        "\n",
        "Niveau: <font color='grey'>`Debutant`\n",
        "\n",
        "\n",
        "**Objectifs:**\n",
        "\n",
        "- Comprendre les base des l'apprentissage automatique\n",
        "- Entrainer un modèle de regression lineaire\n",
        "- Entrainer un réseau de neurones pour la classification à plusieurs classes.\n",
        "\n",
        "**Prérequis:**\n",
        "\n",
        "- Familiarité avec [Numpy](https://numpy.org/doc/stable/user/quickstart.html).\n",
        "\n",
        "**Outline:**\n",
        "\n",
        ">[Dive into Machine Learning: Learning by Implementing](#scrollTo=m2s4kN_QPQVe)\n",
        "\n",
        ">>>[1.1 Types des problèmes d'appentissage automatique](#scrollTo=v2k8dcYR9Hvb)\n",
        "\n",
        ">>>[1.2 Les données](#scrollTo=1KK-dbRw730T)\n",
        "\n",
        ">>[Régression](#scrollTo=e9NW58_3hAg2)\n",
        "\n",
        ">>>[2.1 Régression linéaire](#scrollTo=bA_2coZvhAg3)\n",
        "\n",
        ">>>>[La fonction de coût et son optimisation](#scrollTo=hNJgESq_LP4R)\n",
        "\n",
        ">>>>[Entraînement un modèle à l'aide de Jax](#scrollTo=q9dQh9DdLYPE)\n",
        "\n",
        ">>>[2.2 Régression non-linéaire et réseaux de neurones](#scrollTo=BKtMEnRkhAg9)\n",
        "\n",
        ">>>>[Représentation du modèle](#scrollTo=XStsgHB2MarI)\n",
        "\n",
        ">>>>[Fonctions d'activation](#scrollTo=fkpytbBzMvMj)\n",
        "\n",
        ">>>>[Construire un réseau de neurones avec Jax](#scrollTo=3Wrxt2orM7sk)\n",
        "\n",
        ">>[Classification](#scrollTo=fbTsk0MdhAhC)\n",
        "\n",
        ">>>[3.1 Régression logistique](#scrollTo=wMgxJU0TOX6O)\n",
        "\n",
        ">>>>[Logits and Fonction Sigmoïde](#scrollTo=SE1L3rmaO4UP)\n",
        "\n",
        ">>>>[Extension à la multi-classification](#scrollTo=HjQNjDC2cG2t)\n",
        "\n",
        ">>>>[Simple réseau de neurones pour la classification](#scrollTo=EcXXE56hPOhK)\n",
        "\n",
        ">>>>[Entraîner le modèle](#scrollTo=GcSvlekHPWxW)\n",
        "\n",
        ">>>>[Évaluation du modèle](#scrollTo=sGPvmGWkP1fT)\n",
        "\n",
        ">>[Resumé](#scrollTo=fV3YG7QOZD-B)\n",
        "\n",
        ">>>[Appendix](#scrollTo=742JhcnAxTof)\n",
        "\n",
        ">>>[Base de JAX [OPTIONAL]](#scrollTo=742JhcnAxTof)\n",
        "\n",
        ">>>[Derivation of partial derivatives for exercise 2 [OPTIONAL]](#scrollTo=kh_8f4gKyufu)\n",
        "\n",
        ">>>[Intuition pour la function cout avec l'entropie croisée multi-classes.: exercise 3 [OPTIONAL]](#scrollTo=fRYbQvz01Zlm)\n",
        "\n",
        ">>[Feedback](#scrollTo=o1ndpYE50BpG)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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      "source": [
        "## Install and import anything required. Capture hides the output from the cell.\n",
        "# @title Installer et importer les packages requis. (Exécuter la cellule)\n",
        "!pip install -q clu\n",
        "\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "import flax\n",
        "import flax.linen as nn\n",
        "from typing import NamedTuple, Any, Dict\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "from clu import parameter_overview\n",
        "\n",
        "from sklearn.datasets import fetch_openml\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FVw9C8GugkAj"
      },
      "source": [
        "**Qu'est ce que l'apprentissage automatique (Machine Learning)**\n",
        "\n",
        "Pendant les deux dernières décennies, le domaine de l'intelligence artificielle (IA) a considérablement évoluer pour influencer d'autres domaines que celui de l'informatique. Les appications telles que YouTube et Netflix utilisent l'IA pour suggérer du contenu à chaque utilisateur en fonction de ces préférences.\n",
        "<center>\n",
        "<img src=\"https://www.simplilearn.com/ice9/free_resources_article_thumb/AIvsML.png\" width=\"80%\"/>\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6pRWdqAi7FTZ"
      },
      "source": [
        "L'IA est une science qui a pour objectif le development des systèmes intelligents. **L'apprentissage automatique** est un sous-ensemble de l'IA où l'apprentissage se fait à partir des données en utilisant les techniques de la modélisation statistique. **L'apprentissage profond (deep learning)** quant à lui est un sous-ensenmble de l'apprentissage automatique qui utilise les réseaux de neurones artificielles pour les modélisations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v2k8dcYR9Hvb"
      },
      "source": [
        "### 1.1 Types des problèmes d'appentissage automatique\n",
        "\n",
        "L'apprentissage automatique se base sur l'apprentissage sur les données.  Lors de la formulation d'un problème d'apprentissage automatique, la première question à se poser est de savoir quel type de tâche nous avons. En general les tâches de l'apprentissage automatique peuvent être divisées en 3 catégories.\n",
        "\n",
        "<center>\n",
        "<img src=\"https://www.researchgate.net/publication/354960266/figure/fig1/AS:1075175843983363@1633353305883/The-main-types-of-machine-learning-Main-approaches-include-classification-and.png\" width=\"80%\" />\n",
        "</center>\n",
        "\n",
        "<font color='red'>Apprentissage supervisé (Supervised Learning)</font>: Dans apprentissage supervisé, nous avons un ensemble de données étiquetées, où chaque point de données d'entrée est associé à la sortie correcte (étiquette). L'objectif est d'apprendre une correspondance entre les entrées et les sorties basée sur les données d'entraînement, de manière à ce que le modèle puisse faire des prédictions précises sur de nouvelles données non vues.\n",
        "\n",
        "<font color='red'>Apprentissage non supervisé (Unsupervised Learning): </font>: Dans l'apprentissage non supervisé, nour avons des données non labelisées et l'objectif est de trouver des patterns, structures ou relations entre les données. L'algorithme groupe les données similaires et reduit leur dimensions afin de trouver les structures cachées.\n",
        "\n",
        "<font color='red'>Apprentissage par renforcement (Reinforcement learning):</font>: Dans l'apprentissage par renforcement, l'apprenant apprend à prendre des décisions grâce à l'interaction avec un environment. L'apprenant, (agent) reçoit un feedback comme un gain (encouragement) ou pénalité en fonction des ses actions. Ensuite il apprend à maximiser le gain cumulé au cour du temps.\n",
        "\n",
        "**Exercise 1.1**: Pour chaque tâche suivante, identifier à quelle catégorie elle appartient.\n",
        "  -  Apprendre à un robot à marcher.\n",
        "  -  Prévoir la météo\n",
        "  -  Classification des emails/spam\n",
        "  - Apprendre à un ordinateur à jouer aux échecs\n",
        "  -  Grouper les differentes types de révues de films."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "cLaRGDzv4wR2"
      },
      "outputs": [],
      "source": [
        "# @title Solution - Exercise (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts !)\n",
        "print(\"Apprendre a un robot a marcher -- Reinforcement learning\")\n",
        "print(\"Prevoir la meteo -- Supervised learning\")\n",
        "print(\"Classification des emails/spam -- Supervised learning\")\n",
        "print(\"Apprendre a un ordinateur a joue aux echecs -- Reinforcement learning\")\n",
        "print(\"Grouper les differentes types de revues de films -- Unsupervised learning\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1KK-dbRw730T"
      },
      "source": [
        "### 1.2 Les données\n",
        "\n",
        "A la fin du tutoriel nous allons construire un classificateur pour le dataset des nombres. Ce dataset contient les images des nombres écrits à la main.\n",
        "\n",
        "Avant de continuer avec les concepts de l'apprentissage automatique, nous allons visualiser quelques images."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w8g4rsOy_86b"
      },
      "source": [
        "Nous allons telecharger les données avec [sklearn](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.fetch_openml.html)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "h3uN_gxbG2Em",
        "outputId": "314eba53-e454-42e6-91dc-9378ad14e2d9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Images have shape: (70000, 784), and labels have shape: (70000,)\n",
            "Number of classes is: 10\n",
            "Minimum value in images is: 0\n",
            "Maximum value in images is: 255\n"
          ]
        }
      ],
      "source": [
        "# Load the MNIST digits dataset\n",
        "mnist = fetch_openml(name='mnist_784', version=1, as_frame=False, parser='auto')\n",
        "# Extract the data and labels\n",
        "images, labels = mnist.data, mnist.target\n",
        "\n",
        "# Convert labels to integers (they are originally stored as strings)\n",
        "labels = labels.astype(int)\n",
        "\n",
        "# Print shapes of the data\n",
        "print(f\"Images have shape: {images.shape}, and labels have shape: {labels.shape}\")\n",
        "\n",
        "# Verify that we have 10 classes\n",
        "print(f\"Number of classes is: {len(np.unique(labels))}\")\n",
        "\n",
        "# Print the min and max values of the images\n",
        "print(f\"Minimum value in images is: {np.min(images)}\")\n",
        "print(f\"Maximum value in images is: {np.max(images)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bNV9b-6bH45y"
      },
      "source": [
        "Notre ensemble d'aprrentissage consiste de 70000 images en noir et blanc. Chaque image est convertie en un vecteur de taille 784 à partir de sa forme originale 28x28. Nous allons utiliser le code suivant pour afficher quelques images. Notez que chaque fois que vous executez la cellule suivante, vous obtiendrez des images differentes affichees car nous échantillonnons aleatoirement à chaque fois."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 746
        },
        "id": "-qXlDhYWH_mW",
        "outputId": "4c739c72-0b22-4709-8806-219ce4e52505"
      },
      "outputs": [
        {
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3sp65TlGXLl1UNtcrMZ+Jj6xh9r/NnTtXZV89FeaaEyLuP/NHjhzJ4Ogu++mnn1T+6quv3PYxe3aeeeYZq2vC/W82cy2NQ4cOqbxr166Qjymn4R0LAAAAANaYWAAAAACwxsQCAAAAgLWI7rEoUaKEyj169PB5zPr161U+efKk1/25Lzr7qF27tsq9evXyur/ZP/P666+rfOLEiaCMC1lv9OjRKg8aNMjr/mZPRcuWLVXmdSMymPdbm+sfZAXznnAzm72FOZG5nlShQoW87n/u3DmVzf46EfueCl/Kli3rts0cFwJXvnx5lUeOHKmy2Ss5depUlVNTU0MzsByMVygAAAAA1phYAAAAALDGxAIAAACAtYjusciI+++/X+WLFy9anc/T/a7lypVT+ddff7W6BoLjlVdeUblixYpe9x84cKDK06dPD/aQkEXM59zfeeedXj9uPpP+rrvuUpmeCmTUxIkTVTb7B8x7xEeNGhXyMYU7X+tPmRYvXqzy8uXLgzkcj8y+q1tvvdVtn927d4d8HNmd+Xvc7L01mT0WCD7esQAAAABgjYkFAAAAAGtMLAAAAABYi6geC/Pe088++8znMRs2bFB53759Xvdv2rSpyh07dlS5cOHCPq9pPnfcXDvDvN8zJSXF5zkRGPMeeBGRv/3tb16P2bJli8r+1Bcik3mfbd26dVU2eybuvvturx8H/PXkk0+q/Nhjj6ls9lSY/T0LFiwIybgiSaVKlVROT0/PmoF4UaFCBZXNvwuA7Ip3LAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsBZRzdsFCxZU2VxwxlMD17Jly7zuM3LkSJWHDh2qsqcF8ALVo0cPlR9++GGV27ZtqzIL6vlmNsKZjdnmYngi7k2RP//8s8pvv/22yr///rvNEBEm2rRp47btwQcf9HrM1q1bVeZnEhlhLrQoIlKjRo2AzmHW3tGjR63GlB2Yr+Wmc+fOqWy+1meGsmXL+tynZMmSKpv1kpaWFtQx5UR79+5V+fz581k0kpyDdywAAAAAWGNiAQAAAMAaEwsAAAAA1iKqx8IXTz0WH3/8scorV65UuUmTJir76qk4duyYyrNmzXLb59ChQyr36dNH5dq1a6s8cOBAlZ966imvY4BIXFycyhlZzO7dd99V2eyxCAZzob4nnnjC6/69evVS+ciRI8EeUrZXvnx5lV988UW3fa677jqVzYU0H3jggeAPDDnOI4884rbN/H3gy0svvRSs4WQb//nPf1T+y1/+orL58/3FF194/biIyKVLlwIaw80336zykCFDVPa1IKuISPPmzVX+4YcfVDb/HklKSlJ5/vz5Ku/YscPnNbM7s//yxx9/VPnUqVOZORyPzN9RIiIjRoxQ+e9//7vXc5if59y5c1WeNm2ayp9//nkAI7TDOxYAAAAArDGxAAAAAGCNiQUAAAAAa1GOrwdCu3Y07ufKCu3atVN5wYIFPo/Zt2+fyhUqVAjomr/88ovKnTp1Utm819OTAgUKeB2T+azqWrVqqXz48GGf1wiUn992j8KhFiZMmKCyr94FEfd+hVatWqnsz/fSG7NfR8T9HtjChQt7PcekSZNUNvtvQiHSa8H08ssvq/zcc8+57WP2Y5lrXZjr3wSqS5cubttiYmK8HrNmzRqVU1JSrMaQERmthXCsg6yQmJio8tdff+3zGPM++scee0zlqVOn2g8sQOH+mlCtWjWVv//+e5Xz58/v9fhNmza5bVu0aJHKZl9G7969Ve7QoYPKvl7bDx486LbthRdeUHnhwoUqm32Ad999t8qbN29W2awdT59noMK9Fho0aKDy2rVrVTbXMKlfv77KZ8+eDc3ArpInTx6VZ8yY4bZP165dvZ7DXJvF/NpGR0erbPaS3HDDDW7nDPRvS39rgXcsAAAAAFhjYgEAAADAGhMLAAAAANYiah2Lp59+OuBjAu2peOutt1T+xz/+ofKZM2cCHoN5r5vZU1G8eHGVS5YsqXIoeiwiTUJCgsr9+/f3uv/evXvdtk2fPl3lYPdUeOrzKFKkSEDn5F71wD3zzDMq+/M60bNnT5V99VSUK1dOZbNvw+y9MtdZEfG9Ro7ZzzV06FCVzeeU53T58uVT+Z133lHZ/PnMyL3i5j3vX375pdf9zTWI/LmmOW7zvnq4M9drMH+eP/nkE5XNdSvMNSg8bTP7H3z5/fffVU5OTlZ5xYoVbseY62yZzNeV2267TWVzjGZPj7m+h4jIzp07vV4zu6lRo4bK5utGZvRYmH1SvvopRNzXUtq6davX/SdOnKjyHXfcobKnvg5/1lrJCN6xAAAAAGCNiQUAAAAAa0wsAAAAAFgL63UsihUrpvJPP/2kcpkyZayvYZ4zFM84Nu+tNnsmYmNjVa5Tp47Ku3btsh6DKdyfTW3617/+pXL37t297r9kyRK3bW3btg3omiVKlFD5vffeU7lRo0Yqe+qn+O233wK6xpYtW1Ru2bKlyuZ9vMEQabVg3i9t3rtsfl+++uort3OYX1ez76lfv34qjx8/3usYQsH8vphrJJjP7g/FNf2VGXVQsGBBlc3vSa9evVQ2x+TpZ+fQoUMq33TTTV7HYJ4zI18vc32SFi1aqOypPyyzRdprgslcN8Bc/8H8fSLivvaFudbNtm3bVJ43b57K5t8SmdETZf5tsX37dpU9rZ1jvo4cOHDA6zXCvRbM77XZZ1KvXj2V58yZo/Lf//53t3Pa/t1n/i1w7NgxlT19Tc2eio8++khlsx5NZh+guV7azJkz3Y558MEHvZ7TxDoWAAAAADINEwsAAAAA1phYAAAAALAW1utYmPel/fnnnyoHo8eiR48eKofimcbNmzdX2byv3lznwuaexuzK07oA3pjPhs8Is6fCvE/XZD63XETkjTfeUPnFF19U2ayF+fPnqxyKnopIZ94za/ZUmMyfcRGRixcvqvzYY4+pbK5n48vp06dVNl+7RESuv/76gM4ZDveqZyXzefO+eipMJ0+eVNm8h1nEvU+lffv2Ko8dO1blQoUKeb2m6ejRo27bzGfHh0NPRXZj/nyba0VFR0f7PMfIkSNVfumll+wHFmTmfffm3w5ly5Z1O8bssTB7RSKN+b02XxfMvsX77rtPZXP9BxGRdevWWY3p2Wef9frx48ePu20z+0J99VSYKlas6PXj5t8WocQ7FgAAAACsMbEAAAAAYI2JBQAAAABrYd1jEQpJSUkq/+c//wn5Nbt06eL14/v371d59+7doRxOjvDf//7X+hw33nhjQPtXqlTJbdtTTz2lsq9+ALMHA6ExY8YMlT31YVxtz549Km/atElls5fm22+/dTvHmjVrVG7YsKHXa5q9V6Ho/wpnZp/U/fff73X/hQsXqmz2yZhffxH3n1nzZ37nzp0q33zzzV7HYDpz5ozbNvOcCD3zd3Du3O5/+uzYsUNlT/feh7tHHnlE5S+++MJtn+eff17lSO+xMP38888qP/fccyq/9tprKnta56hx48Y+97ma2e/ra00ds39TxHNfnjcJCQkqL1682Ov5Vq9eHdD5bfCOBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1iKqeXvjxo0q33DDDT6PMRtYzMYd28XoPC1iNXDgQJW7du3q9RyZuXBJpDK/zr4WD1uwYIHbtjFjxqj8wQcfqPzJJ5+obDZH+VKnTh23bbVq1VLZXBjn3nvvDegaENm+fbvK5gMYzK95uXLl3M7RqVMnr9fYt2+fyrfffrvKR44cUblly5Yqm4sdiYg0aNDA6zXNhzaYzcpbt271enx206RJE5XNn3lzATx/mrVN5mvzoEGDvO6fK5f+vzhfi1hVqFDBbZv5+2HChAlez4HMYf78nThxIotGknG//fabz308/Z7KzqZOnapyv379VPa0sNycOXNUNl8XPv30U5ULFy6scsmSJVU2/878y1/+4mXEnt1yyy0qz507V+VLly6p3LZtW5Uzs555xwIAAACANSYWAAAAAKwxsQAAAABgLaJ6LMx7q/2xYsUKlW3vU77uuutUNns2RNwXRTOdO3dOZV+Lr8B9kRuzv8a8T9LT4nbmgltDhgxR2eypCLT/xtP91uY9r+bCOWvXrg3oGnC/V9TXwkKeFoCKiYnxeox5j+yiRYu87h8XF6eyp8USTZs3b1b51VdfVfn777/3eY7spFq1aiqb3yPz5/GPP/5Q2VdPhfnz7mmbr5/5bdu2qfz777+rbPbieDJs2DCV69Wrp3Lfvn1VzmkLI2aVKlWqqFy6dGmVDx8+nJnD8UuNGjVU/ve//+3zGLNXNbszFxo1e/DMfgoRkb/97W8qf/jhhypv2LBB5R9++CGgMZn9EiLui+yZvSBmLl68uMqPP/64yuvXrw9oTMHEOxYAAAAArDGxAAAAAGCNiQUAAAAAaxHVY/Hf//434GPM58tPmTJFZfM+NfM+X5PZD/HEE0/4HMP58+dVfvDBB1X29Mx7aOZaBW3atFHZfK60p3vc8+TJo7J5T22gzLUM/vzzT7d9Vq9erfLnn39udU0EzrxX2h/m/f2e7on1ZubMmW7bvvjiC5WTk5NVjsTn5geT+TNdrFgxr/uXKlVK5a+//lplc90LT8/vz5s3r8rma/XIkSNVnj17tsrm/dsrV65UuWbNmm7XNHtDzDVTzOfRw57589ioUSO3fapWraryqlWrVH7zzTdV/uWXX1Q2+zkzomnTpiqbfX+tWrVSOTExUeWyZcuq7Ok15fnnn7cYYeQzf2Y7dOjgto/5c/7Xv/5V5fr163vNvnh6bTP/vi1YsKDK5hpYL7/8ssrvvvtuQGMIJd6xAAAAAGCNiQUAAAAAa0wsAAAAAFiLcvx8WL95v2pWMO+JN9ekiI6OzszhiIjIyZMn3baZfRjmPY3m8+uzQqBrNFwtHGrBl549e7ptM+tn6NChKg8cONDrx82vmXm/q9kHEikivRbMe1Efeughlc01KUREBg0apLLZf3P06FGV33//fZV37dqlsrlWhqd7mz2tcxJuMloLwaiDhx9+WOVJkyapbK4hFOiYPH1u5jozEydOVNlcW8SXZs2aqWz28Im4v/7v3LkzoGtkhkh/TfBlzJgxbtuefPJJlQOtN/M1ISPi4+NVzpXL+//9mq8pZp9Rjx493I7Zv39/QGPK7rXgD7OXpU+fPioXLlxY5Y4dO6rsz2uRadasWSq//fbbKq9bt87nOYLN31rgHQsAAAAA1phYAAAAALDGxAIAAACAtYjqsTBVrlxZ5b/85S9u+3Tp0kXl22+/XWVzvYOFCxeqbK5VMHfuXJUjdV0C7puEC7UAl6zssTCZvTI1atRQecCAAV6PX7t2rcrmuiEi7s+rP3ToUCBDzLZy4muC2R9z9913q2yuVWD2P5j34QfDzz//rLK5Tspnn32msrlWTjDkxFqAZ/RYAAAAAMg0TCwAAAAAWGNiAQAAAMBaRPdYIOO4bxIu1AJcwqnHAlmH1wTfzM/T7PG88cYbVb7pppvczvHJJ594vcaePXtU9rRuVqhRC3ChxwIAAABApmFiAQAAAMAaEwsAAAAA1uixyKG4bxIu1AJc6LGACK8J+B9qAS70WAAAAADINEwsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgLcpxHCerBwEAAAAgsvGOBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMBatp1YjBgxQqKiojJ07IwZMyQqKkpSUlKCOyhkCWoBLtQCXKgFuFALcKEW7EXExML1zXL9i4mJkbJly0qrVq3krbfekpMnT4Z8DFOmTJEZM2b4te/Ro0dlzJgx0rhxYylRooQUKVJEEhMTZfbs2aEdZA5ALcAl0mph9erVarzmv5dffjm0g83GIq0WXE6ePCnPPPOMxMfHS3R0tJQrV046deokZ86cCc0gc4BIrIVz587Jq6++KjVq1JB8+fJJuXLlpHPnzrJ169bQDTIHiMRauNquXbskJiZGoqKi5Pvvvw/uwEIoynEcJ6sH4cuMGTOkd+/eMmrUKImPj5eLFy/K4cOHZfXq1bJ8+XKpUKGCJCcnS61ata4ck5aWJmlpaRITExPw9S5duiQXL16U6OjoKzPXm266SeLi4mT16tU+j1+0aJF06NBBWrduLc2aNZPcuXPLvHnzZNWqVfLCCy/IyJEjAx4TLqMW4BJptZCamirLly93256UlCTLli2TDRs2yK233hrwuBB5tSAicuLECWnSpIns379f+vbtKwkJCXLkyBH58ssvJSkpSYoWLRrwuBCZtdCxY0dJTk6Whx9+WG6++WY5ePCgTJ48Wc6ePStbtmyRihUrBjwuRGYtXO2ee+6RlStXyunTp+W7776TW265JeBzZAknAkyfPt0REee7775z+9iKFSuc2NhYp2LFis6ZM2dCNoaaNWs6TZo08Wvf3bt3OykpKWpbenq607x5cyc6Oto5depUCEaYM1ALcIm0WriWhIQEp2rVqsEZUA4VibXQr18/p0iRIs7u3btDNqacKNJqYf/+/Y6IOE8//bTavnLlSkdEnHHjxoVghDlDpNXC1ZYuXerkzZvXGTp06DU/h3AVEbdCedO8eXMZNmyY7N27V2bOnHllu6f75M6ePSsDBgyQuLg4KViwoNxzzz1y4MABiYqKkhEjRlzZz7xPrlKlSrJ161ZZs2bNlbfUmjZtes0xxcfHu/0PQ1RUlLRv317Onz8vu3fvtv684Y5agEs41oInGzZskJ07d0r37t0z+qnCh3CshePHj8v06dOlb9++Eh8fLxcuXJDz588H89OGB+FYC67bcUqVKqW2lylTRkREYmNjLT5jXEs41oLLxYsX5cknn5Qnn3xSqlSpEoxPN1NF/MRCRKRnz54iIrJs2TKv+/Xq1UsmTpworVu3ltdee01iY2OlTZs2Ps8/YcIEKV++vFSvXl2SkpIkKSlJhgwZEvA4Dx8+LCIicXFxAR8L/1ALcImEWpg1a5aICBOLEAu3Wvjqq6/k3LlzkpCQIJ06dZJ8+fJJbGysNGjQQDZv3hzQ54bAhFstVKlSRcqXLy9vvPGGfPbZZ7J//37ZsGGDPProoxIfHy9du3YN7BOE38KtFq4+7o8//pChQ4f694mEmdxZPYBgKF++vBQuXFh27dp1zX02bdokc+bMkYEDB8r48eNFROSxxx6T3r17y48//uj1/O3bt5ehQ4dKXFyc9OjRI0NjPHbsmEybNk0aNWp05X8iEHzUAlzCvRYuXboks2fPlvr160tCQkLAx8N/4VYLv/zyi4iI/OMf/5AqVarIBx98ICdOnJCRI0dK8+bNZevWrbw2hEi41UKePHlk3rx50q1bN7nnnnuubK9Xr56sW7dOihQp4t8nhoCFWy2IXP5PxxdffFHGjh0rhQoV8v+TCSPZ4h0LEZECBQp47fBfunSpiFwuiKv1798/pOMSEUlPT5fu3bvL8ePHZeLEiSG/Xk5HLcAlnGthxYoVkpqayrsVmSScauHUqVMicvm2yBUrVki3bt2kX79+smDBAvnjjz9k8uTJQb8m/iecakFEpGjRolKnTh157rnnZMGCBTJ27FhJSUmRzp07y7lz50JyTVwWbrXw7LPPSuXKleWhhx4KyfkzQ7Z4x0Lk8gt1yZIlr/nxvXv3Sq5cuSQ+Pl5tz4z/Kezfv78sXbpUPvjgA6ldu3bIr5fTUQtwCedamDVrllx33XXSpUuXkF8L4VULrvvm27ZtKwUKFLiyPTExUeLj42XdunVBvyb+J5xq4cSJE9KoUSMZPHiwPPXUU1e233LLLdK0aVOZPn269OvXL+jXxWXhVAvr16+XpKQkWbFiheTKFbn/7x+5I7/K/v375cSJE2F5O8HIkSNlypQpMnr06Cv38yF0qAW4hHMtnD17Vj799FO588473Zo2EXzhVgtly5YVEfeGXRGRkiVLyh9//JHZQ8oxwq0W5s2bJ6mpqeo2KBGRJk2aSKFCheTrr7/OopFlf+FWC88884w0atRI4uPjJSUlRVJSUuT3338XEZFDhw7Jvn37sniE/skWE4ukpCQREWnVqtU196lYsaKkp6fLnj171PadO3f6dY2MrMQ4efJkGTFihAwcOFCeffbZgI9H4KgFuIRrLYiIJCcny8mTJ7kNKpOEWy3Uq1dPREQOHDjg9rGDBw9KiRIl/D4XAhNutZCamioil3uuruY4jly6dEnS0tL8PhcCE261sG/fPlm7dq3Ex8df+Td48GARubymxdXrbYSziJ9YrFy5Ul588UWJj4/3+kvaVThTpkxR2/29zz1//vxy/Phxv8c1e/ZsGTBggHTv3l3GjRvn93HIOGoBLuFaCy4ffvih5MuXT+69996Aj0VgwrEWbrjhBqldu7YsXLjwyv9Iilx+Os2vv/4qLVu29Os8CEw41kK1atVEROTjjz9W25OTk+X06dNSt25dv86DwIRjLbz77rvy6aefqn+uXo6xY8deeYpguIuoHoslS5bItm3bJC0tTVJTU2XlypWyfPlyqVixoiQnJ3tdKbFevXrSsWNHmTBhghw9elQSExNlzZo1smPHDhHxPausV6+eTJ06VV566SVJSEiQkiVLSvPmzT3uu2HDBnnggQekePHi0qJFC7diuOOOO6Ry5coBfva4GrUAl0ipBZdjx47JkiVLpGPHjur+etiLpFoYP368tGzZUho2bCiPPPKInDhxQsaNGyfVqlXjnvogiJRaaNu2rdSsWVNGjRole/fulcTERNm5c6dMmjRJypQpI3369Mn4FwEiEjm18Ne//tVtm2tS0qRJE1beDibX6omuf3nz5nVKly7ttGzZ0nnzzTedP//80+2Y4cOHO+and/r0aefxxx93ihUr5hQoUMBp3769s337dkdEnNGjR7tdb8+ePVe2HT582GnTpo1TsGBBR0S8rqRojtf8N336dNsvSY5FLcAl0mrB5e2333ZExElOTs7w5w4tUmth+fLlTmJiohMTE+MUK1bM6dmzp3Po0KEMfx0QmbVw7NgxZ9CgQU61atWc6OhoJy4uzunatSursluKxFq41ucQSStvRzmO4wRrkhKJNm/eLHXr1pWZM2dyv3MORy3AhVqAC7UAF2oBLtTCtUV8j0Ugzp4967ZtwoQJkitXLmncuHEWjAhZhVqAC7UAF2oBLtQCXKiFwERUj4Wt119/XTZu3CjNmjWT3Llzy5IlS2TJkiXSt29fuf7667N6eMhE1AJcqAW4UAtwoRbgQi0EKKvvxcpMy5Ytcxo0aOAULVrUyZMnj1OlShVnxIgRzsWLF7N6aMhk1AJcqAW4UAtwoRbgQi0EJsf3WAAAAACwl6N6LAAAAACEBhMLAAAAANaYWAAAAACw5vdToXytLojIYtNaQy1kL9QCXDJaC9RB9sJrAlyoBbj4Wwu8YwEAAADAGhMLAAAAANaYWAAAAACwlqNW3gYAILPs27fPbVuhQoVULlKkSCaNBgBCj3csAAAAAFhjYgEAAADAGhMLAAAAANbosQAAIANq166t8nvvvafynj173I4ZNGhQSMcEAFmJdywAAAAAWGNiAQAAAMAaEwsAAAAA1nJcj8X999+v8vDhw1W+4YYbVJ4wYYLKL7zwgsonT54M3uAQNHXq1HHbNn78eJWbNm2qcnp6utdzTps2TeV///vfKn/zzTdux/z2229ezwkgcrz66qsqd+nSReVKlSqp3Lt3b7dzbNq0KejjAoBwwTsWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYi3Icx/Frx6ioUI8lJN544w2VH3/8cZXz5MkT0Pn+85//qNypUye3fXbt2hXQObOCn992jyKhFpo1a+a2bfHixSpHR0erHOjXxPw6HD161G2fhg0bqrxjx46ArpEZsnstwH8ZrYXsWgcjRoxQ2Xx4x7lz51Tu1auXyp988onbOW1+3jILrwkiBQsWVPmpp55S+bbbblN57dq1Xs+3ZcsWt22LFi3K4OgyD7UAF39rgXcsAAAAAFhjYgEAAADAGhMLAAAAANayVY9Fjx493La9++67Kpv31dt688033bb93//9X1CvEQo58b7J1157TeXHHntMZbMHo3nz5ioXK1ZMZfPr4Olr+umnn6r84IMPqnzmzBkvI84cObEW4FlO77EYN26cyh07dlTZfA0w77s3f99Eqpz4mmAujrthwwaV8+fP7/V4X78PLl686HaM+Ttp6tSpKqempnq9ZmbIibUAz+ixAAAAAJBpmFgAAAAAsMbEAgAAAIC1iO6xMPslNm/e7LZPtWrVVD5y5IjKM2fOVLlo0aIqm88lN02fPt1t20MPPeT1mHCQE++bNJ9LXqBAAZUPHTqkcsmSJVVOTExUuU2bNir36dPH5xgqVaqk8v79+30eE2o5sRZs5cql/0/GXA/H7N8Rce/Zufvuu71eo23btipnxjPvc1qPRe3atVVeuHChyhUqVFD5gQceUNn8/ZFd5MTXhPvvv1/lpKQkr/tv2rRJ5a1bt6ps9mzUr1/f5xgWLFigsqd1sjJbTqwF8/X8gw8+UHnZsmUqe/o7MKs98cQTKvft29dtn1q1agV0TnosAAAAAGQaJhYAAAAArDGxAAAAAGAtd1YPwEbu3Hr4Zj+FiMiBAwdUfuaZZ1T++OOPVW7SpInK5toY5jUROU6ePOk1m3777TeVk5OTVf7hhx9U9qe3ZuDAgSo//fTTPo9B5jN/zs17UYcNG6Zyu3btAr6Gr/tVGzZsqHJm9FhkJ4UKFVJ52rRpbvuYfVJLly5V2fy+nzp1KkijQ1bq2rWr2zZzDQmTua6F2QN19OhRlc1+TbMHQ8S9j8/sA0TomX1WIiJjxoxRuUWLFirXrFlT5fnz56t84sSJII3u2sz+FfP1zewHO3fuXMjH5MI7FgAAAACsMbEAAAAAYI2JBQAAAABrEd0wcPbsWZXNZ4572ufYsWNez7lmzRqVT58+rXLhwoUDGSKyMfP+bH+e8WzzTHAEj3n/fUJCgspDhgxR+d577w35mGDHXJemXr16KntaE2Dt2rUqm896//PPP4M0OoSTv//9727bzPox17xq3769ymZPhemPP/5QOS0tLYARIlT69++v8n333ee2zx133OH1HOvWrVM5M3oqTI8//rjK5pprZv1l5poovGMBAAAAwBoTCwAAAADWmFgAAAAAsBbRPRbp6ekqm2tWZESxYsVUvu6666zPiezBXCfFXMvAH7Nnzw7WcCKS+extEZHSpUurbPahmPc6m89+98XTPbSDBg1S2VN/FiLLv/71L5X96Yt55513VPZ13zxyjgsXLqhsrmsUCvv37w/5NXKa8ePHq/y3v/1NZXMtMxGRn376SeUZM2ao/N///jc4g7MwdOhQrx9///33VV69enUIR6PxjgUAAAAAa0wsAAAAAFhjYgEAAADAWkT3WISCuTaB+Wxr5FxmbfjqDfDk8OHDQR1TpMmbN6/bNrM36vz58yp/+umnKnft2jX4A/PBXA/HvN/67bffVrlq1apu5/D07HxvFi1aFND+Od3KlStV9qfHYvHixaEaDiJc7tz6z6OiRYuqbK4T4MvDDz/sti0mJkZlc10VBK5OnToq33777Sq//vrrKk+fPj3UQwqJ9957T2WzP2zKlCmZORyFdywAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALBG8zbgp4IFC6rsabE30xNPPKEyCyD5Fh0drXIomrXPnTun8q+//qqyuSDS+vXrVV61apXX88+bNy/gMX3++ecqf/vttwGfIyfz9fP4z3/+022b2ZSPnMHTQohmLZQqVUrlRx99VOVJkyapfPLkSa/XNH++ERzVq1dX+c0331Q5f/78KkfKA1Tq16+vstn8by4Iai4kay7wmJl4xwIAAACANSYWAAAAAKwxsQAAAABgjR4Lw5133hnQ/suXLw/RSJDVbrrpJpX79eunsrkg3urVq93OMWfOnKCPK5KlpaW5bTMX+mnUqJHKCQkJKm/fvj2ga3r6Hqxbt07lFStWBHTOQoUKqXzXXXep3LJlS5/nOHbsmMpm38bFixcDGlNON3bsWK8f37Ztm9u2UH+Nq1Sp4ratW7duAZ3DXCDyp59+shoTRO6//363bb169VJ52rRpKr/44osqt27dWmXzdctk9uiJ+NendzWzD4TXCJFy5cqpvHnzZpW/+uorlZcsWRLqIQXFbbfdprK58N/TTz+t8okTJ0I9JL/xjgUAAAAAa0wsAAAAAFhjYgEAAADAWo7vsYiLi1O5QYMGXvc3nxVsPt8ekat48eIqf/LJJyqXKFFC5d9++03l++67z+2cnp6XnpNdunTJbdsjjzyict68eVVu3ry5ykuXLg3+wALUokULlT/66COfx5i10L59e5W//vpr63EhtJo2baqyWasm85n6IiI33HBDQNeMjY1V+fnnnw/oePjns88+U/nVV19V+R//+IfKt99+u8qvvPKKymYP3uOPP+52zQIFCgQ0xo4dO6q8cOHCgI7Pjk6fPq3y4MGDVTZ/fsJVUlKSyjfeeKPKo0ePVjmc+2t4xwIAAACANSYWAAAAAKwxsQAAAABgLcf3WJjPGY+Pj/e6/wcffKDy3r17gz4mZA7zueLm8+KrVq3q9fgLFy6oTD9FcJhf13DoqTB5eg6+LwsWLFCZnoqsZ/ZIXH/99Sqb9zXffffdKkdHR4dmYFcZNGiQyvRYhIb5+v3666+rbPZ6JSYmqmz2YKSnp1uP6eDBgyr/8ssv1ueMdOb6DfPnz1e5fPnyKqekpIR6SAHbsmWL27aaNWuq/Pbbb6s8d+7ckI4pmHjHAgAAAIA1JhYAAAAArDGxAAAAAGAtx/VY5M6tP+UePXoEdPz3338fzOEgC7Vr105lX2uYnDp1SuUOHToEfUwIT7fddpvKrVq1Cvgc9GNlrSZNmrhtq127tsrdu3fPrOEgC5UqVcptm9ljZ97znj9/fpXNdSrMngrz457MmjVL5U2bNqn83nvvqXzmzBmf58zuzPVDXnvtNa/7//vf/1bZ7FuZM2eO2zHmektpaWkq33nnnV6v+eOPP6rcq1cvlc1eLhH3evnb3/6mcunSpVU+fPiw1zFkJd6xAAAAAGCNiQUAAAAAa0wsAAAAAFjLcT0W5r3Sjz32mNf9z507p/Lu3buDPiZkjrJly6o8dOhQlX3dEztq1CiVN27cGJyBIezFxcWpbK6B4g9zDRzYSUhIUDlXLu//T9amTRvra65fv15lc80V8/n0Fy9edDvHwIEDvV7jxIkTKg8YMCCAEcIT82voaS0Q82c82DytQ9CnTx+VzXv54e7ee+9V2dfv7datW3v9+EMPPeS2zTyn+TNZpEgRr+eMioryej5/mD0U4dxTYeIdCwAAAADWmFgAAAAAsMbEAgAAAIC1HNdjMWTIkID2nzdvnsrmOhbms61FRM6ePauy+XxrhF6LFi3cto0fP17lqlWrqmzeBzl16lSVJ06cGKTRIdKYteLLkiVL3LalpqYGazgQkSeffFJlc42iYDDvlT5w4IDKZg9eo0aNVK5Vq5bPa5jPzDf7AZKSknyeA5q5zsDLL7+scmxsbMDnNPsfFi1apLJ577/JUw+HOY6TJ08GPK6cxuyVKl68uMq33nqryvfdd5/KS5cu9XkNcw2JzZs3q1yoUCGVzVp45ZVXVDb/tjBfNzyNy+zpjCS8YwEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgLVs1bztadEqs4mmWbNmAZ3zk08+Ubl79+4qDxo0yO2Y7du3q2wuiHTkyJGAxgDfHn74YZXffPNNt33y5s3r9RyHDh1SeezYsSqbi2Eh+ypZsqTK/fr1C+j433//3W3b+fPnrcaEzGc2XXbs2NH6nObrSNeuXVVesGCB9TVyOvNvgYw0a2/dulXlt99+W2Xz4R5mE76padOmbtvMRVvNvx3gztODMa42c+ZMlc2HPGQG8yEOt99+u8rdunVzO8bX5xVJeMcCAAAAgDUmFgAAAACsMbEAAAAAYC2ieiwqV66s8l//+leVW7du7XaMuZhKoDJyv2vdunVVbtCggcrm4j07d+4M+Bo5jXkv6ogRI1Tu06dPwOc0F786fPiwyubChu3atVPZvB/W7PPwR3Jysspr1qwJ+BwIPvMe2EAXyEPojR49WuU6deqonCdPHp/nKFasmMoJCQnW47qap96cr776SmXzXn7Y++OPP1Q+ffq0yp4Wtt23b5/KrVq1Utn8/QC43HDDDSqbfwOafR/ZqZ/CE96xAAAAAGCNiQUAAAAAa0wsAAAAAFgL6x6LRx55ROWJEyeqfN1112XmcDLs+uuvVzk6OjqLRhK5vvnmG5XLly+vsvm8+Yww74vcs2eP1/3NHo2MjMFcL4Eei6xRqlQplR999FGr8/3nP/+xOh6+HThwQGXz2fH+MPv2mjdv7nX/N954Q2XzZ/7pp59W2RyjCD0VmWH16tUqDx06VOXx48e7HVO0aFGVzXqaP3++yoH2XZljEhE5ePBgQOdAeGjbtq3K5s99TEyMypMnTw75mMIJ71gAAAAAsMbEAgAAAIA1JhYAAAAArIV1j4X5XPJQ9FScOHFC5V9//VVl81653bt3q1yhQgW3c5rHFCpUSOVTp04FPM6cbseOHSqbPRaRwvw8nnnmmSwaCa7WtWtXlatVqxbQ8ebrQlJSkvWYEHrm983MpmnTpoVyOAiRuXPnquxpzaEaNWqo/P7776vcvn17lbt06RLQGH766Se3bSdPngzoHMgacXFxKt91110qmz11Z86cUXnbtm2hGViY4h0LAAAAANaYWAAAAACwxsQCAAAAgLUox8+H75vP7M8M5j2MY8aMUblcuXIq//77727n+Pjjj1X+/vvvVTbXDTh+/LjKuXPrNpRjx46pXKRIEbdrmseYPRf79+93Oyaz2az7kBW10KRJE5XN50j78/mY99UWLFhQ5UWLFqls9kOYTp8+7fV4T3755ReVzR6frBBptRAKy5cvV7lFixYBHT948GCVzfUOIkVGayG71AEuy+6vCe3atXPb9txzz6l86623BnRO8/NetmyZyp06dXI7xvwdEo6yey3Af/7WAu9YAAAAALDGxAIAAACANSYWAAAAAKyFdY8FQof7JuFCLQTeY7Fr1y6VGzVqpPLhw4eDM7BMRo8FRHLma0Lx4sVVHjhwoMr/+Mc/vB4/dOhQlceNG6fyhQsXMj64LJQTawGe0WMBAAAAINMwsQAAAABgjYkFAAAAAGv0WORQ3DcJF2pB5M4771TZfAa96dKlSyr/5S9/UXnbtm3BGVgmo8cCIrwm4H+oBbjQYwEAAAAg0zCxAAAAAGCNiQUAAAAAa0wsAAAAAFjLndUDAIDMdtttt6n8/PPPB3T8dddd5zUDAJAT8Y4FAAAAAGtMLAAAAABYY2IBAAAAwBoL5OVQLHoDF2oBLiyQBxFeE/A/1AJcWCAPAAAAQKZhYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYM3vdSwAAAAA4Fp4xwIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGvZdmIxYsQIiYqKytCxM2bMkKioKElJSQnuoJAlqAW4UAtwoRbgQi3AhVqwFxETC9c3y/UvJiZGypYtK61atZK33npLTp48GfIxTJkyRWbMmOH3/ufOnZNXX31VatSoIfny5ZNy5cpJ586dZevWraEbZA4QibUgIpKcnCw333yzxMTESIUKFWT48OGSlpYWmgHmEJFWC0ePHpUxY8ZI48aNpUSJElKkSBFJTEyU2bNnh3aQOUCk1YKIyKBBg+Tmm2+WYsWKSb58+eTGG2+UESNGyKlTp0I3yBwgEmth9uzZ0qNHD6latapERUVJ06ZNQza2nCQSayE7vC5EOY7jZPUgfJkxY4b07t1bRo0aJfHx8XLx4kU5fPiwrF69WpYvXy4VKlSQ5ORkqVWr1pVj0tLSJC0tTWJiYgK+3qVLl+TixYsSHR19ZeZ60003SVxcnKxevdqvc3Ts2FGSk5Pl4YcflptvvlkOHjwokydPlrNnz8qWLVukYsWKAY8LkVkLS5YskTZt2kjTpk3l/vvvly1btsjkyZOlb9++MnXq1IDHhMsirRYWLVokHTp0kNatW0uzZs0kd+7cMm/ePFm1apW88MILMnLkyIDHhMsirRZERBo2bCj16tWThIQEiYmJkR9++EH++c9/yi233CJr166VXLki4v/9wk4k1kLTpk1l48aNcuutt8rmzZulVq1afh+La4vEWsgWrwtOBJg+fbojIs53333n9rEVK1Y4sbGxTsWKFZ0zZ86EbAw1a9Z0mjRp4te++/fvd0TEefrpp9X2lStXOiLijBs3LgQjzBkirRYcx3Fq1Kjh1K5d27l48eKVbUOGDHGioqKc//73vyEYYc4QabWwe/duJyUlRW1LT093mjdv7kRHRzunTp0KwQhzhkirhWsZO3asIyLON998E5xB5UCRWAv79u1zLl26lKFjcW2RWAueRNrrQgRMfbxr3ry5DBs2TPbu3SszZ868st3TfXJnz56VAQMGSFxcnBQsWFDuueceOXDggERFRcmIESOu7GfeJ1epUiXZunWrrFmz5spbat7eqnS9vVaqVCm1vUyZMiIiEhsba/EZ41rCsRZ+/vln+fnnn6Vv376SO3fuK9sfe+wxcRxH5s6dG5TPHVo41kJ8fLzbO5VRUVHSvn17OX/+vOzevdv684a7cKyFa6lUqZKIiBw/fjzgY+FbuNbC9ddfHxn/E52NhGsteBJprwvZopJ79uwpIiLLli3zul+vXr1k4sSJ0rp1a3nttdckNjZW2rRp4/P8EyZMkPLly0v16tUlKSlJkpKSZMiQIdfcv0qVKlK+fHl544035LPPPpP9+/fLhg0b5NFHH5X4+Hjp2rVrYJ8g/BZutfDDDz+IiMgtt9yitpctW1bKly9/5eMIvnCrhWs5fPiwiIjExcUFfCz8E661kJaWJr///rscPHhQli1bJkOHDpWCBQtK/fr1/fvEELBwrQVkvnCthUh/Xcjte5fwV758eSlcuLDs2rXrmvts2rRJ5syZIwMHDpTx48eLyOX/Ne7du7f8+OOPXs/fvn17GTp0qMTFxUmPHj18jidPnjwyb9486datm9xzzz1XtterV0/WrVsnRYoU8e8TQ8DCrRYOHTokIv97t+pqZcqUkYMHD/o8BzIm3GrBk2PHjsm0adOkUaNGHmsEwRGutfD999/L7bfffiXfcMMNkpycLMWKFfP7HAhMuNYCMl+41kKkvy5ki3csREQKFCjgtcN/6dKlInK5IK7Wv3//kIynaNGiUqdOHXnuuedkwYIFMnbsWElJSZHOnTvLuXPnQnJNXBZOtXD27FkREYmOjnb7WExMzJWPIzTCqRZM6enp0r17dzl+/LhMnDgx5NfL6cKxFmrUqCHLly+XBQsWyDPPPCP58+ePqKe/RKpwrAVkjXCshUh/XcgW71iIiJw6dUpKlix5zY/v3btXcuXKJfHx8Wp7QkJC0Mdy4sQJadSokQwePFieeuqpK9tvueUWadq0qUyfPl369esX9OvisnCqBVc/zfnz590+du7cOfptQiycasHUv39/Wbp0qXzwwQdSu3btkF8vpwvHWihUqJDceeedIiLSrl07+fDDD6Vdu3ayadMmaiKEwrEWkDXCsRYi/XUhW7xjsX//fjlx4kTY/NDPmzdPUlNT1W1QIiJNmjSRQoUKyddff51FI8v+wq0WXLe3uG6JutqhQ4ekbNmymT2kHCPcauFqI0eOlClTpsjo0aOv3OeL0AnnWrhahw4dRETk448/zuKRZF+RUgsIvUiphUh7XcgWE4ukpCQREWnVqtU196lYsaKkp6fLnj171PadO3f6dY1AVmJMTU0VkcvPNL6a4zhy6dIlFkYLoXCrhTp16ojI5Xsmr3bw4EHZv3//lY8j+MKtFlwmT54sI0aMkIEDB8qzzz4b8PEIXLjWgun8+fOSnp4uJ06csD4XPIuUWkDoRUotRNrrQsRPLFauXCkvvviixMfHS/fu3a+5n6twpkyZorb7e29z/vz5/X7UV7Vq1UTEfXaZnJwsp0+flrp16/p1HgQmHGuhZs2aUr16dXn33XfVRHPq1KkSFRUlnTp18us8CEw41oLI5RV2BwwYIN27d5dx48b5fRwyLhxr4fjx43Lx4kW37dOmTRMR96fIITjCsRaQNcKxFrLL60JE9VgsWbJEtm3bJmlpaZKamiorV66U5cuXS8WKFSU5OdnrSon16tWTjh07yoQJE+To0aOSmJgoa9askR07doiI71llvXr1ZOrUqfLSSy9JQkKClCxZUpo3b+5x37Zt20rNmjVl1KhRsnfvXklMTJSdO3fKpEmTpEyZMtKnT5+MfxEgIpFTCyIiY8aMkXvuuUf++te/SteuXeWnn36SSZMmyUMPPSQ33nhjxr4AuCJSamHDhg3ywAMPSPHixaVFixYya9Ys9fE77rhDKleuHOBnj6tFSi2sXr1aBgwYIJ06dZKqVavKhQsX5Msvv5T58+fLLbfcwtOEgiBSakFEZO3atbJ27VoRETly5IicPn1aXnrpJRERady4sTRu3DjQTx9XiZRayDavC1m9Qp8/XKsnuv7lzZvXKV26tNOyZUvnzTffdP7880+3Y4YPH+6Yn97p06edxx9/3ClWrJhToEABp3379s727dsdEXFGjx7tdr09e/Zc2Xb48GGnTZs2TsGCBR0R8bmS4rFjx5xBgwY51apVc6Kjo524uDina9euzu7du62+FjldJNaC4zjOp59+6tSpU8eJjo52ypcv7wwdOtS5cOFChr8OiLxaMMdr/ps+fbrtlyTHirRa2Llzp/PAAw84lStXdmJjY52YmBinZs2azvDhw1mB3VKk1cLV1/f0b/jw4TZfjhwt0mohu7wuRDmO4wRxnhJxNm/eLHXr1pWZM2d6fTsM2R+1ABdqAS7UAlyoBbhQC9cW8T0WgfC0ZsCECRMkV65cvNWYw1ALcKEW4EItwIVagAu1EJiI6rGw9frrr8vGjRulWbNmkjt3blmyZIksWbJE+vbtK9dff31WDw+ZiFqAC7UAF2oBLtQCXKiFAGX1vViZadmyZU6DBg2cokWLOnny5HGqVKnijBgxwrl48WJWDw2ZjFqAC7UAF2oBLtQCXKiFwOT4HgsAAAAA9nJUjwUAAACA0GBiAQAAAMAaEwsAAAAA1vx+KpSv1QURWWxaa6iF7IVagEtGa4E6yF54TYALtQAXf2uBdywAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa7mzegBAVqlRo4bKy5cvV7lMmTIqR0VFqbxw4UKV161b53aNzZs3q7xs2bJAh4lMkJiYqPKIESNUbtmypcq5cun/k0lPT1d58eLFbtcwz7lp06YARwkAQHjjHQsAAAAA1phYAAAAALDGxAIAAACAtSjHcRy/djTuL88pGjZsqPJf/vIXlTt06OB2TIsWLbyec8iQISq/+uqrGRxdxvn5bfcoUmvB7KlYunSpyuXKlVP52LFjKicnJ3s9f+3atd223XjjjSqvX79e5bFjx6q8ZMkSr9cIhZxYC+bPtdkvU7hwYa/Hm5+3P1/Dn376SeXbbrtN5fPnz/s8R6hltBbCoQ5y59Ytg59++qnKrVu39nkOX70zv/zyi8pmL43ZR3Py5Emf1wxHOfE1IVDma8jatWtVNr8OkyZNcjtH//79gz+wIKMW4OJvLfCOBQAAAABrTCwAAAAAWGNiAQAAAMBaju+xKFu2rMofffSRyo0aNfJ6vKf7ovPkyaOyed/uuXPnVN67d6/K77zzjsoTJkzwOoaMyO73TVavXt1tm7lOhfm9N++ffuWVV1T+4IMPvF4zLi7ObVvbtm1V7tevn8pmD8bdd9+t8po1a7xeMxiyey3UqlXLbdsXX3yhcrFixVQ+fvy4ymZ/TYMGDVQ2v/e+ejRE3L/XZs9PVojkHot8+fKp/Pnnn6t8++23+zxHRnpnrmauZXPvvfe67XP06NGAzpkVsvtrQjCYaxL56q3cvn272zaz7y8cZbdaGDRokMqefj888MADAZ3TV2/W888/r/Jrr70W0PnDBT0WAAAAADINEwsAAAAA1phYAAAAALCW7XssoqOjVe7bt6/K5nOkExISvJ7PvA/fXJNCRKRIkSIqv/vuu76GqZjP1Pd0n66t7HbfZP78+VXeunWr2z7XX399QOfcvHmzyvXq1Qt4XKaOHTuqPGfOHJVXrVql8v3336/ykSNHrMdgym610LRpU5VHjhzpto/ZI2GuWTJmzBiv2dSsWTOVzX4eT+ixCK1q1aqpbPbRiIg89NBDKk+bNs3rOZ966imVzddm8+vQpUsXt3PMnTvX6zXCQXZ7TQiGJk2aqGz+jF933XVej6fHImvUqVNH5Y0bN6ps8/m5+OrN+uabb1T21bsbruixAAAAAJBpmFgAAAAAsMbEAgAAAIC13Fk9gFBr3ry5ym+++abX/c3n10+ePFnl0aNHq3z69Gm3czzxxBMBjFAkLS1N5dWrVwd0fE5UunRplXv37q1yoP0U4cK8V79Hjx4qjx8/PjOHExEKFCigsrn+SP369X2ew/w6m8+o92Xbtm0B7S8SuTUaKXbs2OFzn/Xr1wd0TrMnyuyxOHXqlMpmTx4il9lP6aunAqFRvHhxlVu2bKmy2TdboUIFr+fztK6M+dph9muZY/B1TvN3UnbHOxYAAAAArDGxAAAAAGCNiQUAAAAAa9m+x+Ivf/lLQPv36dNH5U8//TSg/UVE3njjDa/H/Pbbbyr37NlTZX+egZ/TTZo0SeVgrPVh9rp88skn1uc0/fDDDyqnpKSoXKlSJZWfffZZlemxcF+zZOrUqSqbPRWe1v6YOXOmyl9++WWQRue/7t27q/zee+9l+hjg3U033aTyhAkTVDafX//hhx+q/OOPP4ZkXMh8sbGxWT0EiEiHDh1UNl//fZk1a5bKU6ZMcdvH/D1t/i3QunVrr9eYP3++ykuWLAlkiBGPdywAAAAAWGNiAQAAAMAaEwsAAAAA1rJ9j4V5D6xp3759Kq9YsULlhIQElc37+Vq0aOFzDGZPRePGjVX253nrOZ35zP9ff/016Nd47rnnVA5FP8Pu3btVTkpKUnnYsGFBv2Z2U6ZMGZXvv/9+lX///XeVu3Tp4naOtWvXBnVM1atXD/iY//73v0EdA+xFR0erbL4GlCpVSuWDBw+q3K9fv9AMDBFv3LhxWT2EbGHo0KFWxz/wwAM+93n11VdV9tVTsWbNGpUHDx4c+MCyEd6xAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAWrZv3v7Pf/7j9eMVKlRQ+eWXX1bZXLyuUKFCPq85e/ZslQcNGqTy4cOHfZ4DWrly5VR+/PHHrc/58ccfq/zmm29anzNQ/jT/w7tjx46p3KlTJ5W/+uqrkI+hffv2AR+zcOHC4A8EVr7++muV69Spo/LKlStVfvjhh0M9JGQR8yERcXFxAR2/fft2lc2/C5Ax5gN5fD2gx5f77rvPbdszzzwT0Dk+++wzlc3XhUOHDqls/u2R3fCOBQAAAABrTCwAAAAAWGNiAQAAAMBatu+x+O677wLa39e9++fPn1fZ00Io7777rsoXLlwIaAzw7brrrgv4GPOe1yFDhqicnp5uNSZ/mD095oJb8C0lJUXlG2+8UeWjR49m4mgQKapVq+a2zVyQsm7duio7jqNy8eLFVe7QoYPK5sKLGzduDHicCA9du3ZV2VP9eGMurnjy5EnrMUGkfv36KlepUkXlJ554QuXk5GSv5zN/xq+1zZuxY8d6Pd78G/C1117zeU7ztWTy5Mkqr1+/PpAhZiresQAAAABgjYkFAAAAAGtMLAAAAABYy/Y9FrbMNSeefPJJlT/55JPMHA4s3HXXXSrv3bs308dw6623qmzeH2r65ZdfQjmciJSWlqZyVvRU/PWvf1W5b9++Po8x19T54osvgjomeNe/f3+3bd26dVPZ1zPxzXUtzGwe/95777mdY8CAASqbfXsID/fff7/V8ampqUEaCa5m/k1mZnMtGl9+//13t20//fSTynnz5lXZ9ndOdHS027abb75ZZfO1yfyd8/e//13lxYsXW40pmHjHAgAAAIA1JhYAAAAArDGxAAAAAGCNHgsf7rvvPpW/+uqrLBpJzpKYmKjyhAkTvO5/6dIllc3nSouI/Prrr9bjymyHDh3K6iFA3O+x/fzzz1U210DxdA+uec+s2SuC0Nq6davbtnXr1qn85ptvBnTOhx56SOWWLVuq3KdPH7djli5dqvKnn34a0DURGiVKlFC5YMGCAR2/bds2lflbITKsWrXKbVuLFi1Ujo2NVXn//v1W18yXL5/bttatW6v8zjvvqGyuofPPf/5T5Xbt2qmcletc8I4FAAAAAGtMLAAAAABYY2IBAAAAwFq26rEoVKiQ27aPPvrI6pysI5A14uLiVP7uu+9UNu95rFChgsrPP/98aAYWoAIFCqjcs2dPr/ub992zTkrWyJ8/v8qLFi1S2eypcBxH5Y8//tjtnOY92Mhcb7/9tl/bAjF37lyVze9xQkKC2zFdunRRmR6L8HDHHXeoXK1atYCOP3XqlMrHjh2zHhOyRqjXRjpz5ozbNvO1ZPfu3SovX75cZbPnonz58kEanT3esQAAAABgjYkFAAAAAGtMLAAAAABYi+gei/r166vs6X7066+/3uoa5vGpqalW50PGPPbYY14/PnPmzEwaSWDmzJmjcqtWrbzu/9///ldleiyyxtNPP61yo0aNvO6fkpKi8ltvvRXsISECLF68WOUnn3wyi0aCQPnqf/MlKSkpSCMBRDZt2qTyo48+qrLZx/fGG2+obPZsZCbesQAAAABgjYkFAAAAAGtMLAAAAABYi6gei4IFC6o8Y8YMlT31U/z0008qL1y4UOUhQ4Z4veb3338fwAiRUU899ZTKtWvX9rr/H3/8ofLEiRODPqZgaNCgQUD7+6pH+FalShWV69at67ZP586dvZ6jdevWAV3T7IUx1y8REalTp47Xc/z2228qlyxZUmXzufj79u0LYITIClFRUVk9BPipatWqAe3/888/q2z20wHBNGzYMJXNtZPMtZWyEu9YAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgLaKat1966SWVq1evrvLevXvdjjEXJDMX1UN4eOedd1Q2m7HNJvrmzZurfPr06dAMzIsmTZqonJyc7LaPpybeq3399dcqf/755/YDy+bKlSun8rvvvqtyvXr1VI6Liwv5mAYPHuw1+2P37t0qV65cWeUDBw6obDaDmw80QNYzGyyRfZg/b+bDFwAbZcuWVblEiRJe9w+nRVl5xwIAAACANSYWAAAAAKwxsQAAAABgLax7LCpWrKhy7969ve7/9NNPu207dOiQym3atLEfGIKuWbNmKpuLmp05c0blzOipKFKkiMotWrRQuVevXir76qcQcb9P3rwXPy0tzf8B5hDR0dEqjxw5UmWzjyoUli9frnJGvk/mwn27du3yuv/27dtVNvuQsqKvKJIkJib63Gf9+vVBvWagi6wha9x2221u28qXLx/QOehpQigtXrxYZV89Fr/++msohxMQ3rEAAAAAYI2JBQAAAABrTCwAAAAAWAvrHgvz3mnzHnbzudHz5s1zO0eePHlUvvHGG71ek2dRZ433339f5eLFi6v87bffhnwM5voHzz//vMrt27cP+JzmOhVmT0VmfF6RrlixYiqbvS2hMGLECJVfffVVlS9duhTwOUuVKqVyampqwOeA/wYNGqSypzUlunbtGtRrmj18nq45bdq0oF4TgTP7N0Xce+p8mTBhQnAGA4hIu3btVK5Vq5bK5mtJSkqKyps3bw7FsDKEdywAAAAAWGNiAQAAAMAaEwsAAAAA1sK6x6J58+ZeP753716VzX4KEZEnnnhC5QYNGng9p6+1MhAa//znP1U2exFiY2NVrlGjhtfzeVrbwFc9NWzYUOVChQp53d+8R37OnDlu+5hrq7BORXgyeypGjx6tckZ6Kkz0VGStzp07u2377LPPVJ41a5bXc+TLl0/l2bNnqxwVFaXyTz/95HaOrVu3er0GQs/8PvrDXFdmx44dwRoOstB9993ntu32229XeerUqSrbfu8LFizotm3gwIEq58ql/98/PT1d5R49eqi8c+dOqzEFE+9YAAAAALDGxAIAAACANSYWAAAAAKyFdY/FRx99pLJ5L9ytt96q8sqVK93O4aunwlxngHUFsob5bPd7771XZfOZzlu2bAn6GC5evKjykSNHVDbr8Z133lF527ZtQR8T7Jm9WCLu9fXzzz+rTC9M5DPvgz558qTbPkOHDlV5165dXs9p9kzdddddKp8/f15l875pEZFDhw55vQZCz1zjxB/mWksHDhwI1nCQhTytNdO/f3+VzfVp7r77bpV99VyY63J98MEHbvs0atRIZbOnwuwH27Rpk9drZiXesQAAAABgjYkFAAAAAGtMLAAAAABYi3I83WDmaUfj+dyZISEhQeVVq1apXK5cOZU9jdH89MyeirZt26p8/PjxQIcZkfz8tnuUGbVQpUoVlc174nv27KmyeY+jp16Z1q1bq/zvf/9bZfNe/E8++cS/wUa4cK8F83neffv2VXnYsGEqjxo1SuV//etfbuc8d+5ckEaXvWS0FrLi90OgzNcQEfceizp16qgc6Nfj0UcfVdnsHYsU4f6aYMvT2gVmD53JvAd+3bp1QR1TuMrutdCsWTO3bePHj1f5pptuUtn8W8Fco8j8mhUoUEDlmjVr+hyX2Ytlvn59//33Ps8RbP7WAu9YAAAAALDGxAIAAACANSYWAAAAAKyFdY+FqVKlSiqPGTNGZfMeSBH3++SHDx+u8rFjx4IzuAiT3e+bhP+oBbhk5x4LTwoWLKiy+fvBfH69eV+z2afl6z79SJHdXxNq1Kjhtu2LL75QuVSpUirTYxG4SKgFT8x1J2bMmKGyuX6N+Xlm5Gtm9ve2aNFC5R9//DHgcwYbPRYAAAAAMg0TCwAAAADWmFgAAAAAsMbEAgAAAIC1iGreRvDkxIYseEYtwCWnNW/DM14T4EItuD/koU+fPl73NxdtNZu/f/31V7dj1q5dq/KmTZsCGGHmoHkbAAAAQKZhYgEAAADAGhMLAAAAANboscihuG8SLtQCXOixgAivCfgfagEu9FgAAAAAyDRMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArPm9jgUAAAAAXAvvWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsMbEAgAAAIA1JhYAAAAArDGxAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsZduJxYgRIyQqKipDx86YMUOioqIkJSUluINClqAW4EItwIVagAu1ABdqwV5ETCxc3yzXv5iYGClbtqy0atVK3nrrLTl58mTIxzBlyhSZMWOG3/ufOnVKBg4cKOXLl5fo6Gi58cYbZerUqaEbYA4RibUwaNAgufnmm6VYsWKSL18+ufHGG2XEiBFy6tSp0A0yB4jEWjh37py8+uqrUqNGDcmXL5+UK1dOOnfuLFu3bg3dIHOASKyF2bNnS48ePaRq1aoSFRUlTZs2DdnYcpJIq4WjR4/KmDFjpHHjxlKiRAkpUqSIJCYmyuzZs0M7yBwg0mph9erVarzmv5dffjm0gw2SKMdxnKwehC8zZsyQ3r17y6hRoyQ+Pl4uXrwohw8fltWrV8vy5culQoUKkpycLLVq1bpyTFpamqSlpUlMTEzA17t06ZJcvHhRoqOjr8xcb7rpJomLi5PVq1f7dXzjxo3l+++/l8cff1yqVq0qn3/+uSxcuFBefvllef755wMeEy6LtFoQEWnYsKHUq1dPEhISJCYmRn744Qf55z//KbfccousXbtWcuWKiPl92InEWujYsaMkJyfLww8/LDfffLMcPHhQJk+eLGfPnpUtW7ZIxYoVAx4XIrMWmjZtKhs3bpRbb71VNm/eLLVq1fL7WFxbpNXCokWLpEOHDtK6dWtp1qyZ5M6dW+bNmyerVq2SF154QUaOHBnwmHBZpNVCamqqLF++3G17UlKSLFu2TDZs2CC33nprwOPKdE4EmD59uiMiznfffef2sRUrVjixsbFOxYoVnTNnzoRsDDVr1nSaNGni175z5sxxRMR5//331faOHTs6MTExTmpqaghGmDNEWi1cy9ixYx0Rcb755pvgDCoHirRa2L9/vyMiztNPP622r1y50hERZ9y4cSEYYc4QabXgOI6zb98+59KlSxk6FtcWabWwe/duJyUlRW1LT093mjdv7kRHRzunTp0KwQhzhkirhWtJSEhwqlatGpwBZYKI/6/S5s2by7Bhw2Tv3r0yc+bMK9s93Sd39uxZGTBggMTFxUnBggXlnnvukQMHDkhUVJSMGDHiyn7mfXKVKlWSrVu3ypo1a668JeXtbesvv/xSRES6du2qtnft2lXOnTsnCxcutPuk4VE41sK1VKpUSUREjh8/HvCx8C0ca8H1tnupUqXU9jJlyoiISGxsrMVnjGsJx1oQEbn++ut5tzKThWMtxMfHu71TGRUVJe3bt5fz58/L7t27rT9vuAvHWvBkw4YNsnPnTunevXtGP9VMly1e1Xr27CkiIsuWLfO6X69evWTixInSunVree211yQ2NlbatGnj8/wTJkyQ8uXLS/Xq1SUpKUmSkpJkyJAh19z//Pnzct1110nevHnV9nz58omIyMaNG31eExkTbrXgkpaWJr///rscPHhQli1bJkOHDpWCBQtK/fr1/fvEELBwq4UqVapI+fLl5Y033pDPPvtM9u/fLxs2bJBHH31U4uPj3f4jAsETbrWArBMptXD48GEREYmLiwv4WPgnEmph1qxZIiIRNbHIndUDCIby5ctL4cKFZdeuXdfcZ9OmTTJnzhwZOHCgjB8/XkREHnvsMendu7f8+OOPXs/fvn17GTp0qMTFxUmPHj18jueGG26QS5cuyfr166Vhw4ZXtrveyThw4IA/nxYyINxqweX777+X22+//Uq+4YYbJDk5WYoVK+b3ORCYcKuFPHnyyLx586Rbt25yzz33XNler149WbdunRQpUsS/TwwBC7daQNaJhFo4duyYTJs2TRo1anTlHU0EX7jXwqVLl2T27NlSv359SUhICPj4rJIt3rEQESlQoIDXDv+lS5eKyOWCuFr//v2DPpZu3bpJ4cKF5e9//7ssX75cUlJS5N1335UpU6aIyOW31RA64VQLLjVq1JDly5fLggUL5JlnnpH8+fPzVKhMEG61ULRoUalTp44899xzsmDBAhk7dqykpKRI586d5dy5cyG5Ji4Lt1pA1gnnWkhPT5fu3bvL8ePHZeLEiSG/Xk4XzrWwYsUKSU1Njah3K0SyyTsWIpcf71qyZMlrfnzv3r2SK1cuiY+PV9tDMQssXbq0JCcnS8+ePeWvf/2riIgUKlRIJk6cKA8++KAUKFAg6NfE/4RTLbgUKlRI7rzzThERadeunXz44YfSrl072bRpk9SuXTtk183pwqkWTpw4IY0aNZLBgwfLU089dWX7LbfcIk2bNpXp06dLv379gn5dXBZOtYCsFc610L9/f1m6dKl88MEH/G7IBOFcC7NmzZLrrrtOunTpEvJrBVO2eMdi//79cuLEibD6BdC4cWPZvXu3/PDDD/LVV1/JgQMHJDExUUREqlWrlsWjy77CsRY86dChg4iIfPzxx1k8kuwr3Gph3rx5kpqaqm6DEhFp0qSJFCpUSL7++ussGln2F261gKwTzrUwcuRImTJliowePfrK/f8InXCuhbNnz8qnn34qd955p9sDP8JdtphYJCUliYhIq1atrrlPxYoVJT09Xfbs2aO279y5069rZGQlxuuuu07q1KkjDRo0kAIFCsgXX3whInLlf64RfOFaC6bz589Lenq6nDhxwvpc8CzcaiE1NVVELt83ezXHceTSpUuSlpbm97kQmHCrBWSdcK2FyZMny4gRI2TgwIHy7LPPBnw8AheutSAikpycLCdPnoy426BEssHEYuXKlfLiiy9KfHy812+Aq3BcfQ4u/t7DmD9/fqtHgx45ckRee+01qVWrFhOLEAnHWjh+/LhcvHjRbfu0adNE5PJtMAi+cKwF1zuV5rtUycnJcvr0aalbt65f50FgwrEWkDXCtRZmz54tAwYMkO7du8u4ceP8Pg4ZF6614PLhhx9Kvnz55N577w342KwWUT0WS5YskW3btklaWpqkpqbKypUrZfny5VKxYkVJTk72ulJivXr1pGPHjjJhwgQ5evSoJCYmypo1a2THjh0i4ntWWa9ePZk6daq89NJLkpCQICVLlpTmzZtfc/8mTZrI7bffLgkJCXL48GF599135dSpU7Jo0SKeXR4EkVILq1evlgEDBkinTp2katWqcuHCBfnyyy9l/vz5csstt/AEmSCIlFpo27at1KxZU0aNGiV79+6VxMRE2blzp0yaNEnKlCkjffr0yfgXASISObUgIrJ27VpZu3atiFz+j6fTp0/LSy+9JCKXb6Vt3LhxoJ8+rhIptbBhwwZ54IEHpHjx4tKiRYsrjxd1ueOOO6Ry5coBfva4WqTUgsuxY8dkyZIl0rFjx8jsyc3qFfr84Vo90fUvb968TunSpZ2WLVs6b775pvPnn3+6HTN8+HDH/PROnz7tPP74406xYsWcAgUKOO3bt3e2b9/uiIgzevRot+vt2bPnyrbDhw87bdq0cQoWLOiIiM+VFAcNGuRUrlzZiY6OdkqUKOF069bN2bVrl9XXAZFXCzt37nQeeOABp3Llyk5sbKwTExPj1KxZ0xk+fDgrqlqKtFpwHMc5duyYM2jQIKdatWpOdHS0ExcX53Tt2tXZvXu31dcip4vEWnBd39O/4cOH23w5crRIqwVzvOa/6dOn235JcqxIqwWXt99+2xERJzk5OcOfe1aKchzHCd40JfJs3rxZ6tatKzNnzozIe9kQPNQCXKgFuFALcKEW4EItXFuOuifH0/oREyZMkFy5cvG2cw5DLcCFWoALtQAXagEu1EJgIqrHwtbrr78uGzdulGbNmknu3LllyZIlsmTJEunbt69cf/31WT08ZCJqAS7UAlyoBbhQC3ChFgKU1fdiZaZly5Y5DRo0cIoWLerkyZPHqVKlijNixAjn4sWLWT00ZDJqAS7UAlyoBbhQC3ChFgKT43ssAAAAANjLUT0WAAAAAEKDiQUAAAAAa0wsAAAAAFjz+6lQvlYXRGSxaa2hFrIXagEuGa0F6iB74TUBLtQCXPytBd6xAAAAAGCNiQUAAAAAa0wsAAAAAFhjYgEAAADAGhMLAAAAANaYWAAAAACwxsQCAAAAgDUmFgAAAACsMbEAAAAAYI2JBQAAAABrTCwAAAAAWGNiAQAAAMAaEwsAAAAA1phYAAAAALDGxAIAAACANSYWAAAAAKzlzuoBAEC4K1iwoNePr1q1SuW6dev6POcDDzyg8qxZswIfGLLUnDlzVB43bpzK69evz8zhAECW4x0LAAAAANaYWAAAAACwxsQCAAAAgLVs1WNRvHhxt209e/ZUuUOHDio3atRI5blz56p84sQJr3nkyJFu1/zzzz99DxYhFRUV5bataNGiKk+ePFnlLl26BHROx3FUfvXVV92OGTNmjMrHjx/3eg1kjZtuuknlYcOGqVy1alWvx994440qHz161G2fYsWKqVynTh2V6bEIfw0aNFC5U6dOKpu/H+ixiBz33Xefyubre6VKlVR+4oknvJ7P1+8LT/71r3+pvGXLFpU/+eQTn+cAshrvWAAAAACwxsQCAAAAgDUmFgAAAACsRVSPhfks+b///e8qP/XUU27HnD9/XuXRo0er/PDDD3u9ZoUKFVS+9957Ve7cubPbMe+//77XcyL0SpYs6bbt4MGDXo/xdQ+sr48/99xzbtv69++v8p133qnyhg0bvJ4TmeOVV15RuXXr1gEdb65j8cUXX7jt8/LLLwc+MIQVs6cCkaF+/foqjx8/3m2fxMRElf3pifAmIz0Wzz//vNeP02OBSMA7FgAAAACsMbEAAAAAYI2JBQAAAABrYd1jYd6PPm3aNJV37Nih8muvveZ2jvfee0/lCxcuBDSG7du3q7x8+XKVzR4MhIe+fftm9RBERCR//vwq/9///Z/KXbt2zczh4P+rV6+eym3atFHZvB/afK1ZvHixyhs3blTZfN1B9hAXF5fVQ4AfqlWrpvKcOXNULl++fMDn/O2331Q2+zdNuXLp/7eNiYlx28fT2lsILnP9kaZNm6p8zz33uB3Trl07lTPSL+ONp/WsbrvtNpV37txpdY2sxDsWAAAAAKwxsQAAAABgjYkFAAAAAGth1WORkJCg8tSpU1X+448/VDbvTz927FhoBnaV6OholQPt2UDm+Oijj9y2jRgxIqBzfPvttyp/9dVXKpvrqBQtWtTnOc17f5E1GjdurLJ5P3R6errK5vd6/fr1KlevXl3lfPny+RzDl19+6XMfhBez789k9uQhaxQrVkzljPRUbN68WeW2bduqfOjQoYDO52nNK0+/p+Cdud7I4MGDVTa/97Vq1VK5cOHCPq9hu6aVL0WKFHHbZq6l1LNnT5V99fSEE96xAAAAAGCNiQUAAAAAa0wsAAAAAFgLqx6L119/XeXKlSur3KRJE5Uzo6fCFB8fr/LKlSvd9hkzZozK48ePD+mY4C4lJcVt24IFC1QuXbq0ymYPxahRo1QuVaqUyg8//HDA49q6dWvAxyD0zJ4KX/fQli1bVmWztjwdP3/+fJXNNXEQ/szv6++//66yWQfIHGbv2ocffqiyuQ6BJx06dFB54cKFVmMaNGiQysOGDXPbx59x5XR33XWXyvPmzVM5b968Kvtac8LXz7CIyMcff6zy7t27vX7cZP5+eOmll1Ru3bq12zFm/U2fPl3lJUuWeL1mOOEdCwAAAADWmFgAAAAAsMbEAgAAAIC1TO2xyJMnj8rmOhXt27dX2Xx2vHkPfFY4fPiwyqdOnXLbp1evXiq//fbbKp89ezbo44KWlpbmtu2+++5TOSYmRuXTp097Pad5326hQoUCHtfixYsDPgbhp0uXLipXrVpVZU89FuPGjVOZ14HIs2LFCq8f37lzZyaNBFerXbu2yhUqVFDZn3UHAu2pMNeqeeedd1Tu1q2bzzH4Gpe5lkZOZPY27t27V+WDBw+qXK5cOZWnTJmi8p49e1T+7LPPbIfo5siRIyoPHDhQZU89FqZbb71VZXosAAAAAOQoTCwAAAAAWGNiAQAAAMAaEwsAAAAA1jK1ebtw4cIq9+7dW+XZs2d7zeHAXKSvTJkybvvkz59fZbOx8z//+U/wBwafLl26pLLZrJ0rl55nV69eXWVzcUR/mI1mc+fODfgcCL5NmzYFtP+nn36qsrkok+m9996zvibCj7mY1iOPPKKyuQDm6NGjQz4muH9fvvnmm6Bfo2DBgiqbC9/ef//91tfYsGGDyh07drQ+Z6SbMWOGysnJySqbCyUXK1bM68ezQmxsbFYPIVPxjgUAAAAAa0wsAAAAAFhjYgEAAADAWqb2WNx5551eP/7EE0+oHI4LSJUoUUJlc5EcTxo0aKAyPRbhaejQoSoPHz48oOMvXLjgtu3ee+9V2dPCfch8a9asUfnLL79UuVGjRiqXLFnS6/m2b9+ucr9+/SxGh3BlLohqLrL5448/ZuZw8P+tWrVKZfPnNyMSExNVfvHFF1Vu1qxZQOc7c+aM27ajR496vcahQ4cCukZO4KtnIhx6Kkxmb67Zzykikp6ernJUVFRIxxRKvGMBAAAAwBoTCwAAAADWmFgAAAAAsJapPRapqaleP966dWuVzWf+Z0XPRfny5VXu0aOHz2O+/fZbld99992gjgnB0bdvX5X79OkT0PHmvZwfffSR2z7ccx0ZNm7cqHLDhg0DOr59+/ZBHA3CRenSpVV+6qmnVDbvi/b1Ow7hy7wP3vxeB9pTYVq8eLHbtmCsfYHwV7lyZZXN1w0REcdxVF6wYEEohxRSvGMBAAAAwBoTCwAAAADWmFgAAAAAsJapPRbfffedyl988YXKM2bMULl69eoq7969W2Xz2fGelCpVSuUtW7aobD7v2rxX2nyWdbFixXxe01yr4NKlSz6PQea74447VDb7aXx55ZVXVB4/frz1mBAZzH6aHTt2ZNFIEEr16tVTOTY2VuXVq1ervGnTplAPCUFg9lOIuH8vPd0HH4gOHTqovHDhQqvzIXJUqlRJ5e7du/s85vz58yrv378/mEPKVLxjAQAAAMAaEwsAAAAA1phYAAAAALCWqT0Wp06dUrlVq1Yqm/eod+7cWeWqVauqbD73NyNOnjyp8oYNG1Q277HNly+fyj///LP1GBCZPvzww6weAjJo6tSpKnfr1i2g48uVKxfM4SBCmL9zIvk+6OysePHiKk+fPl3lxo0bux1j9lT4+vvim2++UXnKlCkq01ORc5k9FnFxcT6Pefvtt1U+evRoMIeUqXjHAgAAAIA1JhYAAAAArDGxAAAAAGAtU3ssfBk0aJDKI0aMULl06dJBv+bZs2dV3rdvn9f98+bNqzLPLY9cX3/9tcrNmjVT2de6FmPHjlX5wQcfdNvH9lno8C13bv0ydvPNN6v86aefuh1jvpZERUWp7Ov+avM5+C+88ILKo0aN8no8gOAxeyrMNSRat24d8DnNe9yXLVum8sCBA73uj5yra9euAR+TnJwcgpFkDd6xAAAAAGCNiQUAAAAAa0wsAAAAAFgLqx4L04kTJ7zmrHDhwgWVzR4NRI733ntP5U8++UTl3r17q/z888+rbK59kCuX+zy9e/fuNkOEHx566CGVJ02a5PMYs4di7969Kpu18cADD6hsrqnTp08flemxADKP2VNhrlOTEfPnz1e5X79+1ucMVJEiRVQuWLBgQMebr1siIrVq1VK5S5cuAY8L2g033KDyww8/7HX/1NRUt207d+4M6piyEu9YAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgLaybtyPB8ePH3baZDVeIDOb3cvz48SqvWrVK5bVr16rcsWNHt3O+9dZbKn/77bcWI4Qnw4YNC/iYjz76SOVnnnlG5UOHDqlcrVo1lc3m7Xz58qnsaXHF/fv3BzxOAL4NHTrU+hxr1qxRefDgwdbnvFqdOnXctvXo0cPrMeZCnObin74W8kTmGDJkiMq+vi/m/iIiBw4cCOqYshLvWAAAAACwxsQCAAAAgDUmFgAAAACs0WNh6aeffnLbZi6kU6FCBZX37dsX0jEhNEqWLKlyVFSUynny5HE75tlnn1XZXMgJ9kqXLq2yeX/rjh073I75xz/+obLZU2F6/PHHVb7zzjtVLlu2rMqJiYlu55g7d67XayD81KhRI6uHAA8WLFigsqeepkA1a9ZMZXNBXrNfzlPPxNWaNm2qcnp6eobH5mIuwrpt2zaVFy9erHJSUpLbOX788UfrceR0NWvWVLl9+/Ze9zcXUp4+fXqwhxRWeMcCAAAAgDUmFgAAAACsMbEAAAAAYI0eC0s7d+5021a4cGGVH3nkEZVLlSql8sCBA1U+depUcAYHK+b3cerUqSqbaxd4Yj53HMFn9rqYPP2MHj582Oqa5r3O5v3T5j21iEw33HBDVg8BHph9i8FYz8H8GTbP2b9//6Cez5MzZ86obPZMmK91zz33nMopKSkBjBAZZf7N5utvgVdeeSWEowk/vGMBAAAAwBoTCwAAAADWmFgAAAAAsEaPhSVPz4Q276U074O8cOGCys8880zwB5bNFC9eXOW+ffuqPG/ePJU9rV1gMp9Rb64/cscdd6hcqVIln+c07d27N+BjEJgDBw6oXKZMGZVbt27tdszQoUNVXrp0qddrPP300yqbfVLmGMx7owEET5s2bVSeP3++ytWrV1fZ/J1r/j4JhXXr1qm8efNmt31mzpyp8vnz530eg8yXkJCgcpcuXbzuf/DgQZWz+7oVJt6xAAAAAGCNiQUAAAAAa0wsAAAAAFijx8LS999/H/AxS5YsUfnYsWPBGk62df3116s8ePBglQcMGKDynj173M7xww8/qNy5c2eVbe+7NZ9B7ukaCL677rpL5UWLFqlcvnx5t2PMHothw4apHOhz8f3p6QEQHIcOHVLZfJ2tWrWqyua6Mp5eE4Jt7ty5Ib8GMofZU5E/f36v+2/YsEFl23WTIg3vWAAAAACwxsQCAAAAgDUmFgAAAACsRTl+3kwcFRUV6rFkG8nJySqbz9zu2rWryp988knIx2QK9B7yq4VDLbzwwgsqm+sM+LoHMhh++uknlV9//XW3fWbNmhXycdiK9Fowmb0yvXv3dtvH7LEoWLCgyr6+Jo899pjKH330kconT570Oc5wlNFaCMc6CAZznaJdu3apbN57ffHixZCPKTNkt9cEZFxOrAVz3Yrt27erbH5NzPVHWrRoofL69euDOLqs428t8I4FAAAAAGtMLAAAAABYY2IBAAAAwBo9FiEwduxYlRs2bKhy69atVc6KdSyy232TTz31lMqe+h0CtXPnTpXnz5+v8tdff62yuX5CpMhutYCMo8cCIrwm4H9yYi3885//VPnBBx9U2fyamH9vPP/886EZWBajxwIAAABApmFiAQAAAMAaEwsAAAAA1phYAAAAALBG83YOlRMbsuAZtQAXmrchwmsC/ie710LNmjXdtn311VcqFypUSGXza/Loo4+qPG3atCCNLrzQvA0AAAAg0zCxAAAAAGCNiQUAAAAAa/RY5FDZ/b5J+I9agAs9FhDhNQH/k91rIX/+/G7bkpKSVG7Xrp3K5uK59erVU/nUqVNBGl14occCAAAAQKZhYgEAAADAGhMLAAAAANboscihsvt9k/AftQAXeiwgwmsC/odagAs9FgAAAAAyDRMLAAAAANaYWAAAAACw5nePBQAAAABcC+9YAAAAALDGxAIAAACANSYWAAAAAKwxsQAAAABgjYkFAAAAAGtMLAAAAABYY2IBAAAAwBoTCwAAAADWmFgAAAAAsPb/AIcpEBXs1hn7AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 800x800 with 24 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# @title Affiches des images\n",
        "def plot_images(images, labels):\n",
        "  rows = 4\n",
        "  cols = 6\n",
        "  num_images = images.shape[0]\n",
        "\n",
        "  fig, axes = plt.subplots(rows, cols, figsize=(8, 8))\n",
        "\n",
        "  for ir in range(rows):\n",
        "    for ic in range(cols):\n",
        "      sample = np.random.randint(0, num_images)\n",
        "      image = images[sample].reshape(28, 28)\n",
        "      axes[ir, ic].imshow(image, cmap='gray')\n",
        "      axes[ir, ic].axis('off')\n",
        "      axes[ir, ic].set_title(f\"Digit {labels[sample]}\")\n",
        "\n",
        "  plt.tight_layout()\n",
        "  plt.show()\n",
        "\n",
        "plot_images(images, labels)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jzHwlZp2WfKM"
      },
      "source": [
        "**Excercise:** Exécutez la cellule ci-dessus plusieurs fois et regardez les images. Pouvez-vous identifier certaines images qui pourraient être difficiles à classer ?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e9NW58_3hAg2"
      },
      "source": [
        "## **Régression**\n",
        "\n",
        "Avant de construire notre classificateur de chiffres, nous devons d'abord comprendre quelques concepts clés de l'apprentissage automatique."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ME59aXJRwE3"
      },
      "source": [
        "La figure ci-dessous est une répresentation des données generées en utilisant la fonction sinus. En general, nous avons besoin de trouver une fonction qui assigne les entrées dans une dimension à des sorties dans une autre dimension. Le processus qui permet de trouver une telle fonction (**modèle**) est communément appelé **régression**. Dans l'apprentissage automatique, cela fait réference à la recherche d'une fonction qui mappe un ensemble de valeurs numériques appelées **features** à un autre ensemble de valeurs numeriques appelees **labels**. Si la fonction est linaire, le processus est appele **regression lineaire**.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "kDix480DPCgA",
        "outputId": "9c80a727-ac0b-485c-a4c4-67d8d4377163"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# @title Code d'aide pour tracer une courbe sinus.\n",
        "amplitude = 2\n",
        "x = np.linspace(0, 2*np.pi, 1000)\n",
        "y = amplitude*np.sin(x) + np.random.randn(1000)*0.1   # Calculate y values using the sine function\n",
        "yfit = amplitude*np.sin(x)\n",
        "\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.scatter(x, y, label=\"data\", color='red')\n",
        "plt.plot(x, yfit, label=f'Sine Curve with Amplitude = {amplitude}', color='black')\n",
        "plt.title('Sine Curve')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.legend()\n",
        "# plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bA_2coZvhAg3"
      },
      "source": [
        "### 2.1 Régression linéaire"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GGTQetYgNBda"
      },
      "source": [
        "Supposons que nous avons un dataset, avec des élements $y$ répresentant les labels et les élements $\\mathbf{x}$ répresentant nos variables.\n",
        "Notre objectif est de trouver une fonction $f$ qui relie une variable $\\mathbf{x} \\in \\mathbb{R}^d$ à une variable cible $y$:\n",
        "\n",
        "Les modèles de régression linéaire peuvent être répresentés mathématiquement comme suit:\n",
        "$$ f(\\mathbf{x}) = \\mathbf{w}^T \\mathbf{x} + b,$$\n",
        "Avec $\\mathbf{w} \\in \\mathbb{R}^d$. $\\mathbf{w}$ et $b$ sont les paramètres du modèle communément appelé poids. Le terme $b$ est communément appelé le biais et peut être inclu dans $\\mathbf{w}$ en étendant le vecteur de caractéristiques $\\mathbf{x}$ avec 1.\n",
        "\n",
        "Une façon intuitive de comprendre les équations ci-dessus est de se rappeler l'équation d'une ligne $$y \\, = \\, mx + c,$$ avec les poids et le biais correspondant à la pente et l'intercept, $m$ et $c$ réspectivement.\n",
        "\n",
        "**Note: pour le reste du tutoriel, nous utiliserons le framework JAX. Si vous n'êtes pas familier avec JAX, veuillez d'abord suivre la section facultative de l'annexe sur [JAX](#scrollTo=742JhcnAxTof) avant de continuer.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1SVA5XSjcfpH"
      },
      "source": [
        "Démonstration: modèle linéaire"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sBe3ytk5WyvD"
      },
      "outputs": [],
      "source": [
        "# Example implementation of a linear function computation.\n",
        "\n",
        "x_key = jax.random.PRNGKey(0)\n",
        "dim = 10\n",
        "x = jax.random.uniform(x_key, (dim,))\n",
        "\n",
        "w_key = jax.random.PRNGKey(1)\n",
        "w = jax.random.uniform(w_key, (dim,))\n",
        "\n",
        "b_key = jax.random.PRNGKey(2)\n",
        "b = jax.random.uniform(b_key, (1,))\n",
        "\n",
        "y = jnp.dot(w,x) + b  # can also be achieved using: y = x @ w + b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LH73KxFOdAMK"
      },
      "source": [
        "**Tâche de code:**\n",
        "\n",
        "Dans le precedant code nous avons demontré comment utilise un modèle de régression linéaire avec un seul example dans notre donnée d'apprentrissage. Lorsque nous implementons les modèles d'apprentissage automatique nous tirons l'avantage de l'Algèbre linéaire et et des réssources informatiques disponibles pour traiter des lots de données en une seule fois.\n",
        "\n",
        "Avec un dataset ou ensemble d'apprentissage $\\mathbf{X} \\in \\mathbb{R}$, écrivez une function qui applique la régression linéaire sur un lot de données $\\mathbf{X}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-Psjm_oQY_b7"
      },
      "outputs": [],
      "source": [
        "# @title Exécutez ce code pour générer les données\n",
        "# store the parameters in a dictionary\n",
        "params = dict(w=w, b=b)\n",
        "\n",
        "batch_size = 5\n",
        "X = jax.random.uniform(x_key, (batch_size, dim))\n",
        "data = jax.random.uniform(x_key, (batch_size,))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Qh-eOfEdh-f0"
      },
      "outputs": [],
      "source": [
        "def linear_model(params: Any, X: jnp.ndarray) -> jnp.ndarray:\n",
        "  # complete this code\n",
        "  w = params['w']\n",
        "  b = ... # update me. hint look at the above line for w\n",
        "\n",
        "  # compute m = f(x) here using w,b and X\n",
        "  m = ... # update me.\n",
        "\n",
        "  return m\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "1iL92mYSlCkM"
      },
      "outputs": [],
      "source": [
        "# @title Exécutez votre code\n",
        "\n",
        "def test_linear_model():\n",
        "  assert (linear_model(params, X) == X @ w + b).all()\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_linear_model()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "yFR2NtnTKgJK"
      },
      "outputs": [],
      "source": [
        "# @title Solution - modèle linéaire (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts!)\n",
        "def linear_model(params: Dict[str, jnp.ndarray], X: jnp.ndarray) -> jnp.ndarray:\n",
        "  # complete this code\n",
        "  w = params['w']\n",
        "  b = params['b']\n",
        "\n",
        "  # compute m = f(x) here using w,b and X\n",
        "  m = X @ w + b\n",
        "\n",
        "  return m"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hNJgESq_LP4R"
      },
      "source": [
        "#### La fonction de coût et son optimisation\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zV6jTdQN2NvO"
      },
      "source": [
        "**Fonction de coût**\n",
        "\n",
        "Quant nous utilisons un modèle pour apprendre à partir des données, nous avons besoin d'une fonction qui mésure la performance du modèle. Cette fonction est appelée **fonction de coût**. Elle mesure la quantite d'erreur entre notre modèle et les données."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "HI8NPCQn3gn1",
        "outputId": "8673ab16-3000-4466-a134-977edee722bd"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# @title Code d'aide pour tracer les erreurs\n",
        "# Set random seed for reproducibility\n",
        "np.random.seed(42)\n",
        "\n",
        "# Number of points to generate\n",
        "num_points = 20\n",
        "\n",
        "# Generate random points and lines\n",
        "points_x = np.random.rand(num_points)\n",
        "slope_random_line = np.random.rand()\n",
        "intercept_random_line = np.random.rand()\n",
        "\n",
        "points_y = slope_random_line*points_x + intercept_random_line + np.random.normal(0, 1, num_points)*0.15\n",
        "\n",
        "# Function to calculate distance from point (x, y) to the line y = mx + b\n",
        "def distance_to_line(x, y, m, b):\n",
        "    return abs(y - m * x - b) / np.sqrt(1 + m**2)\n",
        "\n",
        "# Calculate distances from each point to the random line\n",
        "distances = distance_to_line(points_x, points_y, slope_random_line, intercept_random_line)\n",
        "\n",
        "# Create the scatter plot\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "# Plot the random line\n",
        "plt.plot(np.sort(points_x), slope_random_line * np.sort(points_x) + intercept_random_line, c='blue', label='Model')\n",
        "\n",
        "# Plot the points\n",
        "plt.scatter(points_x, points_y, c='red', label='Data', marker='o', s=50)\n",
        "\n",
        "# Plot lines from each point to the random line (in different colors)\n",
        "for i in range(num_points):\n",
        "    plt.plot([points_x[i], points_x[i]], [points_y[i], slope_random_line * points_x[i] + intercept_random_line],\n",
        "             c='green', alpha=0.7)\n",
        "\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.title(\"Errors for each data point\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fj_aG5jG3b8K"
      },
      "source": [
        "\n",
        "Considérer la figure ci-dessous avec les points en rouge. Si la ligne bleue est notre modèle, alors les lignes verticales répresentent les erreurs que nous faisons sur chaque point de données. La fonction de coût capture l'erreur total que nous faisons pour chaque point de données. Une fonction de coût que nous pouvons utilisér dans ce cas est l'erreur moyenne quadratique entre les valeurs prédites et les vraies valeurs.\n",
        "\n",
        "\n",
        "C'est équivalent a la somme de toutes les distances en vert. Cela peut être écrit mathématiquement comme suit:\n",
        "$$ \\mathcal{L}(\\mathbb{θ}) \\, = \\, \\frac{1}{m}∑_{i}({y_i - \\hat{y}_i})^2,$$\n",
        "Avec $\\mathbb{θ} = [\\mathbf{w}, b]$,  $\\mathcal{L}$ denote la fonction de coût, $\\hat{y}$ répresente la valeur prédite par le modèle et $m$ est le nombre total des points de données.\n",
        "\n",
        "En inserrant la fonction de régression linéaire dans la fonction de coût, nous obtenons:\n",
        "\n",
        "$$\\mathcal{L}(\\mathbb{θ}) \\, = \\, \\frac{1}{m}∑_{i}(y_i - \\mathbf{w}^T\\mathbf{x}_i - b)^2. $$\n",
        "\n",
        "\n",
        "<font color='red'>Note: il existe différentes fonctions de coût que nous pouvons utilisér dans ce cas. Vous pouvez voir d'autres fonctions de coût communes [ici](https://www.geeksforgeeks.org/ml-common-loss-functions/).</font>\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "coIwS0_5I-p-"
      },
      "source": [
        "**Code task:** implémenter la fonction de perte pour le modèle linéaire défini ci-dessus..\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "C5ji0ISCJWQ3"
      },
      "outputs": [],
      "source": [
        "def loss_fn(params: Dict[str, jnp.array], X: jnp.array, y: jnp.array):\n",
        "  # complete this code\n",
        "\n",
        "  pred = linear_model(params, X)\n",
        "\n",
        "  loss = ... # your code here\n",
        "\n",
        "  return 0"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O0m0EZVqMUw7",
        "outputId": "330dbe00-e94d-4fd2-f7f7-55ccdb579278"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Nice! Your answer looks correct.\n"
          ]
        }
      ],
      "source": [
        "# @title Run to test my code\n",
        "def test_linear_loss_fn():\n",
        "  pred = linear_model(params, X)\n",
        "  loss = jnp.mean((pred-data)**2)\n",
        "  assert loss_fn(params, X, data) == loss\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_linear_loss_fn()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "ehK1Y1pgZ83Y"
      },
      "outputs": [],
      "source": [
        "# @title Sample solution (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts !')\n",
        "def loss_fn(params: Dict[str, jnp.array], X: jnp.array, y: jnp.array):\n",
        "  # complete this code\n",
        "\n",
        "  pred = linear_model(params, X)\n",
        "\n",
        "  loss = jnp.mean((pred-y)**2)\n",
        "\n",
        "  return loss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NM7aMj_A75M_"
      },
      "source": [
        "**Exercice:** Discutez en groupes de la manière dont nous pouvons trouver les paramètres, $\\mathbb{θ}$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7SwSstfO9hml"
      },
      "source": [
        "**C'est quoi l'optimisation?**\n",
        "\n",
        "L'optimisation comme son nom l'indique, est la procédure qui permet de trouver les paramètres optimaux du modèle. C'est à dire un ensemble des paramètres qui minimise la fonction de coût. Mathématiquement, nous avons:\n",
        "\n",
        "\n",
        "\n",
        "$$\\hat{\\theta} \\,= \\, \\underset{\\mathbf{\\theta}}{\\operatorname{argmin}} \\frac{1}{m}∑_{i}(y_i - \\mathbf{w}^T\\mathbf{x}_i - b)^2.$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kxUMu1HP_D-m"
      },
      "source": [
        "<font color='red'>Comment optimiser?</font>: La figure ci-dessous montre une courbe de la fonction perte pour différentes valeurs de $\\mathbf{w}$ et de $b$ pour une ligne droite. La valeur minimale est indiquée is par l'étoile. Notre objectif est de trouver le point optimal par le procéssus d'optimisation.   "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "ZjZAVVBK_Fsd",
        "outputId": "18682ca9-b8c3-4fa7-88a5-a063db80745b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 800x500 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# @title Code d'aide (pour visualiser la function cout).\n",
        "# Define the loss function (Mean Squared Error)\n",
        "from matplotlib.colors import LogNorm\n",
        "\n",
        "def loss_function(y_true, y_pred):\n",
        "    return np.mean((y_true - y_pred) ** 2)\n",
        "\n",
        "# Create a grid of weight (slope) and bias (intercept) values\n",
        "weight_values = np.linspace(-10, 10, 200)\n",
        "bias_values = np.linspace(-10, 10, 200)\n",
        "weight_grid, bias_grid = np.meshgrid(weight_values, bias_values)\n",
        "\n",
        "# Generate random data points for demonstration\n",
        "np.random.seed(0)\n",
        "x = np.linspace(0, 20, 200)\n",
        "y_true = 3 * x + 5 + 0.1 * np.random.normal(0, 1, 200)\n",
        "y_min = 3*x + 5\n",
        "minima = np.array([5, 3])\n",
        "loss_min = loss_function(y_true, y_min)\n",
        "\n",
        "# Compute the loss for each combination of weight and bias values\n",
        "loss_grid = np.zeros_like(weight_grid)\n",
        "for i in range(len(weight_values)):\n",
        "    for j in range(len(bias_values)):\n",
        "        y_pred = weight_values[i] * x + bias_values[j]\n",
        "        loss_grid[i, j] = loss_function(y_true, y_pred)\n",
        "\n",
        "fig = plt.figure(figsize=(8, 5))\n",
        "ax = plt.axes(projection='3d', elev=50, azim=-50)\n",
        "\n",
        "surf = ax.plot_surface(weight_grid, bias_grid, loss_grid, norm=LogNorm(), rstride=1, cstride=1,\n",
        "                edgecolor='none', alpha=.8, cmap=plt.cm.jet)\n",
        "ax.plot(*minima, loss_min, 'r*', markersize=10)\n",
        "\n",
        "ax.set_xlabel('$w$')\n",
        "ax.set_ylabel('$b$')\n",
        "# Remove z-axis ticks and labels\n",
        "ax.set_zticks([])\n",
        "ax.set_zticklabels([])\n",
        "\n",
        "# Add color bar for reference\n",
        "cbar = plt.colorbar(surf, shrink=0.5, aspect=10)\n",
        "cbar.ax.set_ylabel('Loss')\n",
        "\n",
        "# ax.set_xlim((xmin, xmax))\n",
        "# ax.set_ylim((ymin, ymax))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hj1vWUunykNe"
      },
      "source": [
        "Une approche brutale **(brute force)** sérait de calculer la fonction de coût pour diverses valeurs de $\\theta$ et choisir une valeur de $\\theta$ avec un coût minimale. Bien que cette approche puisse marcher avec un modèle de 1 ou 2 paramètres, elle se complique pour plusieurs paramètres."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8h9sZ2vW97-d"
      },
      "source": [
        "**Gradient based optimization**\n",
        "\n",
        "La meilleur approche est d'utilisér l'analyse linéaire. La derivée d'une fonction est zero à tout point critique (maximum et mininum). Pour trouver $\\theta$ qui minimise le coût, nous devons resoudre l'équation. $$\\frac{\\partial \\mathcal{L}}{\\partial \\theta} \\,=\\, 0.$$\n",
        "\n",
        "**Exercice 2:** [OPTIONAL] Pouvez-vous verifier ces éxpressions de dérivation de la fonction de perte ?\n",
        "\n",
        "$$\\frac{∂ \\mathcal{L}}{\\partial \\mathbf{w}} = \\frac{2}{m}∑_{i}\\mathbf{x}_i(\\mathbf{w}^T\\mathbf{x}_i + b - y_i),$$\n",
        "\n",
        "$$\\frac{∂ \\mathcal{L}}{\\partial b} = \\frac{2}{m}∑_{i}(\\mathbf{w}^T\\mathbf{x}_i + b - y_i).$$\n",
        "\n",
        "Solution ici dans [l'appendix](#scrollTo=kh_8f4gKyufu)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tq4p7ME6GWXO"
      },
      "source": [
        "Heuresement nous ne pouvons pas calculer cette fonction par nous même. Les libraries de machine learning nous permettent d'ptimiser ces fonctions. En _jax_ nous pouvons utiliser jax.grad."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Yq2SMvz09fW1",
        "outputId": "8fc94df0-a69c-40fe-e320-7132a31ffa81"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gradient of the function x**2 at x = 1 is 2.0 as expected.\n"
          ]
        }
      ],
      "source": [
        "# @title Calcul des dérivées avec jax.grad\n",
        "# Computing derviatives with jax\n",
        "\n",
        "def quadratic_fn(x):\n",
        "  return x**2\n",
        "\n",
        "\n",
        "# Compute the derivative of quadratic_fn when x = 1\n",
        "grad_fx =  jax.grad(quadratic_fn)(1.0)\n",
        "assert grad_fx == 2.0\n",
        "print(f\"Gradient of the function x**2 at x = 1 is {grad_fx} as expected.\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LER9QyoXR_ph"
      },
      "source": [
        "Plus important Jax calcule la derivée de la même façon même si nos paramètres sont passés dans un autre type de données comme un dictionnaire. Par example, nous pouvons calculer la derivée de notre fonction de coût comme suit."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UfVKXN_ToRcn",
        "outputId": "8fc780ed-9b3d-45fc-c596-ce43ae36bb33"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "gradients: {'b': Array([4.6627536], dtype=float32), 'w': Array([2.091345 , 1.9300239, 2.740008 , 2.705566 , 1.4073546, 1.8641709,\n",
            "       1.5042092, 3.331741 , 2.4481251, 2.5431075], dtype=float32)}\n"
          ]
        }
      ],
      "source": [
        "# Compute derivatives of the loss_fn with respect to params\n",
        "\n",
        "grads = jax.grad(loss_fn)(params, X, data)\n",
        "print(f\"gradients: {grads}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zl0_zYWxlGDO"
      },
      "source": [
        "Une autre fonction similaire est `jax.value_and_grad`; elle retourne la valeur de la fonction et celle de sa dérivée.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CzKxdMqIlsVk",
        "outputId": "1bddf9b6-6238-46b3-ef86-a83b2510981b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "loss: 5.745656490325928\n",
            "gradients: {'b': Array([4.6627536], dtype=float32), 'w': Array([2.091345 , 1.9300239, 2.740008 , 2.705566 , 1.4073546, 1.8641709,\n",
            "       1.5042092, 3.331741 , 2.4481251, 2.5431075], dtype=float32)}\n"
          ]
        }
      ],
      "source": [
        "# Compute derivatives of the loss_fn with respect to params\n",
        "\n",
        "loss, grads = jax.value_and_grad(loss_fn)(params, X, data)\n",
        "print(f\"loss: {loss}\")\n",
        "print(f\"gradients: {grads}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q9dQh9DdLYPE"
      },
      "source": [
        "#### Entraînement un modèle à l'aide de Jax"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q1I8M0zkhAg3"
      },
      "source": [
        "**La Descente de gradient (Gradient Descent)**\n",
        "\n",
        "Maintenant que nous avons la derivée de notre fonction de coût, nous pouvons utiliser la methode de la descente de gradient pour trouver les paramètres qui minimisent le coût. La descente de gradient est une methode itérative qui commence avec un ensemble aléatoire des paramètres et les met à jour à chaque itération en utilisant la formule suivante:\n",
        "\n",
        "\n",
        "1. Initialise les paramètres avec des valeurs aléatoires.\n",
        "2. Boucle pour un nombre d'itérations et à chaque itération met à jour les paramètres en utilisant la formule suivante.\n",
        "\n",
        "$$ \\mathbf{\\theta} = \\mathbf{\\theta} - η\\frac{∂\\mathcal{L}}{∂\\theta},$$\n",
        "$\\eta$ c'est notre frequence d'apprentissage. c'est un hyperparamètre de notre modèle, nous devons le choisir avant.\n",
        "\n",
        "Intuitivement, si ce paramètre est optimal, le gradient $\\frac{∂\\mathcal{L}}{∂\\theta}$ sera zero et les paramètres deviennent statiques, raison pour laquelle le critère que nous utilisons pendant l'entrainment est de vérifier si les paramètres ont arreté de changer (convergence).\n",
        "Lorsque nous utilisons un seul point pour calculer la descente de gradient, l'algorithme est appelé **la descente du gradient stochastique.**\n",
        "Lorsque nous utilisons l'ensemble de notre dataset l'agorithme est appelée la descente **du gradient en batch.** En pratique l'approche utilise un petit groupe de données à chaque étape. Cette approche est celle du **mini batch gradient descent.**\n",
        "\n",
        "\n",
        "Pendant l'apprrentissage nous parcourons notre dataset à chaque itération. Le parcours de notre dataset s'appele epoch.\n",
        "\n",
        "Raison pour laquelle un autre hyperparamètre dont nous sommes familier c'est l'epoch."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qoFbSQWGhAg7"
      },
      "outputs": [],
      "source": [
        "# @title Code demonstration: Batch gradient descent implementation\n",
        "def batch_gradient_descent(loss_fn, params, training_data, val_data, learning_rate=0.01, num_epochs=20, batch_size=10):\n",
        "  \"\"\"Batch gradient descent basic jax implementation.\n",
        "\n",
        "  Args:\n",
        "    loss_fn\n",
        "      the loss function for our model.\n",
        "    params:\n",
        "      the initial parameters of the model.\n",
        "    training_data\n",
        "      a tuple with the features and targets for training.\n",
        "    val_data\n",
        "      a tuple with the features and targets for validation.\n",
        "    learning_rate\n",
        "      learning rate\n",
        "    num_epochs\n",
        "      number of epochs\n",
        "    batch_size:\n",
        "      size of every mini batch\n",
        "  \"\"\"\n",
        "\n",
        "  X_train, y_train = training_data\n",
        "  X_val, y_val = val_data\n",
        "\n",
        "  num_samples, num_features = X_train.shape\n",
        "\n",
        "  # Create empty list to store the training and validation loss\n",
        "  loss_train = [] # training loss\n",
        "  loss_val  = [] # valisation loss\n",
        "\n",
        "  # Define a function that computes loss and gradients\n",
        "  loss_and_grad = jax.value_and_grad(loss_fn)\n",
        "\n",
        "  n_iter = 0 # number iterations\n",
        "  for epoch in range(num_epochs):\n",
        "    # Shuffle the data before every epoch\n",
        "    shuffled_indices = np.arange(num_samples)\n",
        "    np.random.shuffle(shuffled_indices)\n",
        "\n",
        "    for start_idx in range(0, num_samples, batch_size):\n",
        "      end_idx = start_idx + batch_size\n",
        "      if end_idx > num_samples:\n",
        "        end_idx = num_samples\n",
        "\n",
        "      batch_indices = shuffled_indices[start_idx:end_idx]\n",
        "      X_batch = X_train[batch_indices]\n",
        "      y_batch = y_train[batch_indices]\n",
        "\n",
        "      # Compute loss and gradients using value_and_grad\n",
        "      loss, grads = loss_and_grad(params, X_batch, y_batch)\n",
        "      loss_train.append(loss)\n",
        "\n",
        "      # Compute the validation loss\n",
        "      loss_v = loss_fn(params, X_val, y_val)\n",
        "      loss_val.append(loss_v)\n",
        "\n",
        "      # Update the parameters\n",
        "      params = jax.tree_map(lambda p, g: p -learning_rate*g, params, grads)\n",
        "\n",
        "      # Update the iter count\n",
        "      n_iter += 1\n",
        "\n",
        "\n",
        "  # Plot training and validation loss\n",
        "  iters = range(1, n_iter+1)\n",
        "  plt.plot(iters, loss_train, label='Training Loss')\n",
        "  plt.plot(iters, loss_val, label='Validation Loss')\n",
        "  plt.xlabel('Iteration')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.title('Training and Validation Loss')\n",
        "  plt.legend()\n",
        "\n",
        "  # Display the plot\n",
        "  plt.show()\n",
        "\n",
        "  return params"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5gbBCDwQhAg8"
      },
      "outputs": [],
      "source": [
        "# @title Creation d'un ensemble de données factice pour tester le code\n",
        "def create_dummy_data_linear_regression():\n",
        "  \"\"\"We will generate some random data using our linear function above to test the gradient decent implementation\"\"\"\n",
        "\n",
        "  num_samples = 200\n",
        "  num_features = 1  # Modify this to have more features\n",
        "\n",
        "  # Generate random X values in the range [0, 10] for each feature\n",
        "  key = jax.random.PRNGKey(0)\n",
        "  X = jax.random.uniform(key, (num_samples, num_features), minval=0, maxval=10)\n",
        "\n",
        "  # Generate y values based on a linear relationship with some noise\n",
        "  w = jnp.array([3.0]*num_features)  # True coefficients for each feature\n",
        "  b = jnp.array([5.0])\n",
        "\n",
        "  params = dict(w=w, b=b)\n",
        "  y = linear_model(params, X)\n",
        "\n",
        "  # Add some noise\n",
        "  noise = jax.random.normal(key, shape=(num_samples,))*0.30\n",
        "  y = y + noise\n",
        "\n",
        "  # Step 2: Split the data into training and validation sets\n",
        "  train_fraction = 0.8\n",
        "  num_train_samples = int(train_fraction * num_samples)\n",
        "\n",
        "  # Shuffle the indices to randomly split the data\n",
        "  key, subkey = jax.random.split(key)\n",
        "  shuffled_indices = jax.random.permutation(subkey, jnp.arange(num_samples))\n",
        "\n",
        "  # Split the indices into training and validation sets\n",
        "  train_indices = shuffled_indices[:num_train_samples]\n",
        "  val_indices = shuffled_indices[num_train_samples:]\n",
        "\n",
        "  # Get the corresponding data points for training and validation sets\n",
        "  X_train, y_train = X[train_indices], y[train_indices]\n",
        "  X_val, y_val = X[val_indices], y[val_indices]\n",
        "\n",
        "  train_data = (X_train, y_train)\n",
        "  val_data = (X_val, y_val)\n",
        "\n",
        "  # create some random initial params\n",
        "  w_init = jax.random.normal(key, shape=(num_features,))\n",
        "  b_init = 0.0\n",
        "  initial_params = dict(w=w_init, b=b_init)\n",
        "\n",
        "  return train_data, val_data, initial_params\n",
        "\n",
        "\n",
        "def plot_linear_fit(params, X, y):\n",
        "  \"\"\"Overlay the data and fitted model\"\"\"\n",
        "\n",
        "  y_pred = linear_model(params, X).squeeze()\n",
        "  xval = X[:,0]\n",
        "\n",
        "  plt.figure(figsize=(8, 6))\n",
        "  plt.scatter(xval, y, label='Data', color='blue')\n",
        "  plt.plot(xval, y_pred, label='Fit', color='red')\n",
        "  plt.xlabel('X')\n",
        "  plt.ylabel('Y')\n",
        "  plt.legend()\n",
        "  plt.title('Scatter Points and Fitted Curve')\n",
        "  plt.show()\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CyvVrWO0YdDe"
      },
      "outputs": [],
      "source": [
        "train_data, val_data, initial_params = create_dummy_data_linear_regression()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "upnIeZ2Zaued",
        "outputId": "8fc91fc9-3c59-4f90-e983-5fa453d920c8"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "params = batch_gradient_descent(loss_fn, initial_params, train_data, val_data, learning_rate=0.01, num_epochs=2, batch_size=10)\n",
        "\n",
        "# plot the results on validation data\n",
        "Xval, yval = val_data\n",
        "plot_linear_fit(params, Xval, yval)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qzpzC6C25R2K"
      },
      "source": [
        "Our model seems to be **underfitting** that data because the fitted line is going through very few of the points.\n",
        "\n",
        "Notre modèle semble **Sous-ajuste** les données parce que la ligne ajustée passe par très peu de points.\n",
        "\n",
        "**Exercice:** Discuter en groupe comment nous pouvons ameliorer notre modèle.\n",
        "\n",
        "**Code task:** Modifier le taux d'apprentissage, la taille du lot et le nombre d'epochs et observer leurs éffets sur les resultats.\n",
        "\n",
        "**Tips:**\n",
        "\n",
        "- En pratique, les gens choisissent généralement des taux d'apprentissage dans la plage de 0,01 et 1e-5.\n",
        "- Les petites tailles de lots peuvent introduire trop de bruit dans les gradients et cela peut affecter la vitesse de convergence.\n",
        "- D'autre part, les grandes tailles de lots peuvent prendre plus de temps à converger car les paramètres ne sont pas mis à jour très fréquemment.\n",
        "- Noter que l'utilisation d'un très grand nombre d'epochs rendra l'entraînement long car nous n'avons inclus aucun critère d'arrêt."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "rB8DMH4Z7seC",
        "outputId": "a5d344c5-6074-4423-f56e-836940d94463"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# @title Votre code\n",
        "learning_rate = 0.00291 #@param {type:\"slider\", min:1e-5, max:1e-2, step:1e-4}\n",
        "batch_size = 20 #@param {type:\"slider\", min:1, max:5000, step:10}\n",
        "num_epochs = 100 #@param {type:\"slider\", min:2, max:500, step:20}\n",
        "\n",
        "params = batch_gradient_descent(loss_fn, initial_params, train_data, val_data, learning_rate=learning_rate, num_epochs=num_epochs, batch_size=batch_size)\n",
        "\n",
        "# plot the results on validation data\n",
        "Xval, yval = val_data\n",
        "plot_linear_fit(params, Xval, yval)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BKtMEnRkhAg9"
      },
      "source": [
        "### 2.2 Régression non-linéaire et réseaux de neurones"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "xNYVOlb-bUml",
        "outputId": "b3584ec2-2680-4d26-a758-0a5b425623b0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# @title Code pour tracer des données non linéaires\n",
        "def plot_nonlinear_data():\n",
        "\n",
        "  x = np.linspace(-5, 5, 100)\n",
        "  y = np.cos(x)*x + x**2 + np.exp(-x/7)*3 + 0.3*x*np.sin(x)**4\n",
        "\n",
        "  plt.scatter(x, y)\n",
        "  plt.title(\"Example of non linear data\")\n",
        "  plt.show\n",
        "\n",
        "plot_nonlinear_data()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2FIcY0XAzFw"
      },
      "source": [
        "La régression linéaire est une methode simple et puissance pour la prédiction. Cette methode possède des limitiations lorsqu'on doit capturer des rélations complexes. Pour modeliser ce genre de complexité, we avons besoin des modèles puissants. Par example aucune line ne peut s'ajuster aux données de la figure précédente.\n",
        "Les modèles non-linéaire comme la régression polynomiale, exponentielle ou les fonctions trigonométriques offrent des solutions à ce problème.\n",
        "\n",
        "A cause de l'explosion des techniques de l'apprentissage profond (deep learning) ajuster les fonctions prédéfinies à nos dataset etait les methodes par excellence pour les algorithmes d'apprentissage automatique.\n",
        "le Support Vector Machine (SVM), Naive-Bayes et K-means sont des approches classiques.\n",
        "\n",
        "Dans cette section nous allons introduire les réseaux de neurones qui sont à la base des methodes d'apprentissage profond et du succès récent dans le domaine de l'apprentissage automatique."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XStsgHB2MarI"
      },
      "source": [
        "#### Représentation du modèle\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K7NYiMuVIUPR"
      },
      "source": [
        "<center>\n",
        "<img src=\"https://www.tibco.com/sites/tibco/files/media_entity/2021-05/neutral-network-diagram.svg\" width=\"80%\" />\n",
        "</center>\n",
        "\n",
        "      Image of a neural network with 3 hidden layers. Credit: https://www.tibco.com/reference-center/what-is-a-neural-network\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WAcehBE0J-G0"
      },
      "source": [
        "Les réseaux de neurones sont un ensemble de modèles d'apprentissage automatique inspirer par manière dont le cerveau humain fonctionne.  \n",
        "\n",
        "Contrairement à la régression linéaire qui applique une seule transformation aux données, les réseaux de neurones traitent les données d'entrée à travers une série des transformations avant d'atteindre la couche de prédiction finale. Le terme <font color='red'>Deep Learning</font> vient des nombreuses transformations appliquées aux données d'entrée.\n",
        "\n",
        "\n",
        "Dans l'image ci haut les cercles répresentent les noeuds et les liens qui les connectent répresentent les paramètres du modèle."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fkpytbBzMvMj"
      },
      "source": [
        "#### Fonctions d'activation\n",
        "\n",
        "Les fonctions d'activation sont importantes pour les réseaux de neurones. L'entrée de chaque noeud est une fonction linéaire des noeuds de la couche précédente. Sans appilquer la fonction d'activation ou la non-linéairité, l'ensemble du réseau, peu importe le nombre de couches  se réduit à un simple modèle linéaire. Pour cette raison, les fonctions d'activation sont utilisées pour construire des rélations non-linéaires et complexes.\n",
        "\n",
        "\n",
        "L'équation pour le noeud $i$ dans la couche $j$ d'un réseau de neurones peut être exprimer comme suit:\n",
        "\n",
        "$$ \\text{Output}_{ij} = \\text{Fonction d'activation} \\left( \\sum_{k=1}^{n} \\text{Weight}_{ijk} \\times \\text{Output}_{(j-1)k} + \\text{Bias}_{ij} \\right)$$\n",
        "\n",
        "Where:\n",
        "- $\\text{Output}_{ij}$ est la sortie du noeud $i$ de la couche $j$.\n",
        "- $\\text{Weight}_{ijk}$ est le poids connectant le noeud $i$ de la couche $j$ au noeud $k$ de la couche $j-1$.\n",
        "- $\\text{Output}_{(j-1)k}$ est la sortie du noeud  $k$ de la couche $j-1$.\n",
        "- $\\text{Bias}_{ij}$ est le biais du noeud $i$ de la couche $j$.\n",
        "- $\\text{Fonction d'activation}$ est la fonction d'activation choisie pour introduire la non-linéairité à la sortie de la neurone.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qnXa2-o8RFK3"
      },
      "source": [
        "\n",
        "\n",
        "Voici quelques fonctions d'activation les plus utilisées:\n",
        "\n",
        "- $\\text{ReLU}(x) \\, = \\, \\text{max}(0, x)$\n",
        "\n",
        "    La fonction d'activation Rectified Linear Unit (ReLU) est la plus populaire. Elle mappe son entrée dans l'intervalle $[0, ∞]$ en transformant toutes les valeurs négatives en 0. La fonction et sa derivée sont monotones. Cependant, cette fonction d'activation à le probleme de transformer toutes les entrées négatives en 0 et de diminuer la capacité du modèle à bien s'adapter aux donnees.\n",
        "\n",
        "- $\\text{Sigmoid}(x) \\, =\\, \\frac{1}{1+e^{-x}}$\n",
        "\n",
        "    La fonction d'activation sigmoid mappe son entrée dans l'intervalle $[0, 1]$. C'est ideal pour prédire les probabilités. La fonction est différentiable et monotone mais sa derivée n'est pas monotone. Parce que sa derivée n'est pas monotone, il n'est pas ideal d'utiliser cette fonction d'activation pour les couches cachées car elle bloque le transfert d'informations entre les couches. Par conséquent, l'activation est appliquée uniquement aux couches de sortie.\n",
        "\n",
        "- $\\text{tanh}(x)\\, = \\, \\frac{e^x - x^{-x}}{e^x + e^{-x}},$\n",
        "  \n",
        "     L'activation $tanh$ est similaire à l'activation sigmoid mais elle mappe les entrées dans l'intervalle $[-1, 1]$. Cette plage plus large permet une répartition beaucoup plus uniforme lors de la prédiction des probabilités. De même que l'activation sigmoid, le $tanh$ est le plus souvent appliqué aux couches de sortie des reseaux des neurones.\n",
        "\n",
        "\n",
        "Implementation de la fonction d'activation [ReLU](https://arxiv.org/https://arxiv.org/abs/1803.08375abs/1803.08375)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "17JUU2WIMOAO",
        "outputId": "214d7f65-a591-41f2-9678-bfdf34cf2852"
      },
      "outputs": [
        {
          "data": {
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WvwrEYUh3XdpGN/ZgAmkInrEAADRqL325U/sKStUi0qopQ5hAGopiAQBotDbsP6G/fZctSUq/q6eiw4NNTuT7KBYAgEbpdIVd4xdskWFIw3u11fXdWpodyS9QLAAAjdLMpTuVfaxUraJC9dRt3c2O4zcoFgCARueHfcc1d/WZCWRYT0WHMYG4CsUCANColFVU1Uwg91yeoIFdWpgdya9QLAAAjcqLn+9QzokyxUeH6onbupkdx+9QLAAAjcaavcf1jzUHJEkvDk9VVCgTiKtRLAAAjUKprUrjF2RIkv6rT6Ku7hRnciL/RLEAADQK6Z9v18GTp9UmJkyTb2ECcReKBQDA732/55j+tTZHkjRjeKqaWBv8iRaoBcUCAODXissrNWHBFknS/VcmqX/H5iYn8m8UCwCAX5v22Q4dOnVaCbFhenxwV7Pj+D2KBQDAb63aVaB/rzszgQxLUwQTiNtRLAAAfqmovFITP6yeQB7o1059k5uZnKhxoFgAAPzSC0u263BhuZKahWvCzV3MjtNoUCwAAH7nm535en9DriwWaebwNIWHMIF4CsUCAOBXCssq9fiZCeS3/durd/tYkxM1LhQLAIBfeXbJNh0tsql98wiNu5EJxNMoFgAAv/HVtqP6cNNBWSzSrBGpCgsJNDtSo0OxAAD4hVNlFZq8MFOS9NDVHdQriQnEDBQLAIBfmPrJNuUX25QcF6GxN3Q2O06jRbEAAPi8pVlHtPDHQwqwSLNGpCk0mAnELBQLAIBPO1laoScWbpUk/fc1ybo0sanJiRo3igUAwKdN+ThLx0ps6tSiicYM6mR2nEaPYgEA8FmfZx7Wxxl5CgywMIF4CYoFAMAnHS+x6clF1RPIw9d2UFpCjLmBIIliAQDwUU8vztLx0gp1aRmpP17PBOItKBYAAJ+zZEuePs08rMAAi166O03WICYQb0GxAAD4lIJim546M4GMHthRKW2iTU6En6JYAAB8hmEYenJRpk6WVapb6yg9MrCj2ZHwMxQLAIDP+DgjT0uzjioowKJZI1IVEsTDmLfhTwQA4BPyi8s15eMsSdKj13VSj3gmEG9EsQAAeD3DMPTEwq06VVapHvFR+p+ByWZHQi0oFgAAr7do8yEt23ZUwYHVrwIJDuThy1vxJwMA8GpHi8o1ZXH1BPKn6zupa6sokxPhQigWAACvZRiGJn2UqaLyKvVsE62Hr2UC8XYUCwCA1/pw0yF9vSNfIYEBeunuNAUxgXg9/oQAAF7pcOFpTf2kegL58w2d1bllpMmJUBcUCwCA1zEMQ49/mKni8ipdkhCjh65ub3Yk1BHFAgDgdT7YkKuVuwoUEhSgWSOYQHwJf1IAAK9y6NRpPbdkuyRp3I2d1bFFE5MTwRkUCwCA16ieQLaoxFalyxJj9OBVHcyOBCdRLAAAXuPf63L17e5jsp6ZQAIDLGZHgpMoFgAAr5B7okwvfLpNkjT+pi7qEMcE4osoFgAA0zkchiZ+uEWlFXZd0a6pRvXnVSC+imIBADDdO+tytHrvcYUGB2jmcCYQX0axAACYKud4mdI/q34VyOM3d1W75hEmJ0JDUCwAAKZxOAyNX5Chsgq7+rSP1W/6tjM7EhqIYgEAMM3/W7NfP2SfUHhIoGYOT1MAE4jPo1gAAEyx/1ippn+xQ5I0aXBXJTYLNzkRXIFiAQDwuLMTSHmlQ/2Sm+m+PklmR4KLUCwAAB43d/V+rd9/UhEhgXpxWCoTiB+hWAAAPGpfQYlmnJlAJt/aTQmxTCD+hGIBAPAYu8PQuPkZslU5dFXH5vqv3olmR4KLUSwAAB7z9++ytSnnlJpYg/Ti8FRZLEwg/sapYjF79mylpqYqKipKUVFR6tu3rz7//HN3ZQMA+JE9+SWa+eVOSdJTt3VTm5gwkxPBHZwqFm3bttX06dO1ceNGbdiwQdddd53uuOMOZWVluSsfAMAPVNkdemx+hiqqHLq2c5zuvjzB7EhwkyBnrjxkyJBzzr/wwguaPXu21q5dqx49erg0GADAf/z122xl5J5SZGiQpg/ryQTix5wqFj9lt9s1f/58lZaWqm/fvrVez2azyWaz1ZwvKiqq710CAHzQ7qPFemXZLknS07d1V+toJhB/5vTBm5mZmWrSpImsVqsefvhhLVy4UN27d6/1+unp6YqOjq45JSTw9BcANBY1E4jdoeu6ttDwXm3NjgQ3sxiGYThzg4qKCuXk5KiwsFALFizQ3/72N61cubLWcnG+ZywSEhJUWFioqKiohqUHAHi1N7/Zo5lLdyoqNEjLxl6rllGhZkdCPRUVFSk6Ovqij99OF4ufGzRokJKTkzVnzhyXBgMA+LYdR4o05PXvVGk39PLdabrrMp6t8GV1ffxu8PtYOByOc56RAACg0u7QYx9kqNJuaFC3lrrz0jZmR4KHOHXw5qRJkzR48GAlJiaquLhY7777rlasWKGlS5e6Kx8AwAfNXrFXWXlFigkP1rS7UngVSCPiVLHIz8/Xb37zGx0+fFjR0dFKTU3V0qVLdcMNN7grHwDAx2TlFeovy3dLkqbe3kMtIjmuojFxqli8/fbb7soBAPADFVUOjZu/RVUOQzf1aKnb0+LNjgQP47NCAAAu88Y3e7T9cJGahgfr+aG8EVZjRLEAALjE1kOF+t9v9kiSnhuaorhIq8mJYAaKBQCgwWxVdo2bn6Eqh6Fbe7bWbalMII0VxQIA0GCvL9+jHUeK1SwiRM/ewWdHNWYUCwBAg2TkntLslXslSc8PTVGzJkwgjRnFAgBQb+WV1ROI3WFoSFq8BvdsbXYkmIxiAQCot9eW79bu/BI1b2LVs7czgYBiAQCopx9zTmrOmQlk2p0pahoRYnIieAOKBQDAaWcnEIchDb0kXjf2aGV2JHgJigUAwGkvL9ulvQWliou06hkmEPwExQIA4JSNB07or9/ukySl39lTMeFMIPgPigUAoM5OV9g1bv4WGYY07LK2GtS9pdmR4GUoFgCAOpv15U5lHytVyyirnh7S3ew48EIUCwBAnazLPqG/f58tSZp+V6qiw4JNTgRvRLEAAFxUWUWVxi/IkGFId1/eVgO7tjA7ErwUxQIAcFEzvtipA8fL1Do6VE/exgSC2lEsAAAXtHbfcc1bvV+S9OKwVEWFMoGgdhQLAECtSm3VE4gk3ds7Qdd0jjM5EbwdxQIAUKvpn+9Q7onTahMTpsm3dDM7DnwAxQIAcF6r9xzTP9cekFQ9gUQygaAOKBYAgF8osVVp/IItkqRfX5moqzo1NzkRfAXFAgDwC9M+265Dp06rbdMwTRrMBIK6o1gAAM7x7e4CvftDjiRpxvBURViDTE4EX0KxAADUKC6v1MQzE8jIvknql8wEAudQLAAANV74dLvyCsuVGBuuiYO7mh0HPohiAQCQJK3Yma/31udKkmYOT1V4CBMInEexAACo8HSlHv8wU5I0qn879enQzORE8FUUCwCAnluyTUeKytWuWbgm3MQEgvqjWABAI/f1jqNasPGgLBZp1og0hYUEmh0JPoxiAQCNWGHZfyaQ313VXpe3izU5EXwdxQIAGrGpn2Qpv9imDnEReuzGLmbHgR+gWABAI7Vs21F99OMhBZyZQEKDmUDQcBQLAGiETpZWaPLC6gnkoWs66LLEpiYngr+gWABAI/TMJ1kqKLapY4sm+vOgzmbHgR+hWABAI/PF1sNavDmPCQRuQbEAgEbkeIlNTyzcKkl6+NpkXZIQY24g+B2KBQA0Ik9/nKXjpRXq3LKJ/jSok9lx4IcoFgDQSHy65bA+3XJYgQEWvTTiElmDmEDgehQLAGgEjpXY9NTi6glk9IBk9WwbbXIi+CuKBQD4OcMw9NSirTpRWqGurSL1yHVMIHAfigUA+LlPthzW51uPKCjAolkj0hQSxF/9cB9+ugDAj+UXl+vpMxPII9d1VEobJhC4F8UCAPyUYRh6YuFWnSqrVPfWURo9sKPZkdAIUCwAwE8t3pynZduOKjjQopfuTlNwIH/lw/34KQMAP5RfVK4pH2dJkv54XSd1ax1lciI0FhQLAPAzhmFo8sJMFZ6uVM820Xp4QLLZkdCIUCwAwM98tOmQvtqer5DAAM0awQQCz+KnDQD8yJHCcj3zSfUEMuaGTurSKtLkRGhsKBYA4CcMw9DjH21RcXmV0hJi9N9XdzA7EhohigUA+In5Gw5qxc4ChQQFaNbwVAUxgcAE/NQBgB/IO3Vazy3ZJkl67IbO6tSSCQTmoFgAgI8zDEMTP9yiYluVLk2M0e+YQGAiigUA+Lj31ufq293HZA2qfhVIYIDF7EhoxCgWAODDDp4s0/NnJpDxN3VRclwTkxOhsaNYAICPOjuBlFbYdXlSU43q397sSADFAgB81Ts/5Oj7PccVGhygmUwg8BJOFYv09HRdccUVioyMVIsWLTR06FDt3LnTXdkAALXIPVGmaZ9tlyRNuKmr2jePMDkRUM2pYrFy5UqNHj1aa9eu1bJly1RZWakbb7xRpaWl7soHAPgZh8PQ+AUZKquwq3e7WD3Qr53ZkYAaQc5c+Ysvvjjn/Lx589SiRQtt3LhR11xzjUuDAQDO759rD2jtvhMKCw7UzBGpCmACgRdxqlj8XGFhoSQpNja21uvYbDbZbLaa80VFRQ25SwBo1A4cL9X0z3dIkibd0lVJzZhA4F3qffCmw+HQmDFj1L9/f6WkpNR6vfT0dEVHR9ecEhIS6nuXANCoORyGxs/fotOVdvXt0Ey/7pNkdiTgF+pdLEaPHq2tW7fqvffeu+D1Jk2apMLCwppTbm5ufe8SABq1eav3a93+EwoPCdSM4Uwg8E71mkIeeeQRLVmyRKtWrVLbtm0veF2r1Sqr1VqvcACAatnHSjVjafUEMvmWbkqIDTc5EXB+ThULwzD06KOPauHChVqxYoXat+fNWADA3ewOQ+PnZ6i80qGrOjbXfX0SzY4E1MqpYjF69Gi9++67Wrx4sSIjI3XkyBFJUnR0tMLCwtwSEAAau7nfZ2vDgZNqYg3S9GE9ZbEwgcB7OXWMxezZs1VYWKgBAwaodevWNaf333/fXfkAoFHbk1+imUur34jwiVu7qW1TJhB4N6enEACAZ9jPvBGWrcqhqzs116+u4FV18H58VggAeKm/fbtPP+acUqQ1SC8OS2UCgU+gWACAF9p9tFgvLdslSXpqSHfFx3AcG3wDxQIAvEyV3aFx8zNUUeXQwC5xGtHrwi/rB7wJxQIAvMycVfuUcbBQkaFBSr+LCQS+hWIBAF5k55FivfpV9QTyzJAeahUdanIiwDkUCwDwEpVnJpBKu6FB3VrorsvamB0JcBrFAgC8xFsr9irzUKGiw4I17U7eCAu+iWIBAF5gW16R/vL1bknS1Nt7qEUUEwh8E8UCAEz20wnkxu4tdccl8WZHAuqNYgEAJnvzmz3adrhITcOD9QITCHwcxQIATLT1UKHe+HqPJOnZO1IUF2k1ORHQMBQLADBJRVX1BFLlMDQ4pZVuS21tdiSgwSgWAGCS17/erR1HihUbEaLnhqYwgcAvUCwAwARbDp7S/67YK0l67o4UNW/CBAL/QLEAAA+zVdk1bn6G7A5Dt6W21q1MIPAjFAsA8LDXvtqtXUdL1LxJiJ69I8XsOIBLUSwAwIM2557SWyurJ5Dnh/ZUbESIyYkA16JYAICHlFfa9dgHm+UwpDsuidfNKa3MjgS4HMUCADzkla92aW9BqeIirXpmSA+z4wBuQbEAAA/YeOCk/rpqnyRp2p091ZQJBH6KYgEAblZeadf4+RlyGNJdl7bRDd1bmh0JcBuKBQC42aylO7XvWKlaRFo1hQkEfo5iAQButGH/Cb39fbYkafqwnooODzY5EeBeFAsAcJPTFdVvhGUY0ohebXVdVyYQ+D+KBQC4yYylO7T/eJlaR4fqydu6mx0H8AiKBQC4wdp9xzX3+/2SpOnDUhUdxgSCxoFiAQAuVlZRpQkLtkiSfnVFgq7tHGdyIsBzKBYA4GIvfr5DOSfKFB8dqidu7WZ2HMCjKBYA4EKr9x7TP9YckCTNGJ6myFAmEDQuFAsAcJES238mkP/qk6irOjU3ORHgeRQLAHCR9M+26+DJ02oTE6bJtzCBoHGiWACAC3y3+5je+SFHkjRzeKqaWINMTgSYg2IBAA1UXF6piR9WTyC/6Zukfh2ZQNB4USwAoIGmfbZdh06dVkJsmCbe3NXsOICpKBYA0AArdxXo3+tyJUkzh6cpggkEjRzFAgDqqai8Uo+fmUAe6NdOV3ZoZnIiwHwUCwCop+eXbNPhwnK1axauCTd3MTsO4BUoFgBQD9/syNcHGw7KYpFmjkhTeAgTCCBRLADAaYVllXr8o+oJ5Lf92+uKdrEmJwK8B8UCAJw0dUmWjhbZ1KF5hMbdyAQC/BTFAgCc8NW2o/po0yEFnJlAwkICzY4EeBWKBQDU0amyCk1amClJeujqDuqV1NTkRID3oVgAQB0983GWCoptSo6L0J9v6Gx2HMArUSwAoA6WZh3Ros15CrBIs0akKTSYCQQ4H4oFAFzEidIKPXFmAvn9tcm6NJEJBKgNxQIALmLKx1k6VlKhzi2baMygTmbHAbwaxQIALuCzzMP6JCNPgQEWzRqRJmsQEwhwIRQLAKjFsRKbnly0VZL0h2uTldo2xtxAgA+gWABALZ5evFUnSivUtVWkHr2+o9lxAJ9AsQCA81iyJU+fZR5REBMI4BSKBQD8TEGxTU+dmUBGD+yolDbRJicCfAfFAgB+wjAMPbkoUyfLKtWtdZRGD2QCAZxBsQCAn/g4I09Ls44qKMCil0akKSSIvyYBZ/B/DACckV9UrqcXZ0mS/nh9J3WPjzI5EeB7KBYAoOoJZPLCTBWerlRKmyj9YUCy2ZEAn0SxAABJC388pK+25ys4sPpVIMGB/PUI1IfT/+esWrVKQ4YMUXx8vCwWixYtWuSGWADgOUcKy/XMx9UTyJhBndW1FRMIUF9OF4vS0lKlpaXpzTffdEceAPAowzA06aMtKiqvUmrbaP3+mg5mRwJ8WpCzNxg8eLAGDx7sjiwA4HELNh7UNzsLFBIYoJdGpCmICQRoEKeLhbNsNptsNlvN+aKiInffJQDUyeHC03r2k22SpLE3dlanlpEmJwJ8n9ureXp6uqKjo2tOCQkJ7r5LALgowzA08cNMFduqdElCjB66mgkEcAW3F4tJkyapsLCw5pSbm+vuuwSAi3p/fa5W7SpQSFCAZo1IU2CAxexIgF9w+xRitVpltVrdfTcAUGeHTp3W859ulySNv7GLOrZoYnIiwH9wlBKARsUwDE1csEUltir1Smqq317V3uxIgF9x+hmLkpIS7dmzp+Z8dna2Nm/erNjYWCUmJro0HAC42rvrcvTdnmOyBgVo5vBUJhDAxZwuFhs2bNDAgQNrzo8dO1aSNHLkSM2bN89lwQDA1XJPlGnamQlkws1d1SGOCQRwNaeLxYABA2QYhjuyAIDbOByGJn64RaUVdvVuF6tR/dqZHQnwSxxjAaBReOeHA1q997jCggM1Y3iqAphAALegWADweznHyzTtsx2SpMcHd1W75hEmJwL8F8UCgF9zOAyNW5Ch05V2XdkhVvdfmWR2JMCvUSwA+LV/rNmvddknFB4SqBnD0phAADejWADwW/uPlerFL6onkEm3dFNis3CTEwH+j2IBwC/ZHYbGzc9QeaVD/Ts20329eZ8dwBMoFgD80tzvs7XhwElFhATqxWG8CgTwFIoFAL+zt6BEM5fulCQ9cWt3tW3KBAJ4CsUCgF+xOwyNn58hW5VDV3dqrnt7J5gdCWhUKBYA/Mrb3+3TppxTirQG6cVhqbJYmEAAT6JYAPAbe/KLNevLXZKkJ2/rpviYMJMTAY0PxQKAX6iyO/TY/C2qqHLo2s5xuvtyJhDADBQLAH7h/77dp4zcU4oMDdL0YT2ZQACTUCwA+LxdR4v16rLdkqQpQ3qodTQTCGAWigUAn1Zpd+ixDzJUYXfo+q4tNOyyNmZHAho1igUAnzZn5V5lHipUVGiQpt3FBAKYjWIBwGdtP1yk15ZXTyBT7+ihllGhJicCQLEA4JMq7Q6Nm5+hSruhG7q31NBLmEAAb0CxAOCT/vebvcrKK1JMeLBeuDOFCQTwEhQLAD4nK69Qr399ZgK5vYdaRDKBAN6CYgHAp1RUVb8KpMph6OYerXR7WrzZkQD8BMUCgE954+vd2nGkWLERIXqeCQTwOhQLAD5j66FCvbliryTpuTtS1LyJ1eREAH6OYgHAJ9iq7HrsgwzZHYZuTW2tW1Nbmx0JwHlQLAD4hL8s362dR4vVLCJEz97ew+w4AGpBsQDg9TJyT2n2mQnk+aEpasYEAngtigUAr1Zeade4+RlyGNLtafEa3JMJBPBmFAsAXu3Vr3Zrd36JmjexaioTCOD1KBYAvNamnJP6v1XVE8i0O1PUNCLE5EQALoZiAcAr/XQCufPSNrqxRyuzIwGoA4oFAK/08rJd2ldQqhaRVk0Z0t3sOADqiGIBwOtsPHBCf/12nyQp/a6eiglnAgF8BcUCgFc5XWHXuPlbZBjSsMva6vpuLc2OBMAJFAsAXmXm0p3KPlaqllFWPc0EAvgcigUAr7Eu+4Tmrs6WJE0flqrosGCTEwFwFsUCgFcoq6jS+AUZMgzpnssTNLBLC7MjAagHigUArzDji506cLxM8dGheuK2bmbHAVBPFAsApluz97jmrd4vqXoCiQplAgF8FcUCgKlKbdUTiCTd2ztR13SOMzkRgIagWAAw1fTPd+jgydNqExOmJ25lAgF8HcUCgGm+33NM/1x7QJI0Y3iqmliDTE4EoKEoFgBMUVxeqQkLtkiSfn1lovp3bG5yIgCuQLEAYIppn+3QoVOn1bZpmCYNZgIB/AXFAoDHrdpVoH+vy5EkzRyepggmEMBvUCwAeFRReaUe/7B6AnmgXzv1TW5mciIArkSxAOBRLyzZrrzCciU1C9eEm7uYHQeAi1EsAHjMNzvz9f6GXFks1RNIeAgTCOBvKBYAPKLw9H8mkFH92qt3+1iTEwFwB4oFAI94bsk2HS2yqX3zCI2/iQkE8FcUCwBut3z7US3YeFAWizRrRKrCQgLNjgTATSgWANzqVFmFJn2UKUn63VXt1SuJCQTwZxQLAG419ZNtyi+2qUNchB67kQkE8HcUCwBu82XWES388ZACLNKsEWkKDWYCAfwdxQKAW5wsrdDkhVslSf99TbIuS2xqciIAnkCxAOAWUz7O0rESmzq1aKIxgzqZHQeAh1AsALjc55mH9XFGngIDLEwgQCNTr2Lx5ptvql27dgoNDVWfPn20bt06V+cC4KOOl9j05KLqCeThazsoLSHG3EAAPMrpYvH+++9r7NixmjJlijZt2qS0tDTddNNNys/Pd0c+AD7m6Y+zdLy0Ql1aRuqP1zOBAI2N08Xi5Zdf1kMPPaRRo0ape/fueuuttxQeHq6///3v7sgHwIcs2ZKnT7ccVmCARS/dnSZrEBMI0Ng49QlAFRUV2rhxoyZNmlRzWUBAgAYNGqQ1a9ac9zY2m002m63mfFFRUT2jXtjLX+5Usa3KLV8bwMXZHYY+3HhQkjR6QLJS2kSbnAiAGZwqFseOHZPdblfLli3Pubxly5basWPHeW+Tnp6uqVOn1j9hHb23Plf5xbaLXxGAW/WIj9Ij1zGBAI2V2z+zeNKkSRo7dmzN+aKiIiUkJLj8fh7o306lPGMBmCoqNFi/6p2okCBecAY0Vk4Vi+bNmyswMFBHjx495/KjR4+qVatW572N1WqV1Wqtf8I6+p8BHd1+HwAA4MKc+mdFSEiIevXqpeXLl9dc5nA4tHz5cvXt29fl4QAAgG9xegoZO3asRo4cqcsvv1y9e/fWq6++qtLSUo0aNcod+QAAgA9xuljcc889Kigo0NNPP60jR47okksu0RdffPGLAzoBAEDjYzEMw/DkHRYVFSk6OlqFhYWKiory5F0DAIB6quvjN4duAwAAl6FYAAAAl6FYAAAAl6FYAAAAl6FYAAAAl6FYAAAAl6FYAAAAl6FYAAAAl6FYAAAAl3H7x6b/3Nk3+iwqKvL0XQMAgHo6+7h9sTfs9nixKC4uliQlJCR4+q4BAEADFRcXKzo6utZf9/hnhTgcDuXl5SkyMlIWi8VlX7eoqEgJCQnKzc31mc8gIbNn+GJmyTdzk9kzyOwZZD6XYRgqLi5WfHy8AgJqP5LC489YBAQEqG3btm77+lFRUT7zA3AWmT3DFzNLvpmbzJ5BZs8g839c6JmKszh4EwAAuAzFAgAAuIzfFAur1aopU6bIarWaHaXOyOwZvphZ8s3cZPYMMnsGmevH4wdvAgAA/+U3z1gAAADzUSwAAIDLUCwAAIDLUCwAAIDL+GWxaNeunSwWyzmn6dOnmx2rzmw2my655BJZLBZt3rzZ7DgXdPvttysxMVGhoaFq3bq17r//fuXl5Zkdq1b79+/Xgw8+qPbt2yssLEzJycmaMmWKKioqzI52QS+88IL69eun8PBwxcTEmB3nvN588021a9dOoaGh6tOnj9atW2d2pAtatWqVhgwZovj4eFksFi1atMjsSBeUnp6uK664QpGRkWrRooWGDh2qnTt3mh3rombPnq3U1NSaN2zq27evPv/8c7Nj1dn06dNlsVg0ZswYs6Nc0DPPPPOLx72uXbuaksUvi4UkPfvsszp8+HDN6dFHHzU7Up1NmDBB8fHxZseok4EDB+qDDz7Qzp079eGHH2rv3r0aPny42bFqtWPHDjkcDs2ZM0dZWVl65ZVX9NZbb2ny5MlmR7ugiooKjRgxQn/4wx/MjnJe77//vsaOHaspU6Zo06ZNSktL00033aT8/Hyzo9WqtLRUaWlpevPNN82OUicrV67U6NGjtXbtWi1btkyVlZW68cYbVVpaana0C2rbtq2mT5+ujRs3asOGDbruuut0xx13KCsry+xoF7V+/XrNmTNHqampZkepkx49epzzuPfdd9+ZE8TwQ0lJScYrr7xidox6+eyzz4yuXbsaWVlZhiTjxx9/NDuSUxYvXmxYLBajoqLC7Ch1NmPGDKN9+/Zmx6iTuXPnGtHR0WbH+IXevXsbo0ePrjlvt9uN+Ph4Iz093cRUdSfJWLhwodkxnJKfn29IMlauXGl2FKc1bdrU+Nvf/mZ2jAsqLi42OnXqZCxbtsy49tprjT/96U9mR7qgKVOmGGlpaWbHMAzDMPz2GYvp06erWbNmuvTSSzVz5kxVVVWZHemijh49qoceekj//Oc/FR4ebnYcp504cULvvPOO+vXrp+DgYLPj1FlhYaFiY2PNjuGzKioqtHHjRg0aNKjmsoCAAA0aNEhr1qwxMZl/KywslCSf+tm12+167733VFpaqr59+5od54JGjx6tW2+99Zyfa2+3e/duxcfHq0OHDrrvvvuUk5NjSg6PfwiZJ/zxj3/UZZddptjYWK1evVqTJk3S4cOH9fLLL5sdrVaGYeiBBx7Qww8/rMsvv1z79+83O1KdTZw4UW+88YbKysp05ZVXasmSJWZHqrM9e/bo9ddf16xZs8yO4rOOHTsmu92uli1bnnN5y5YttWPHDpNS+TeHw6ExY8aof//+SklJMTvORWVmZqpv374qLy9XkyZNtHDhQnXv3t3sWLV67733tGnTJq1fv97sKHXWp08fzZs3T126dNHhw4c1depUXX311dq6dasiIyM9G8bsp0zqauLEiYakC562b99+3tu+/fbbRlBQkFFeXu7h1HXP/dprrxn9+/c3qqqqDMMwjOzsbNOmEGe/1wUFBcbOnTuNL7/80ujfv79xyy23GA6Hw6szG4ZhHDx40EhOTjYefPBBj2ZtSGZvnEIOHTpkSDJWr159zuXjx483evfubVIq58jHppCHH37YSEpKMnJzc82OUic2m83YvXu3sWHDBuPxxx83mjdvbmRlZZkd67xycnKMFi1aGBkZGTWX+cIU8nMnT540oqKiTJmcfOYtvQsKCnT8+PELXqdDhw4KCQn5xeVZWVlKSUnRjh071KVLF3dFPK+65r777rv1ySefyGKx1Fxut9sVGBio++67T//4xz/cHbVGQ77XBw8eVEJCglavXu3RpzqdzZyXl6cBAwboyiuv1Lx58xQQ4PlVsD7f53nz5mnMmDE6deqUm9PVXUVFhcLDw7VgwQINHTq05vKRI0fq1KlTWrx4sXnh6shisWjhwoXn5PdWjzzyiBYvXqxVq1apffv2Zsepl0GDBik5OVlz5swxO8ovLFq0SHfeeacCAwNrLrPb7bJYLAoICJDNZjvn17zZFVdcoUGDBik9Pd2j9+szU0hcXJzi4uLqddvNmzcrICBALVq0cHGqi6tr7r/85S96/vnna87n5eXppptu0vvvv68+ffq4M+IvNOR77XA4JFW/ZNaTnMl86NAhDRw4UL169dLcuXNNKRVSw77P3iQkJES9evXS8uXLax6YHQ6Hli9frkceecTccH7EMAw9+uijWrhwoVasWOGzpUKq/vnw9N8RdXX99dcrMzPznMtGjRqlrl27auLEiT5TKkpKSrR3717df//9Hr9vnykWdbVmzRr98MMPGjhwoCIjI7VmzRr9+c9/1q9//Ws1bdrU7Hi1SkxMPOd8kyZNJEnJyclq27atGZEu6ocfftD69et11VVXqWnTptq7d6+eeuopJScne+2BWYcOHdKAAQOUlJSkWbNmqaCgoObXWrVqZWKyC8vJydGJEyeUk5Mju91e8/4mHTt2rPlZMdPYsWM1cuRIXX755erdu7deffVVlZaWatSoUWZHq1VJSYn27NlTcz47O1ubN29WbGzsL/5/9AajR4/Wu+++q8WLFysyMlJHjhyRJEVHRyssLMzkdLWbNGmSBg8erMTERBUXF+vdd9/VihUrtHTpUrOjnVdkZOQvjluJiIhQs2bNvPp4lnHjxmnIkCFKSkpSXl6epkyZosDAQN17772eD+Px8cXNNm7caPTp08eIjo42QkNDjW7duhnTpk0z5fiKhjDzGIu62rJlizFw4EAjNjbWsFqtRrt27YyHH37YOHjwoNnRajV37txaj2fwZiNHjjxv5m+++cbsaDVef/11IzEx0QgJCTF69+5trF271uxIF/TNN9+c93s6cuRIs6OdV20/t3PnzjU72gX99re/NZKSkoyQkBAjLi7OuP76640vv/zS7FhO8YVjLO655x6jdevWRkhIiNGmTRvjnnvuMfbs2WNKFp85xgIAAHg/v30fCwAA4HkUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DIUCwAA4DL/H928tr8KNcpuAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Implementation of relu using simple python.\n",
        "\n",
        "def relu(x):\n",
        "  if x > 0 :\n",
        "    return x\n",
        "  else:\n",
        "    return 0\n",
        "\n",
        "def plot_activation(act_fn, label=\"act_fn\"):\n",
        "    max_int = 5\n",
        "    # Generete 100 evenly spaced points from -max_int to max_int\n",
        "    x = np.linspace(-max_int, max_int, 1000)\n",
        "    y = np.array([act_fn(xi) for xi in x])\n",
        "    plt.plot(x, y, label=label)\n",
        "    plt.legend(loc=\"upper left\")\n",
        "    plt.xticks(np.arange(min(x), max(x) + 1, 1))\n",
        "    plt.show()\n",
        "\n",
        "plot_activation(relu, label='ReLU')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NAQn8NUPhAg-"
      },
      "source": [
        "**Code Task:** Implementer et tracer une autre fonction d'activation de votre choix."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bSCO__yzY5vj"
      },
      "outputs": [],
      "source": [
        "# @title Insérer votre code votre code ici\n",
        "def act_fn(x):\n",
        "    # type your code here\n",
        "\n",
        "    y = ...#\n",
        "    return y\n",
        "\n",
        "# Call the plotting function\n",
        "plot_activation(act_fn, label=....) # update this\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Wrxt2orM7sk"
      },
      "source": [
        "#### Construire un réseau de neurones avec Jax\n",
        "\n",
        "Heuresement, nous avons differents modules dans jax qui peuvent être utiliser pour déveloper des réseaux de neurones et nous n'allons rien implementer partir à de zéro. Pour les modèles avec jax nous pouvons utiliser flax ou haiku. Dans cette section nous allons utiliser flax.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "36LsHOHxjPuH"
      },
      "outputs": [],
      "source": [
        "# @title Demonstration: Construction d'un simple réseau de neurones avec flax\n",
        "# Code for a 4-layer neural network using haiku.\n",
        "# Here assume all the hidden layers have the same number of nodes.\n",
        "# We will use the same activation relu for all the layers except the last layer.\n",
        "\n",
        "class Network(nn.Module):\n",
        "  hidden_size: int\n",
        "  output_size: int\n",
        "\n",
        "  @nn.compact\n",
        "  def __call__(self, x):\n",
        "    # First layer with ReLU activation\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Second layer\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Third (output) layer with no activation applied\n",
        "    x = nn.Dense(self.output_size)(x)\n",
        "\n",
        "    return x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lCOgpUEsnvCK"
      },
      "source": [
        "<!--The cell above is a basic example of how we can define a neural network using flax. Each linear transformation is implemented using the `nn.Dense` function, and we use `jax.nn.relu` to apply non-linearities to the output of each layer.-->\n",
        "\n",
        "La cellule ci-dessus démontre comment définir un simple réseau de neurones avec `flax`. Chaque transformation linéaire est implémenté par la fonction `nn.Dense` et `jax.nn.relu` est utilisé pour appliquer la non-linéarité aux sorties de chaque couche."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dYMLCHd2nSS2",
        "outputId": "60e893be-e54d-4fc3-e1a1-ca40a86afcdd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "+-----------------------+--------+------+\n",
            "| Name                  | Shape  | Size |\n",
            "+-----------------------+--------+------+\n",
            "| params/Dense_0/bias   | (5,)   | 5    |\n",
            "| params/Dense_0/kernel | (4, 5) | 20   |\n",
            "| params/Dense_1/bias   | (5,)   | 5    |\n",
            "| params/Dense_1/kernel | (5, 5) | 25   |\n",
            "| params/Dense_2/bias   | (1,)   | 1    |\n",
            "| params/Dense_2/kernel | (5, 1) | 5    |\n",
            "+-----------------------+--------+------+\n",
            "Total: 61\n"
          ]
        }
      ],
      "source": [
        "# @title Démonstration : initialisation du modèle\n",
        "seed = 32\n",
        "input_size = 4\n",
        "hidden_size = 5\n",
        "output_size = 1\n",
        "\n",
        "# Calling the build_neural_network function and applying the required transformations\n",
        "model = Network(hidden_size, output_size)\n",
        "\n",
        "key = jax.random.PRNGKey(seed)\n",
        "dummy = jnp.zeros((1, input_size), dtype=float)\n",
        "initial_params = model.init(key, dummy)\n",
        "\n",
        "# Let's use the CLU: https://github.com/google/CommonLoopUtils to examine the shape of the parameters\n",
        "print(parameter_overview.get_parameter_overview(initial_params, include_stats=False))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UW39m5wCDrBL"
      },
      "source": [
        "<!-- **Exercise:** Do you understand the shape of the different parameters? -->\n",
        "\n",
        "**Exercice:** Comprenez-vous la forme des différents paramètres ?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0Q1_OKVVvR69"
      },
      "source": [
        "Le code ci haut démontre comment créer une instance du modèle pour obtenir les paramètres initiaux. Apres avoir crée une instance du modèle en utilisant la classe `Network` nous appelons la fonction `init` avec un `jax.random.PRNGKey` et quelques entrées factices à partir desquelles la forme des paramètres sera prédite."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KW6s0Pn3vwy7"
      },
      "source": [
        "\n",
        "\n",
        "Pour appliquer le modèle a des données nous avons besoin d'appeler la fonction `model.apply` avec les paramètres actuels et les données d'entrée."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p3YtVINzqWP7",
        "outputId": "438a25c2-c65e-4bb8-b8d9-6775237a36ff"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Model ouput shape: (1, 1), Input shape: (1, 4)\n"
          ]
        }
      ],
      "source": [
        "z = model.apply(initial_params, dummy)\n",
        "print(f\"Model ouput shape: {z.shape}, Input shape: {dummy.shape}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fbTsk0MdhAhC"
      },
      "source": [
        "## **Classification**\n",
        "Maintenant que nous nous sommes familiarisés avec les fondenmentaux de l'ajustement d'un model,et son entrainement et que nous savons comment construire les réseaux des neurones, nous allons nous focaliser sur notre objectif principale qui est la construction de notre classificateur de nombres.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wMgxJU0TOX6O"
      },
      "source": [
        "### 3.1 Régression logistique\n",
        "\n",
        "La régression linéaire a pour objectif de trouver une fonction $f$ qui mappe nos **entrées $x$**, ou $x \\in \\mathbb{R}^d$ aux **sorties/output/target - $y$**, ou $y \\in \\mathbb{R}^n$ (les valeurs de sortie sont continues). Contrairement à la régression, la **sortie/output/target -$y$** ne peut prendre que certaines valeurs dans la régression logistique. Lorsque la **sortie/target** ne peut prendre que l'une des deux valeurs, l'algorithme est appelé **Classification Binaire**. Lorsque nous avons plus de deux catégories, on parle de **Classification Multi-Classes**.\n",
        "\n",
        "C'est pourquoi l'objectif de la régression logistique (dans le cas de la classification binaire) est de mapper les **entrées $x$**, où $x \\in \\mathbb{R}^d$ à $y$, où $y \\in \\{0,1\\}$.\n",
        "\n",
        "\n",
        "Par example, si nous construisons un classificateur d'images pour chien et chat, 1 peut être utilisé pour répresenter les valeurs de sortie pour les chats et 0 pour les chiens."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SE1L3rmaO4UP"
      },
      "source": [
        "#### Logits and Fonction Sigmoïde\n",
        "\n",
        "\n",
        "Vu que la sortie de la régression logistique est discrète. C'est n'est pas facile de définir une fonction qui produit les valeurs discrètes. Pour cette raison, la fonction est construite pour prédire des probabilités. Rappelons que les les probabilités prennent des valeurs dans l'intervale [0, 1], raison pour laquelle nous avons besoin d'une fonction qui produit des probabilités.  La **fonction sigmoïde** est une bonne fonction d'activation.\n",
        "<br>\n",
        "<center>\n",
        "\n",
        " $$\\sigma(x) = \\frac{1}{1+e^{-x}}$$\n",
        "\n",
        " ![sigmoid.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjcAAAGbCAYAAAA4HrGmAAAABHNCSVQICAgIfAhkiAAAABl0RVh0U29mdHdhcmUAZ25vbWUtc2NyZWVuc2hvdO8Dvz4AAAAmdEVYdENyZWF0aW9uIFRpbWUAVGh1IDE3IEF1ZyAyMDIzIDEwOjAyOjM4Xn+IKgAAIABJREFUeJzt3Xl4VPW9x/HPzCSZJGQnewgkIKssQZDcQLV6TYnUUq2t5do+gri0KLXV2FbRElyuxkpFWoul2qL2aa2orctVSqupaJUIylI3FkEgbAkBJBOyTTJz7h9JhsZMIMtMzszk/XqeeZI5OXPmexgy88lvOT+LYRiGAAAAQoTV7AIAAAB8iXADAABCCuEGAACEFMINAAAIKYQbAAAQUgg3AAAgpISZXUA7t9utQ4cOKTY2VhaLxexyAABANxiGodraWmVmZspqDYw2k4AJN4cOHVJ2drbZZQAAgF7Yv3+/hgwZYnYZkgIo3MTGxkpq/ceJi4szuRoAANAdDodD2dnZns/xQBAw4aa9KyouLo5wAwBAkAmkISWB0TkGAADgI4QbAAAQUgg3AAAgpATMmJvucLlcam5uNrsMfEF4eLhsNpvZZQAAICmIws3Jkyd14MABGYZhdin4AovFoiFDhigmJsbsUgAACI5w43K5dODAAUVHRyslJSWgRmQPdIZhqLq6WgcOHNDIkSNpwQEAmC4owk1zc7MMw1BKSoqioqLMLgdfkJKSor1796q5uZlwAwAwXVANKKbFJjDxugAAAklQhRsAAIAz8Rpu3nrrLc2ePVuZmZmyWCx68cUXz3igdevW6ZxzzpHdbtdZZ52lJ5980te1hpSrr75al112mdllSJJycnK0fPny0+7T3f8HAACYzeuYm7q6Ok2aNEnXXHONLr/88jMeZM+ePbrkkku0YMEC/elPf1JZWZmuu+46ZWRkqKioyOdFh4Jf/vKXATPz67333tOgQYPMLgMAAJ/wGm5mzZqlWbNmdfsgK1euVG5urh566CFJ0tixY/X222/r4YcfJtx0IT4+3uwSPFJSUswuAQAAn/HJbKny8nIVFhZ22FZUVKSbb765y8c0NTWpqanJc9/hcPiilIDz/PPP6+6779auXbsUHR2tyZMn66WXXtLChQt14sQJT1dPbW2tFixYoBdffFFxcXH66U9/qpdeekl5eXmeLqOcnBxdd9112rlzp/76179q8ODBeuSRR1RQUKDrrrtOZWVlGj58uFatWqWpU6d6avjLX/6ikpIS7dq1SxkZGbrpppt06623en6ek5Ojm2++2fN6ffrpp7r22mu1ceNGDR8+XL/85S/78V8MGJgam12qa2pRU4tbzhb3f3x1dfje6TLkcrvlcktutyGXYcjlNuRu+3rqe3m2uQ1D7vaG4rYW4y/cldG25dR97z//zx+e2qcHj4WprpmRq+ykaLPL8DufhJvKykqlpaV12JaWliaHw6GGhgav07dLS0t199139+r5DMNQQ7OrV4/tq6hwW7dnBx0+fFhXXnmlHnzwQX3jG99QbW2t/vWvf3ntjiouLtY777yjl19+WWlpaSopKdHmzZuVl5fXYb+HH35Y999/vxYvXqyHH35YV111laZPn65rrrlGS5cu1W233aa5c+fq448/lsVi0aZNm/Ttb39bd911l+bMmaP169frxhtv1ODBg3X11Vd3qsPtduvyyy9XWlqaNmzYoJqamtOGVADeNTa7tO9YvQ7VNKja0aQjtY06Utukoyeb5GhokaOxWbWNLaptbJajsUXOFrfZJWMAmD0pk3DjT4sWLVJxcbHnvsPhUHZ2drce29Ds0riSv/urtNP65J4iRUd075/t8OHDamlp0eWXX65hw4ZJkiZMmNBpv9raWj311FN6+umnddFFF0mSnnjiCWVmZnba96tf/aq+//3vS5JKSkr0m9/8Rueee66uuOIKSdJtt92mgoICVVVVKT09XcuWLdNFF12kxYsXS5JGjRqlTz75REuXLvUabl5//XVt375df//73z3Pf//99/eomxIYSFxuQ58eqdXWihP68GCN9hyt096jdTrsaFRvhtVF2KyKCLPK3nZr/d7m2RZusyrMZpHVYpHN2v5Vslosslotsn1he/v3FotkUesfZq3fq+37jn+std/9z31b73/h523feB7dzcfBXGlxkWaX0C98Em7S09NVVVXVYVtVVZXi4uK6vOie3W6X3W73xdMHrEmTJumiiy7ShAkTVFRUpJkzZ+pb3/qWEhMTO+z32Wefqbm5WdOmTfNsi4+P1+jRozsdc+LEiZ7v21vL/jMwtW87cuSI0tPTtW3bNl166aUdjjFjxgwtX75cLper00X3tm3bpuzs7A7BqqCgoKenDoSsFpdbW/ef0Js7q/Xe3uP68ECN6pzeW5JjI8M0JDFaqbH21lucXSkxdiVERyg2MkyxkeFtX1u/j7GHyWYlBQB95ZNwU1BQoDVr1nTY9tprr/ntQzEq3KZP7jFnoHJUePevwGuz2fTaa69p/fr1+sc//qFHHnlEd955pzZs2NDr5w8PD/d83/6Xk7dtbjdN3ICvuN2GNu49rpe2HtLfPjqsE/UdF/AdFGHTxCEJmpSdoLNSY5SbHK2cwYOUNCiCi1wCJvAabk6ePKldu3Z57u/Zs0dbt25VUlKShg4dqkWLFungwYP6wx/+IElasGCBfv3rX+unP/2prrnmGv3zn//Us88+q1dffdUvRVsslm53DZnNYrFoxowZmjFjhkpKSjRs2DC98MILHfYZPny4wsPD9d5772no0KGSpJqaGu3cuVPnn39+n55/7Nixeueddzpse+eddzRq1CivSyWMHTtW+/fv1+HDh5WRkSFJevfdd/tUAxCsahub9fymA/pD+T7tOVrn2R4fFa7zR6VoxojBmjw0UWelxtDiAgQQrwnh/fff14UXXui53z42Zt68eXryySd1+PBhVVRUeH6em5urV199Vbfccot++ctfasiQIfrd73434KeBb9iwQWVlZZo5c6ZSU1O1YcMGVVdXa+zYsfrggw88+8XGxmrevHn6yU9+oqSkJKWmpmrJkiWyWq19/qvv1ltv1bnnnqt7771Xc+bMUXl5uX7961/r0Ucf9bp/YWGhRo0apXnz5mnp0qVyOBy68847+1QDEGzqnS16av0+/fat3Z5Wmlh7mGZNSNeleVnKz01SmI0LvAOBymu4ueCCC057gTlvVx++4IILtGXLFp8VFgri4uL01ltvafny5XI4HBo2bJgeeughzZo1S6tXr+6w77Jly7RgwQJ97Wtf80wF379/vyIj+zb465xzztGzzz6rkpIS3XvvvcrIyNA999zjdTCxJFmtVr3wwgu69tprNW3aNOXk5OhXv/qVLr744j7VAQQDwzC05sNK3f1/H+tIbeulKoYnD9L8L+Xq8slZGmQPjhZjYKCzGAFymVyHw6H4+HjV1NQoLi6uw88aGxu1Z88e5ebm9vnDPljU1dUpKytLDz30kK699lqzyzmtgfj6IPQccTTqtr98oDd2VEuShiZF6+bCkbo0L4suJ+A0Tvf5bRb+DAkQW7Zs0fbt2zVt2jTV1NTonnvukaROM50A+N76XUf1w2e26OhJpyJsVt1wwQjdeOEI2cO6P4EAQOAg3ASQX/ziF9qxY4ciIiI0ZcoU/etf/1JycrLZZQEh7Xf/+kz3r9kmtyGNSY/Vr78zWWelxppdFoA+INwEiMmTJ2vTpk1mlwEMGIZh6IG/bddv3/pMkvTtqUN0z6XjFdmDyz0ACEyEGwADjmEYuuOFD/XnjfslSYtmjdH3vzzC5KoA+ArhBsCA8/O1O/TnjftltUgPfHOivj21e0u/AAgOQRVuAmRiF76A1wXB5Pdv79HKN3dLkn7+zYm6gmADhJyguApV+5V0nU6nyZXAm/bXxdsVj4FA8saOI7r3lU8kST+9eDTBBghRQdFyExYWpujoaFVXVys8PFxWa1BksgHB7Xarurpa0dHRCgsLiv9OGKAO1zSoePVWSdJ38ofqBsbYACErKD6NLBaLMjIytGfPHu3bt8/scvAFVqtVQ4cOZYFABKxml1s3Pb1Fn9c3a3xWnEq+No7/r0AIC4pwI0kREREaOXIkXVMBKCIigtY0BLRH39it9/d9rlh7mFZ85xymewMhLmjCjdTaQsDl/QH0xO7qk1rxxi5J0v9+Y7yGDR5kckUA/I0/twGELMMwdOcLH8rpcuvLo1L09UmZZpcEoB8QbgCErL9sPqh3PzuuyHCr/vey8YyzAQYIwg2AkNTgdOnBtdslSTcXjlJ2UrTJFQHoL4QbACHpyfV7daS2SUMSo3TNjFyzywHQjwg3AEJOTUOz5yrEtxSOUkQYb3XAQMJvPICQ8/hbn6mmoVmj0mJ02eQss8sB0M8INwBCSk19s1a9s0eSdOvM0bJZGUQMDDSEGwAh5c/vVaje6dKY9FjNHJdmdjkATEC4ARAyml1uPfnOXknSdecNZ+o3MEARbgCEjDUfHlalo1HJMXbNnpRhdjkATEK4ARASDMPQ7/7VOtZmXsEw2cNYPwoYqAg3AELC5orP9eHBGtnDrPrufw0zuxwAJiLcAAgJz753QJI0e1KmkgZFmFwNADMRbgAEvXpni1798LAk6YopQ0yuBoDZCDcAgt7fP67UyaYWDU2K1rTcJLPLAWAywg2AoPfc+61dUt+aMoTp3wAINwCC24HP67V+9zFZLNI36ZICIMINgCD3wuaDkqTpIwYrKyHK5GoABALCDYCg9rePKiVJl+axQCaAVoQbAEGr4li9PjnskM1q0VfGso4UgFaEGwBBa+3HrdO//2t4khK5tg2ANoQbAEGrvUvq4rPTTa4EQCAh3AAISpU1jdpScUIWi1REuAHwHwg3AILSPz5pbbU5Z2iiUuMiTa4GQCAh3AAISmvpkgLQBcINgKBT19Si9/YelyQVjmOWFICOCDcAgk757mNqdhnKTopSzuBos8sBEGAINwCCzlufVkuSzh+ZwlpSADoh3AAIOm/tbAs3o1JMrgRAICLcAAgqFcfqtfdYvcKsFk0fMdjscgAEIMINgKDyZluX1DlDExUbGW5yNQACEeEGQFA51SWVbHIlAAIV4QZA0Gh2uVW++5gkxtsA6BrhBkDQ+PiQQyebWhQfFa7xmfFmlwMgQBFuAASNjXtaW23OzUmS1coUcADeEW4ABI2Ne1qvSpyfm2RyJQACGeEGQFBwuw1PuJlGuAFwGoQbAEFhR1WtHI0tio6w6ezMOLPLARDACDcAgkL7QplThiUqzMZbF4Cu8Q4BIChsaO+SyqFLCsDpEW4ABDzDYLwNgO4j3AAIeHuP1au6tkkRNqsmZSeYXQ6AAEe4ARDw3m8bbzMpO16R4TaTqwEQ6Ag3AALevw+ckCRNHppociUAgkGX4WbFihXKyclRZGSk8vPztXHjxtMeaPny5Ro9erSioqKUnZ2tW265RY2NjT4vGMDA8+/9NZKkSUPokgJwZl7DzerVq1VcXKwlS5Zo8+bNmjRpkoqKinTkyBGvB3n66ad1++23a8mSJdq2bZt+//vfa/Xq1brjjjv8WjyA0NfY7NK2ww5Jrd1SAHAmXsPNsmXLdP3112v+/PkaN26cVq5cqejoaK1atcrrQdavX68ZM2boO9/5jnJycjRz5kxdeeWVZ2ztAYAz+fiQQy1uQ8kxdmUlRJldDoAg0CncOJ1Obdq0SYWFhad2slpVWFio8vJyrweZPn26Nm3a5Akzn332mdasWaOvfvWrfiobwEDx7/2t423ysuNlsbBYJoAzC/vihqNHj8rlciktLa3D9rS0NG3fvt3rQb7zne/o6NGj+tKXviTDMNTS0qIFCxactluqqalJTU1NnvsOh6O35wAghG1tCzeMtwHQXT6ZLbVu3Trdf//9evTRR7V582b99a9/1auvvqp77723y8eUlpYqPj7ec8vOzvZFKQBCTPtMqbyhhBsA3dOp5SY5OVk2m01VVVUdtldVVSk9Pd3rQRYvXqyrrrpK1113nSRpwoQJqqur0/e+9z3deeedslo7Z6hFixapuLjYc9/hcBBwAHTweZ1T+47VS5ImZhFuAHRPp9QRERGhKVOmqKyszLPN7XarrKxMBQUFXg9SX1/fKcDYbK0X2jIMw+tj7Ha74uLiOtwA4D9tbWu1GZ48SPHR4SZXAyBYdGq5kaTi4mLNmzdPU6dO1bRp07R8+XLV1dVp/vz5kqS5c+cqKytLpaWlkqTZs2dr2bJlmjx5svLz87Vr1y4tXrxYs2fP9oQcAOip9sHELLkAoCe8hps5c+aourpaJSUlqqysVF5entauXesZZFxRUdGhpeZnP/uZLBaLfvazn+ngwYNKSUnR7Nmzdd999/XPWQAISR8dbL1438QhXN8GQPdZjK76jfqZw+FQfHy8ampq6KICIEmaXlqmQzWNevb7BawGDgSoQPz8Zm0pAAHp8zqnDtW0LuEyNiPW5GoABBPCDYCA9EnbkgvDBkcrNpLBxAC6j3ADICB9cqg13IzLCIxmbgDBg3ADICB9fKh1MDHhBkBPEW4ABKT2bqmzswg3AHqGcAMg4DQ2u7S7uk6SNC6DaeAAeoZwAyDg7KislcttaPCgCKXF2c0uB0CQIdwACDjtXVLjMuNksVhMrgZAsCHcAAg4nsHEmYy3AdBzhBsAAYdp4AD6gnADIKAYhqEdlbWSCDcAeodwAyCgHDzRoDqnS+E2i3KSB5ldDoAgRLgBEFB2VrW22oxIiVG4jbcoAD3HOweAgLKj8qQkaVQai2UC6B3CDYCA0t5yMzqdcAOgdwg3AAJK+2BiWm4A9BbhBkDAcLkN7apu75aKMbkaAMGKcAMgYOw7Vidni1uR4VZlJ0abXQ6AIEW4ARAw2sfbjEqLldXKsgsAeodwAyBgMFMKgC8QbgAEDM9MKcINgD4g3AAIGDvau6WYBg6gDwg3AAJCU4tLe47WSWKmFIC+IdwACAh7j9bL5TYUaw9Telyk2eUACGKEGwABYXfb9W1GpMbIYmGmFIDeI9wACAi7jrSGm7NS6ZIC0DeEGwABwdNyk0K4AdA3hBsAAeFUuBlkciUAgh3hBoDp3G5Du4+0zpQaQbcUgD4i3AAw3WFHoxqaXQqzWjQ0iTWlAPQN4QaA6Xa3DSYeNjha4TbelgD0De8iAEzXPt6GmVIAfIFwA8B0zJQC4EuEGwCma7/GDeEGgC8QbgCYbnc1M6UA+A7hBoCpahqaVV3bJEkazjVuAPgA4QaAqT5rG2+TFmdXXGS4ydUACAWEGwCmah9vMzyZLikAvkG4AWCqPUdbx9vQJQXAVwg3AEy191hruMlNJtwA8A3CDQBTfVZNyw0A3yLcADCN221o37F6SVLOYMINAN8g3AAwTVVt64KZNqtF2SyYCcBHCDcATNM+mDg7MYoFMwH4DO8mAEzTHm4YTAzAlwg3AEyz1xNuuMYNAN8h3AAwzamWG8bbAPAdwg0A03xGyw0APyDcADBFi8ut/cdbp4Hnco0bAD5EuAFgioMnGtTsMmQPsyojLtLscgCEEMINAFO0j7fJGTxIVqvF5GoAhBLCDQBTeMINg4kB+BjhBoApmAYOwF8INwBMsadtTSmmgQPwNcINAFNUHGttuRmaxEwpAL5FuAHQ71pcbh34vEGSNGwwLTcAfItwA6DfHa5pVIvbUESYVelMAwfgY12GmxUrVignJ0eRkZHKz8/Xxo0bT3ugEydOaOHChcrIyJDdbteoUaO0Zs0anxcMIPjtaxtvk50YxTRwAD4X5m3j6tWrVVxcrJUrVyo/P1/Lly9XUVGRduzYodTU1E77O51OfeUrX1Fqaqqef/55ZWVlad++fUpISPD7CQAIPvuOt463GTaY8TYAfM9ruFm2bJmuv/56zZ8/X5K0cuVKvfrqq1q1apVuv/32TvuvWrVKx48f1/r16xUeHi5JysnJ8V/VAIJaRVvLzdAkxtsA8L1O3VJOp1ObNm1SYWHhqZ2sVhUWFqq8vNzrQV5++WUVFBRo4cKFSktL0/jx43X//ffL5XJ1+cRNTU1yOBwdbgAGhn2EGwB+1CncHD16VC6XS2lpaR22p6WlqbKy0utBPvvsMz3//PNyuVxas2aNFi9erIceekj/+7//2+UTl5aWKj4+3nPLzs7u46kACBYVbQtmMlMKgD/4ZLaU2+1WamqqHnvsMU2ZMkVz5szRnXfeqZUrV3b5mEWLFqmmpsZz279/vy9KARDgDMMg3ADwq05jbpKTk2Wz2VRVVdVhe1VVldLT070eJCMjQ+Hh4bLZbJ5tY8eOVWVlpZxOpyIiIjo9xm63y26397V+AEHmeJ1TJ5taZLFIQxIJNwB8r1PLTUREhKZMmaKysjLPNrfbrbKyMhUUFHg9yIwZM7Rr1y653W7Ptp07dyojI8NrsAEwcO1ra7VJj4tUZLjtDHsDQM957ZYqLi7W448/rqeeekrbtm3TDTfcoLq6Os/sqblz52rRokWe/W+44QYdP35cP/rRj7Rz5069+uqruv/++7Vw4cL+OQsAQYOZUgD8zetU8Dlz5qi6ulolJSWqrKxUXl6e1q5d6xlkXFFRIav1VC7Kzs7W3//+d91yyy2aOHGisrKy9KMf/Ui33XZb/5wFgKDRPlOK8TYA/MViGIZhdhGS5HA4FB8fr5qaGsXFxZldDgA/KX52q/66+aB+UjRaCy88y+xyAPRRIH5+s7YUgH5FtxQAfyPcAOhX+5gGDsDPCDcA+k29s0XVtU2SpGFJrCsFwD8INwD6TfvF++KjwhUfHW5yNQBCFeEGQL9hphSA/kC4AdBvGEwMoD8QbgD0m33H6yTRcgPAvwg3APqNp1uKwcQA/IhwA6DftA8oHkrLDQA/ItwA6BctLrcOft4giW4pAP5FuAHQLw6daFSL21BEmFVpsZFmlwMghBFuAPSL9sHEQ5OiZbVaTK4GQCgj3ADoF6cGE9MlBcC/CDcA+gWDiQH0F8INgH5RQcsNgH5CuAHQL/bRcgOgnxBuAPidYRiqONY+oJgL+AHwL8INAL87VudUndMli0XKTooyuxwAIY5wA8Dv2mdKZcRFyh5mM7kaAKGOcAPA7yrar3HDeBsA/YBwA8DvWDATQH8i3ADwu/Zp4LTcAOgPhBsAftc+DZwFMwH0B8INAL+jWwpAfyLcAPCruqYWHT3ZJIluKQD9g3ADwK/a15RKiA5XfFS4ydUAGAgINwD8itXAAfQ3wg0Avzp1jRvG2wDoH4QbAH5Fyw2A/ka4AeBXFawGDqCfEW4A+BUtNwD6G+EGgN80u9w6eKJBkjSMMTcA+gnhBoDfHDrRIJfbkD3MqtRYu9nlABggCDcA/Ka9S2poUrSsVovJ1QAYKAg3APyGNaUAmIFwA8BvKo61XeOGNaUA9CPCDQC/8cyUouUGQD8i3ADwG65xA8AMhBsAfmEYhqflJodp4AD6EeEGgF9U1zapodklq0XKSogyuxwAAwjhBoBftM+UykyIUkQYbzUA+g/vOAD8gsHEAMxCuAHgF+3TwFl2AUB/I9wA8Iu9LJgJwCSEGwB+wdWJAZiFcAPAL7g6MQCzEG4A+FxNQ7M+r2+WxAX8APQ/wg0An6toG2+THGNXjD3M5GoADDSEGwA+t+94+0wpWm0A9D/CDQCf28dMKQAmItwA8Ln2binG2wAwA+EGgM/tbZspxYKZAMxAuAHgcxXHabkBYB7CDQCfamx2qdLRKIkxNwDMQbgB4FMHPq+XYUgx9jAlDYowuxwAAxDhBoBP7T16atkFi8VicjUABqIuw82KFSuUk5OjyMhI5efna+PGjd064DPPPCOLxaLLLrvMZ0UCCB6sKQXAbF7DzerVq1VcXKwlS5Zo8+bNmjRpkoqKinTkyJHTHmzv3r368Y9/rPPOO88vxQIIfKwpBcBsXsPNsmXLdP3112v+/PkaN26cVq5cqejoaK1atarLA7lcLn33u9/V3XffreHDh/utYACBjZYbAGbrFG6cTqc2bdqkwsLCUztZrSosLFR5eXmXB7rnnnuUmpqqa6+9tltP3NTUJIfD0eEGIPh5rk5MuAFgkk7h5ujRo3K5XEpLS+uwPS0tTZWVlV4P8vbbb+v3v/+9Hn/88W4/cWlpqeLj4z237OzsHpYOINC43IYOfN4ebuiWAmCOPs+Wqq2t1VVXXaXHH39cycnJ3X7cokWLVFNT47nt37+/r6UAMNmhEw1qdhmKsFmVHhdpdjkABqiwL25ITk6WzWZTVVVVh+1VVVVKT0/vdIDdu3dr7969mj17tmeb2+1uPXhYmHbs2KERI0Z0epzdbpfdbu/zCQAIHO1XJh6SFCWblWngAMzRqeUmIiJCU6ZMUVlZmWeb2+1WWVmZCgoKOh1gzJgx+vDDD7V161bP7etf/7ouvPBCbd26le4mYABhTSkAgaBTy40kFRcXa968eZo6daqmTZum5cuXq66uTvPnz5ckzZ07V1lZWSotLVVkZKTGjx/f4fEJCQmS1Gk7gNDmWQ2cZRcAmMhruJkzZ46qq6tVUlKiyspK5eXlae3atZ5BxhUVFbJaubgxgI6YKQUgEFgMwzDMLkKSHA6H4uPjVVNTo7i4OLPLAdALs375L2077NCqq6fqv8eknfkBAIJeIH5+0/wCwCcMw+DqxAACAuEGgE9U1zapzumS1cKYGwDmItwA8Ik9R1tbbYYkRisijLcWAObhHQiAT7SHm9xkuqQAmItwA8AnCDcAAgXhBoBPEG4ABArCDQCfaA83OYQbACYj3ADoM5fb0L62daWGE24AmIxwA6DPDp1okLPFrQibVZkJUWaXA2CAI9wA6LP2Lqmhg6NZDRyA6Qg3APqsfTVwBhMDCASEGwB99ll1a7hhvA2AQEC4AdBn7S03zJQCEAgINwD6jGvcAAgkhBsAfeJscWs/08ABBBDCDYA+2f95vdyGNCjCppRYu9nlAADhBkDftA8mzkkeJIuFaeAAzEe4AdAnu6tPSpJGpMSYXAkAtCLcAOiTXUdaw81ZqYQbAIGBcAOgT2i5ARBoCDcAes0wDO1ua7kZkcpMKQCBgXADoNeOnnTK0dgii0XKGUy4ARAYCDcAeq19vE12YrQiw20mVwMa8xtmAAAZpklEQVQArQg3AHqtfbwNg4kBBBLCDYBeOzWYmC4pAIGDcAOg13a3XcCPmVIAAgnhBkCvnZopRbgBEDgINwB6pd7ZooMnGiTRcgMgsBBuAPRK+5pSSYMilDQowuRqAOAUwg2AXmEwMYBARbgB0Cvt422GJ9MlBSCwEG4A9MrOqtZwMzKNcAMgsBBuAPTKzqpaSdLo9FiTKwGAjgg3AHqssdmlvcdaBxSPTiPcAAgshBsAPbbryEm5DSkhOlwpsXazywGADgg3AHrs0yOtXVKj0mJlsVhMrgYAOiLcAOixHZWtg4npkgIQiAg3AHqsfTDxKGZKAQhAhBsAPbaj8lS3FAAEGsINgB452XRqTSnCDYBARLgB0COftnVJpcbalciaUgACEOEGQI9w8T4AgY5wA6BH2mdKjUwl3AAITIQbAD1yquWGmVIAAhPhBkC3GYahbYcdkqTR6XEmVwMA3hFuAHRblaNJx+qcslktGsOYGwABinADoNs+OVwjSRqRMkiR4TaTqwEA7wg3ALrtk0OtXVLjMuiSAhC4CDcAuu3j9nCTSbgBELgINwC67ZO2wcRnZ8abXAkAdI1wA6BbHI3N2nesXhLdUgACG+EGQLdsP9x6fZvM+EiWXQAQ0Ag3ALrl40OtM6UYbwMg0BFuAHSLZ6YU420ABDjCDYBuaR9MzHgbAIGOcAPgjJwtbs+aUmfTLQUgwHUZblasWKGcnBxFRkYqPz9fGzdu7PIgjz/+uM477zwlJiYqMTFRhYWFp90fQHDZXulQs8tQQnS4hiRGmV0OAJyW13CzevVqFRcXa8mSJdq8ebMmTZqkoqIiHTlyxOtB1q1bpyuvvFJvvPGGysvLlZ2drZkzZ+rgwYN+LR5A//j3/hOSpElDEmSxWEyuBgBOz2u4WbZsma6//nrNnz9f48aN08qVKxUdHa1Vq1Z5Pcif/vQn3XjjjcrLy9OYMWP0u9/9Tm63W2VlZX4tHkD/2NIebrITTK4EAM6sU7hxOp3atGmTCgsLT+1ktaqwsFDl5eXdOmh9fb2am5uVlJTU5T5NTU1yOBwdbgACU3vLzWTCDYAg0CncHD16VC6XS2lpaR22p6WlqbKyslsHve2225SZmdkhIH1RaWmp4uPjPbfs7Owelg6gP9Q0NGt3dZ0kaeIQpoEDCHw+ny31wAMP6JlnntELL7ygyMjILvdbtGiRampqPLf9+/f7uhQAPvDhgdaL92UnRWlwjN3kagDgzMK+uCE5OVk2m01VVVUdtldVVSk9Pf20B/vFL36hBx54QK+//romTpx42n3tdrvsdt4ogUD37wOtXVJ52YkmVwIA3dOp5SYiIkJTpkzpMBi4fXBwQUFBlwd68MEHde+992rt2rWaOnWqf6oF0O+2VLTPlKJLCkBw6NRyI0nFxcWaN2+epk6dqmnTpmn58uWqq6vT/PnzJUlz585VVlaWSktLJUk///nPVVJSoqefflo5OTmesTkxMTGKiYnpp1MB4GuGYWhr+2DioQwmBhAcvIabOXPmqLq6WiUlJaqsrFReXp7Wrl3rGWRcUVEhq/VUo89vfvMbOZ1Ofetb3+pwnCVLluiuu+7yX/UA/OpQTaOOnmxSmNWis1lTCkCQsBiGYZhdhCQ5HA7Fx8erpqZGcXFc3h0IBK98cEg/eHqLzs6M06s/PM/scgAEoED8/GZtKQBdem/PcUnSuTldX7MKAAIN4QZAlza0hZtpuYQbAMGDcAPAq5r6Zu1oWwmclhsAwYRwA8Cr9/cdl2FIw5MHKSWWa1IBCB6EGwBebaRLCkCQItwA8GoDg4kBBCnCDYBO6p0t+uhg65pStNwACDaEGwCdbKk4oRa3ocz4SA1JjDK7HADoEcINgE48XVK5SbJYLCZXAwA9Q7gB0Mnbn1ZLkgqGDza5EgDoOcINgA5q6ps9i2WePyrF5GoAoOcINwA6eGf3UbkN6azUGGUmMN4GQPAh3ADo4K2drV1S54+k1QZAcCLcAPAwDONUuBmVbHI1ANA7hBsAHrurT+pQTaMiwqzKz2UwMYDgRLgB4PHmzqOSpPzcJEVF2EyuBgB6h3ADwIPxNgBCAeEGgCTpZFOLyncfkyR9eTThBkDwItwAkCT9c/sROV1uDU8epJGpMWaXAwC9RrgBIEn6+0eVkqSLx6ez5AKAoEa4AaDGZpfe2HFEUmu4AYBgRrgBoLd2Vqve6VJWQpQmZMWbXQ4A9AnhBoDWtnVJFZ1NlxSA4Ee4AQY4Z4tbr2+rkkSXFIDQQLgBBrg3dhyRo7FFKbF2TRmWaHY5ANBnhBtggHvu/QOSpMsnZ8lmpUsKQPAj3AADWHVtk2eW1LemDDG5GgDwDcINMIC9tPWgXG5Dk7ITNDIt1uxyAMAnCDfAAGUYhp7f1NolRasNgFBCuAEGqI8OOrS9slYRYVZ9fWKm2eUAgM8QboAB6qnyvZJar20THx1uai0A4EuEG2AAOlLbqJe3HpIkXTMjx9xiAMDHCDfAAPTH8n1yutw6Z2iCJg/l2jYAQgvhBhhgGptd+uOGCknSdecNN7kaAPA9wg0wwPx180Edr3NqSGKUZo5LM7scAPA5wg0wgDS1uLTijV2SpPkzchVm4y0AQOjhnQ0YQJ7ZuF8HTzQoNdau70wbanY5AOAXhBtggKh3tuiRf7a22vzwopGKirCZXBEA+AfhBhggnnhnr46ebNLQpGjNOTfb7HIAwG8IN8AAUFnTqN+s2y1JKv7KKIUz1gZACOMdDhgA7v6/j3WyqUV52Qn6+iSWWgAQ2gg3QIh7/ZMq/e2jSoVZLSq9fIKsVovZJQGAXxFugBDmaGxWyUsfSWq9YN/YjDiTKwIA/yPcACHKMAzd/pcPdKimUdlJUfrRRSPNLgkA+gXhBghRfyjfpzUfVircZtEjV57D1G8AAwbhBghBmys+132vbpMk3T5rrPKyE0yuCAD6D+EGCDG7q0/q2iffk9Pl1sxxabpmRo7ZJQFAvyLcACGkytGoub/fqM/rmzVxSLwenpMni4XZUQAGFsINECL2H6/X/zz2rg6eaFBu8iCtuvpcDbKHmV0WAPQ73vmAELCzqlZX/X6DqhxNykqI0h+umabkGLvZZQGAKQg3QJD724eH9ZPnP9DJphaNSovRH67JV3p8pNllAYBpCDdAkGpwuvTztdv15Pq9kqRpuUl67KopSoiOMLcwADAZ4QYIQm/urNbiFz9SxfF6SdL3vzxcP5k5WmEsiAkAhBsgmHx0sEbLXtupf24/IknKiI/Ufd8Yr/8ek2ZyZQAQOAg3QIAzDEP/+vSonlq/V2VtocZmtWhuwTDdOnO0YpgRBQAd8K4IBCDDMLS7+qRe/vdhvbz1oPYea+1+slik2RMzdXPhSA1PiTG5SgAITF120K9YsUI5OTmKjIxUfn6+Nm7ceNoDPffccxozZowiIyM1YcIErVmzxufFAqGsurZJf/vwsEpe+khfXrpOhcve0q/KPtXeY/WKsYfp6uk5er34y/rVlZMJNgBwGl5bblavXq3i4mKtXLlS+fn5Wr58uYqKirRjxw6lpqZ22n/9+vW68sorVVpaqq997Wt6+umnddlll2nz5s0aP368308CCCY1Dc068Hm9Pq06qe2VtdpR6dDOqpM6eKKhw37hNovOG5mir0/K1FfGpXFBPgDoJothGMYXN+bn5+vcc8/Vr3/9a0mS2+1Wdna2brrpJt1+++2dDjJnzhzV1dXplVde8Wz7r//6L+Xl5WnlypXdKsThcCg+Pl41NTWKi4vr7fkA/cblNtTQ7FKDs/VW52zRifpmnah36kRDsz6vd6qmvvXr0ZNOHfy8QYdONKi2qcXr8SwWaXRarM7NSdL5o1I0fcRgAg2AgBeIn9+d3jmdTqc2bdqkRYsWebZZrVYVFhaqvLzc60HKy8tVXFzcYVtRUZFefPHFLp+4qalJTU1NnvsOh6PHxXfH79/eo/1t02XPxEvOU+ctkpfd2vb18ngv+3bx8C6O631vr8f1+lw9eHwP6vJ63C7/Xbwds4u6uv38XTxXN19DGZLbMNTiNtTicqvFbcjlNtTiMtTidrdtb93W7HZ3+FmD06XGZrecLncXVZxZYnS4RqTEaHR6rMZkxGlMeqxGp8cqLjK818cEALTqFG6OHj0ql8ultLSOU0vT0tK0fft2rweprKz0un9lZWWXT1xaWqq77767NzX3yKsfHNLmihN+fx4MbFHhNkVH2JQQHa6E6AglRocrPqr1a0J0uAbH2JWZEKWshChlJkQqOoIWGQDwF9PeYRctWtShtcfhcCg7O9vnz/PNKUM0fURyp+1dLZTsdbOXnbtaZ9nbcS1e9u7J83e5bzdXe+76uXxfl7djnu643vft3r93z2rtvNVqtSjMapHNalG4zSKb1aqwtm1hbffD234eZrMozGqVzWpRVIRNUeFttwib7GFWVt4GgADSKdwkJyfLZrOpqqqqw/aqqiqlp6d7PUh6enqP9pcku90uu93/C/t9N3+Y358DAAAEjk5TwSMiIjRlyhSVlZV5trndbpWVlamgoMDrQQoKCjrsL0mvvfZal/sDAAD4i9duqeLiYs2bN09Tp07VtGnTtHz5ctXV1Wn+/PmSpLlz5yorK0ulpaWSpB/96Ef68pe/rIceekiXXHKJnnnmGb3//vt67LHH+u9MAAAA1EW4mTNnjqqrq1VSUqLKykrl5eVp7dq1nkHDFRUVslpPNfpMnz5dTz/9tH72s5/pjjvu0MiRI/Xiiy9yjRsAANDvvF7nxgyBOE8eAACcXiB+fne5/AIAAEAwItwAAICQQrgBAAAhhXADAABCCuEGAACEFMINAAAIKYQbAAAQUgg3AAAgpBBuAABASPG6/IIZ2i+U7HA4TK4EAAB0V/vndoAseCApgMJNbW2tJCk7O9vkSgAAQE/V1tYqPj7e7DIkBdDaUm63W4cOHVJsbKwsFovPjutwOJSdna39+/cHzJoXvhbq58j5Bb9QP0fOL/iF+jn68/wMw1Btba0yMzM7LKptpoBpubFarRoyZIjfjh8XFxeS/2H/U6ifI+cX/EL9HDm/4Bfq5+iv8wuUFpt2gRGxAAAAfIRwAwAAQortrrvuusvsIvzNZrPpggsuUFhYwPTC+VyonyPnF/xC/Rw5v+AX6ucY6uf3nwJmQDEAAIAv0C0FAABCCuEGAACEFMINAAAIKYQbAAAQUkI23Ozdu1fXXnutcnNzFRUVpREjRmjJkiVyOp0d9vvggw903nnnKTIyUtnZ2XrwwQdNqrjn7rvvPk2fPl3R0dFKSEjwuo/FYul0e+aZZ/q50t7rzjlWVFTokksuUXR0tFJTU/WTn/xELS0t/Vyp7+Tk5HR6zR544AGzy+q1FStWKCcnR5GRkcrPz9fGjRvNLsln7rrrrk6v1ZgxY8wuq9feeustzZ49W5mZmbJYLHrxxRc7/NwwDJWUlCgjI0NRUVEqLCzUp59+alK1vXOmc7z66qs7vaYXX3yxSdX2TGlpqc4991zFxsYqNTVVl112mXbs2NFhn8bGRi1cuFCDBw9WTEyMvvnNb6qqqsqkiv0nZMPN9u3b5Xa79dvf/lYff/yxHn74Ya1cuVJ33HGHZx+Hw6GZM2dq2LBh2rRpk5YuXaq77rpLjz32mImVd5/T6dQVV1yhG2644bT7PfHEEzp8+LDndtlll/VThX13pnN0uVy65JJL5HQ6tX79ej311FN68sknVVJS0s+V+tY999zT4TW76aabzC6pV1avXq3i4mItWbJEmzdv1qRJk1RUVKQjR46YXZrPnH322R1eq7ffftvsknqtrq5OkyZN0ooVK7z+/MEHH9SvfvUrrVy5Uhs2bNCgQYNUVFSkxsbGfq609850jpJ08cUXd3hN//znP/djhb335ptvauHChXr33Xf12muvqbm5WTNnzlRdXZ1nn1tuuUX/93//p+eee05vvvmmDh06pMsvv9zEqv3EGEAefPBBIzc313P/0UcfNRITE42mpibPtttuu80YPXq0GeX12hNPPGHEx8d7/Zkk44UXXujninyvq3Ncs2aNYbVajcrKSs+23/zmN0ZcXFyH1zWYDBs2zHj44YfNLsMnpk2bZixcuNBz3+VyGZmZmUZpaamJVfnOkiVLjEmTJpldhl988b3D7XYb6enpxtKlSz3bTpw4YdjtduPPf/6zGSX2mbf3x3nz5hmXXnqpSRX51pEjRwxJxptvvmkYRuvrFR4ebjz33HOefbZt22ZIMsrLy80q0y9CtuXGm5qaGiUlJXnul5eX6/zzz1dERIRnW1FRkXbs2KHPP//cjBL9YuHChUpOTta0adO0atWqgFqWvq/Ky8s1YcIEpaWlebYVFRXJ4XDo448/NrGyvnnggQc0ePBgTZ48WUuXLg3Kbjan06lNmzapsLDQs81qtaqwsFDl5eUmVuZbn376qTIzMzV8+HB997vfVUVFhdkl+cWePXtUWVnZ4fWMj49Xfn5+SL2ekrRu3TqlpqZq9OjRuuGGG3Ts2DGzS+qVmpoaSfJ87m3atEnNzc0dXsMxY8Zo6NChIfcahv5lCtvs2rVLjzzyiH7xi194tlVWVio3N7fDfu0fkpWVlUpMTOzXGv3hnnvu0X//938rOjpa//jHP3TjjTfq5MmT+uEPf2h2aT5RWVnZIdhIHV/DYPTDH/5Q55xzjpKSkrR+/XotWrRIhw8f1rJly8wurUeOHj0ql8vl9fXZvn27SVX5Vn5+vp588kmNHj1ahw8f1t13363zzjtPH330kWJjY80uz6faf5+8vZ7B+rvmzcUXX6zLL79cubm52r17t+644w7NmjVL5eXlstlsZpfXbW63WzfffLNmzJih8ePHS2p9DSMiIjqNXwy111AKwjE3t99+u9dBsv95++Ib58GDB3XxxRfriiuu0PXXX29S5d3Tm/M7ncWLF2vGjBmaPHmybrvtNv30pz/V0qVL/XgGZ+brcwwGPTnn4uJiXXDBBZo4caIWLFighx56SI888oiamppMPgt80axZs3TFFVdo4sSJKioq0po1a3TixAk9++yzZpeGXvqf//kfff3rX9eECRN02WWX6ZVXXtF7772ndevWmV1ajyxcuFAfffRRUE0g8aWga7m59dZbdfXVV592n+HDh3u+P3TokC688EJNnz6900Dh9PT0TqPE2++np6f7puAe6un59VR+fr7uvfdeNTU1yW639/o4feHLc0xPT+80+8bs19Cbvpxzfn6+WlpatHfvXo0ePdoP1flHcnKybDab19+xQHptfCkhIUGjRo3Srl27zC7F59pfs6qqKmVkZHi2V1VVKS8vz6yy/G748OFKTk7Wrl27dNFFF5ldTrf84Ac/0CuvvKK33npLQ4YM8WxPT0+X0+nUiRMnOrTehOLvZNCFm5SUFKWkpHRr34MHD+rCCy/UlClT9MQTT8hq7dhQVVBQoDvvvFPNzc0KDw+XJL322msaPXq0aV1SPTm/3ti6dasSExNNCzaSb8+xoKBA9913n44cOaLU1FRJra9hXFycxo0b55Pn8IW+nPPWrVtltVo95xcsIiIiNGXKFJWVlXlm6LndbpWVlekHP/iBydX5x8mTJ7V7925dddVVZpfic7m5uUpPT1dZWZknzDgcDm3YsOGMMzaD2YEDB3Ts2LEOgS5QGYahm266SS+88ILWrVvXadjFlClTFB4errKyMn3zm9+UJO3YsUMVFRUqKCgwo2T/MXtEs78cOHDAOOuss4yLLrrIOHDggHH48GHPrd2JEyeMtLQ046qrrjI++ugj45lnnjGio6ON3/72tyZW3n379u0ztmzZYtx9991GTEyMsWXLFmPLli1GbW2tYRiG8fLLLxuPP/648eGHHxqffvqp8eijjxrR0dFGSUmJyZV335nOsaWlxRg/frwxc+ZMY+vWrcbatWuNlJQUY9GiRSZX3jvr1683Hn74YWPr1q3G7t27jT/+8Y9GSkqKMXfuXLNL65VnnnnGsNvtxpNPPml88sknxve+9z0jISGhw+y2YHbrrbca69atM/bs2WO88847RmFhoZGcnGwcOXLE7NJ6pba21vM7JslYtmyZsWXLFmPfvn2GYRjGAw88YCQkJBgvvfSS8cEHHxiXXnqpkZubazQ0NJhcefed7hxra2uNH//4x0Z5ebmxZ88e4/XXXzfOOeccY+TIkUZjY6PZpZ/RDTfcYMTHxxvr1q3r8JlXX1/v2WfBggXG0KFDjX/+85/G+++/bxQUFBgFBQUmVu0fIRtunnjiCUOS19t/+ve//2186UtfMux2u5GVlWU88MADJlXcc/PmzfN6fm+88YZhGIbxt7/9zcjLyzNiYmKMQYMGGZMmTTJWrlxpuFwucwvvgTOdo2EYxt69e41Zs2YZUVFRRnJysnHrrbcazc3N5hXdB5s2bTLy8/ON+Ph4IzIy0hg7dqxx//33B8Uba1ceeeQRY+jQoUZERIQxbdo049133zW7JJ+ZM2eOkZGRYURERBhZWVnGnDlzjF27dpldVq+98cYbXn/f5s2bZxhG63TwxYsXG2lpaYbdbjcuuugiY8eOHeYW3UOnO8f6+npj5syZRkpKihEeHm4MGzbMuP7664MmjHf1mffEE0949mloaDBuvPFGIzEx0YiOjja+8Y1vdPijP1RYDCOE5gUDAIABL+hmSwEAAJwO4QYAAIQUwg0AAAgphBsAABBSCDcAACCkEG4AAEBIIdwAAICQQrgBAAAhhXADAABCCuEGAACEFMINAAAIKYQbAAAQUv4fqiKcqepbGOAAAAAASUVORK5CYII=)\n",
        "</center>\n",
        "<br>\n",
        "<br>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yAWfZN-7oadX"
      },
      "source": [
        "**Cross entropy loss function**: **Fonction de perte d'entropie croisée**\n",
        "\n",
        "Vu que pour la classification binaire nous ne pouvons qu'avoir deux valeurs de sortie, la fonciton de l'erreur moyenne quadratique n''est pas appropriée pour la régression logistique. La fonction la plus utilisée est **la fonction de perte d'entropie croisée**. Elle est défine de la façon suivante:\n",
        "\n",
        "\n",
        "<br>\n",
        "<center>\n",
        "\n",
        " $$ -y_i \\log(p_i) - (1-y_i) \\log (1-p_i),$$\n",
        "\n",
        "</center>\n",
        "where $p_i = \\sigma (z)$ with $z$ being the output of our model function.\n",
        "<br>\n",
        "\n",
        "**Tâche**:\n",
        "\n",
        "1. Implementer la fonction d'activation sigmoïde.\n",
        "2. Implementer la fonction de coût d'entropie croisée.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J9CiEUERAHJ4"
      },
      "outputs": [],
      "source": [
        "def sigmoid(x):\n",
        "    \"\"\"sigmoid function 1/1+e^-x\"\"\"\n",
        "\n",
        "    prob = ... # update me\n",
        "\n",
        "    return prob"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "YzKHb9DEAaMI"
      },
      "outputs": [],
      "source": [
        "# @title Executez cette cellule pour tester votre code\n",
        "def test_sigmoid_fn():\n",
        "  x  = np.array([0.7, 0.3, 0.8, 0.2])\n",
        "  assert jnp.allclose(sigmoid(x), jax.nn.sigmoid(x)), \"Test failed!\"\n",
        "  print(\"Nice! Your answer looks correct!\")\n",
        "\n",
        "  return"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "t75OVB1oBZOZ"
      },
      "outputs": [],
      "source": [
        "# @title Solution fonction sigmoïde (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts !)\n",
        "def sigmoid(x):\n",
        "  prob = 1/(1+jnp.exp(-x))\n",
        "\n",
        "  return prob"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f-YTxxNnuOKI"
      },
      "outputs": [],
      "source": [
        "def cross_entropy_loss(predictions, targets):\n",
        "    # you need to make sure we never have log of 0\n",
        "\n",
        "    # use sigmoid to compute the probs from the predicitions\n",
        "    probs = ... # update me\n",
        "\n",
        "    # your code here\n",
        "    loss = ... # update me\n",
        "\n",
        "    return loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WUW87CN4u9sG"
      },
      "outputs": [],
      "source": [
        "# @title Executez cette cellule pour tester votre code\n",
        "def test_cross_entropy_loss():\n",
        "  predictions = np.array([0.7, 0.3, 0.8, 0.2])\n",
        "  targets = np.array([1, 0, 1, 0])\n",
        "\n",
        "  # Expected cross-entropy loss for the test data\n",
        "  expected_loss = 0.60669523\n",
        "\n",
        "  # Calculate the cross-entropy loss using the implemented function\n",
        "  computed_loss = cross_entropy_loss(predictions, targets)\n",
        "\n",
        "  assert jnp.isclose(computed_loss, expected_loss), \"Test failed!\"\n",
        "\n",
        "  # If the assert statement does not raise an exception, the test is passed.\n",
        "  print(\"Nice! Your anwser looks correct\")\n",
        "\n",
        "  return\n",
        "\n",
        "test_cross_entropy_loss()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Y0VbBhG_u_UL"
      },
      "outputs": [],
      "source": [
        "# @title Solution fonction de perte d'entropie croisée (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts!)\n",
        "def cross_entropy_loss(preds, targets):\n",
        "    eps = 1e-15\n",
        "    probs = sigmoid(preds)\n",
        "\n",
        "    loss = -targets*jnp.log(probs+eps) - (1-targets)*jnp.log(1-probs+eps)\n",
        "\n",
        "    return jnp.mean(loss)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HjQNjDC2cG2t"
      },
      "source": [
        "#### Extension à la multi-classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dlr8evx-dCoE"
      },
      "source": [
        "Avec la multi-classification, le modèle est construit de façon à supporter plusieur classes. Avec chaque classe qui répresente une categorie ou une étiquette. Par example, dans le cas d'une classification des nombres, nous avons 10 classes, chaque classe répresente un nombre de 0 à 9.\n",
        "\n",
        "La sortie du modèle est la distribution de probabilité pour chaque classe. La dimension de notre sortie correspond donc nombre de classes. Par example un classificateur avec 3 classes aura un vecteur à 3 dimensions.\n",
        "Pour prédire le modèle, on selectionne la classe avec la plus grande probablilité."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BqLug2dpf8Zn"
      },
      "source": [
        "**Encodage One-hot: or one-hot encoding**\n",
        "\n",
        "L'encodage one-hot est une façon de répresenter les variables catégoriques comme des vecteurs binaries. Dans le cas d'une classification binaire avec 3 classes, notre sortie est representée comme un vecteur one-hot de la manière suivante.\n",
        "\n",
        "**classe 1** [1, 0, 0]: ceci veut dire que notre donnée appartient à la premiere classe. Le premier élement du vecteur est 1 et les autres zeros.\n",
        "\n",
        "\n",
        "**classe 2** [0, 1, 0]: ceci veut dire que notre donnée appartient à la deuxieme classe. Le deuxieme élement du vecteur est 1 et les autres zeros.\n",
        "\n",
        "**classe 3** [0, 0, 1]: ceci veut dire que notre donnée appartient à la troisieme classe. Le troisieme élement du vecteur est 1 et les autres zeros.\n",
        "\n",
        "__Exercice__ discuter comment on défine la fonction de coût pour la multi-classification.\n",
        "\n",
        "\n",
        "La fonction de coût pour une multi-classification est définie de la même manière que la fonction pour un classificateur binaire. Par contre pour ce cas nous définissons la fonction de coût comme la somme de coût pour chaque classe pris séparement...\n",
        "\n",
        "On peut utiliser la fonction `jax.nn.one_hot` pour encoder les données.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "u_-jrxWPjVzf"
      },
      "outputs": [],
      "source": [
        "# An example using one hot encoding\n",
        "num_classes =  3\n",
        "targets = jnp.array([2, 0, 1])\n",
        "one_hot_targets = jax.nn.one_hot(targets, num_classes)\n",
        "print(f\"Example of One hot encordings: {one_hot_targets}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ckIDzLRgj7_b"
      },
      "source": [
        "<!-- **Exercise**: Discuss with your neighbour how we should define the loss function in the case of multi-class classification. -->\n",
        "\n",
        "**Exercice**: Discutez avec votre voisin de la manière dont nous devrions définir la fonction de perte dans le cas d'une classification multi-classes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HMrwPge_lzVt"
      },
      "source": [
        "<!--**Solution**: The loss function for a multi-classification is computed similarly to that of a binary classifier. However in this case we define the loss as the sum of the loss for each of the individual classes.-->\n",
        "**Solution**: La fonction de perte pour une multi-classification est calculée de la même manière que celle d'un classificateur binaire. Cependant, dans ce cas, nous définissons la perte comme la somme des pertes pour chacune des classes individuelles.\n",
        "<br>\n",
        "<center>\n",
        "\n",
        " $$ \\sum_c -y^c_i \\log(p^c_i),$$\n",
        "\n",
        "</center>\n",
        "\n",
        "where $p^c_i = \\text{softmax}(z) = \\frac{e^{z^c_i}}{\\sum_c e^{z^c_i}}$ with $z$ being the output of our model function.\n",
        "\n",
        "<br>\n",
        "<!--The main difference here is that we use a $\\text{softmax}$ activation function instead of $\\text{sigmoid}$ as for the binary case.-->\n",
        "La principale difference ici est l'utilisation de la fonction d'activation $\\text{softmax}$ au lieu de la fonction d'activation sigmoïde utilisée pour la classification binaire\n",
        "\n",
        "\n",
        "**Exercise 3 [OPTIONAL]**: Avez-vous une intuition que cette formule est similaire à celle de la classification binaire ? <!--Do your get the initution why this formula is similar to that for the binary case?-->\n",
        "\n",
        "**Solution**: Défilez jusqu'à l' [Appendix](#scrollTo=fRYbQvz01Zlm)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2QnINsMrpTYP"
      },
      "source": [
        "**Tâche**:\n",
        "  1. Implémenter la fonction d'activation softmax <!--the softmax activation function-->\n",
        "  2. Implémenter une fonction de perte d'entropie croisée pour la classification multiclasse utilisant softmax et un codage \"one-hot\"."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4DWDGiKZpRX0"
      },
      "outputs": [],
      "source": [
        "def softmax(logits):\n",
        "  \"\"\"Compute softmax: `exp(x)/sum(exp(x))`\n",
        "\n",
        "  Args:\n",
        "    logits: array of shape (num_samples, num_classes)\n",
        "\n",
        "  Return:\n",
        "    probs: array of shape (num_samples, num_classes)\n",
        "  \"\"\"\n",
        "\n",
        "  # your code here\n",
        "  # make sure you sum across the right axis\n",
        "\n",
        "  probs = ... # update me\n",
        "\n",
        "  return probs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "background_save": true
        },
        "id": "UlBBgQafDsHQ",
        "outputId": "9eb38583-c3e3-4442-b080-e6d2a8190e87"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Nice! Your answer looks correct.\n"
          ]
        }
      ],
      "source": [
        "# @title Executez cette cellule pour tester votre code\n",
        "def test_softmax():\n",
        "  x = jnp.array([[1.0, 0.4, 0.3], [10.0, 4.6, 8.9]])\n",
        "  assert jnp.allclose(softmax(x), jax.nn.softmax(x, axis=-1))\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_softmax()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5KKM6hKnxFSK"
      },
      "outputs": [],
      "source": [
        "# @title softmax solution (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts !)\n",
        "def softmax(logits):\n",
        "  exp_logits = jnp.exp(logits)\n",
        "  return exp_logits / jnp.sum(exp_logits, axis=-1, keepdims=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WIVjt6T4xTQX"
      },
      "outputs": [],
      "source": [
        "def cross_entropy_softmax_loss(predictions, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        predictions: (num_samples, num_classes)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = ... # update me\n",
        "\n",
        "    num_classes = ... # update me\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = ... # update me\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss = ... # update me\n",
        "\n",
        "    return loss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8Tsbe8OazNq5"
      },
      "outputs": [],
      "source": [
        "# @title Executez cette cellule pour tester votre code\n",
        "def test_cross_entropy_softmax_loss():\n",
        "  # Fixed predictions (logits) for each class\n",
        "  predictions = jnp.array([[1.5, 0.3, 2.7],\n",
        "        [0.8, 1.2, 3.1], [2.3, 1.7, 0.5],\n",
        "        [3.0, 0.5, 1.2], [0.2, 2.8, 1.0]])\n",
        "\n",
        "  # Fixed true class labels\n",
        "  targets = jnp.array([2, 1, 0, 0, 2])\n",
        "\n",
        "  # Expected loss computed manually\n",
        "  expected_loss = 1.0456787\n",
        "\n",
        "  # Compute the cross-entropy softmax loss using your implementation\n",
        "  loss = cross_entropy_softmax_loss(predictions, targets)\n",
        "\n",
        "  # Check if the computed loss matches the JAX built-in loss\n",
        "  assert jnp.allclose(loss, expected_loss), \"Loss value do not match!\"\n",
        "\n",
        "  print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_cross_entropy_softmax_loss()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WG5z8vOjfYiU"
      },
      "outputs": [],
      "source": [
        "# @title Solution: softmax à entropie croisée (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts!)\n",
        "def cross_entropy_softmax_loss(predictions, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        predictions: (num_samples, num_classes)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = softmax(predictions) # update me\n",
        "\n",
        "    num_classes = predictions.shape[-1]\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = jax.nn.one_hot(targets, num_classes) # update me\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss_i = jnp.sum(-targets_one_hot*jnp.log(probs), axis=-1) # update me\n",
        "\n",
        "    return jnp.mean(loss_i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EcXXE56hPOhK"
      },
      "source": [
        "#### Simple réseau de neurones pour la classification\n",
        "\n",
        "Dans cette section nous allons mettre en place toutes les différentes pièces et entrainer notre résau de neurones pour la classification. Rappelons les outils que nous avons mentionner initialement qui sont necessaire pour entrainer un modèle d'apprentissage automatique.\n",
        "\n",
        "- Nos donnée d'apprentissage ou dataset.\n",
        "- La fonction du modèle\n",
        "- la fonction de coût\n",
        "- et la fonction d'optimisation\n",
        "Nous allons utiliser `sklearn`, nous n'allons pas discuter le traitement des données (data processing) mais en pratique nous le faisons avant.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "background_save": true
        },
        "id": "II8gN_lTKoQI"
      },
      "outputs": [],
      "source": [
        "from sklearn import datasets\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "from typing import NamedTuple, Any\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# Let re-adapt our batch gradient descent function\n",
        "def batch_gradient_descent(loss_fn, params, training_data, val_data, learning_rate=0.01, num_epochs=20, batch_size=10):\n",
        "  \"\"\"Batch gradient descent basic jax implementation.\n",
        "\n",
        "  Args:\n",
        "    loss_fn\n",
        "      the loss function for our model.\n",
        "    params:\n",
        "      the initial parameters of the model.\n",
        "    training_data\n",
        "      a tuple with the features and targets for training.\n",
        "    val_data\n",
        "      a tuple with the features and targets for validation.\n",
        "    learning_rate\n",
        "      learning rate\n",
        "    num_epochs\n",
        "      number of epochs\n",
        "    batch_size:\n",
        "      size of every mini batch\n",
        "  \"\"\"\n",
        "\n",
        "  X_train, y_train = training_data\n",
        "  X_val, y_val = val_data\n",
        "\n",
        "  num_samples, num_features = X_train.shape\n",
        "\n",
        "  # Create empty list to store the training and validation loss.\n",
        "  loss_train = [] # training loss\n",
        "  loss_val  = [] # valisation loss\n",
        "\n",
        "  # Define a function that computes loss and gradients\n",
        "  loss_and_grad = jax.value_and_grad(loss_fn)\n",
        "\n",
        "  for epoch in range(num_epochs):\n",
        "    # Shuffle the data before every epoch\n",
        "    shuffled_indices = np.arange(num_samples)\n",
        "    np.random.shuffle(shuffled_indices)\n",
        "\n",
        "    loss_train_epoch = []\n",
        "\n",
        "    for start_idx in range(0, num_samples, batch_size):\n",
        "      end_idx = start_idx + batch_size\n",
        "      if end_idx > num_samples:\n",
        "        end_idx = num_samples\n",
        "\n",
        "      batch_indices = shuffled_indices[start_idx:end_idx]\n",
        "      X_batch = X_train[batch_indices]\n",
        "      y_batch = y_train[batch_indices]\n",
        "      # Compute loss and gradients using value_and_grad\n",
        "      loss, grads = loss_and_grad(params, X_batch, y_batch)\n",
        "      loss_train_epoch.append(loss)\n",
        "\n",
        "      # Update the parameters\n",
        "      params = jax.tree_map(lambda p, g: p -learning_rate*g, params, grads)\n",
        "\n",
        "    # We need to turn the list in to an array before applying jnp.mean\n",
        "    mean_loss = jnp.mean(jnp.array(loss_train_epoch))\n",
        "    loss_train.append(mean_loss)\n",
        "\n",
        "    # Compute the validation loss at the end of the epoch\n",
        "    loss_v = loss_fn(params, X_val, y_val)\n",
        "    loss_val.append(loss_v)\n",
        "\n",
        "  # Plot training and validation loss\n",
        "  epochs = range(1, num_epochs+1)\n",
        "  plt.plot(epochs, loss_train, label='Training Loss')\n",
        "  plt.plot(epochs, loss_val, label='Validation Loss')\n",
        "  plt.xlabel('Epoch')\n",
        "  plt.ylabel('Loss')\n",
        "  plt.title('Training and Validation Loss')\n",
        "  plt.legend()\n",
        "\n",
        "  # Display the plot\n",
        "  plt.show()\n",
        "\n",
        "  return params\n",
        "\n",
        "# Load the mnist dataset\n",
        "def load_dataset(seed):\n",
        "  mnist = fetch_openml(name='mnist_784', version=1, as_frame=False)\n",
        "  # Extract the data and labels\n",
        "  images, labels = mnist.data, mnist.target\n",
        "\n",
        "  # These images consist of integer values from 0 to 255.0\n",
        "  # We scale the images to min and max of 1\n",
        "  x_max = 255.0\n",
        "  x_min = 0.0\n",
        "\n",
        "  images = (images - x_min)/(x_max - x_min)\n",
        "  images = images.astype(jnp.float32)\n",
        "  labels = labels.astype(jnp.float32)\n",
        "\n",
        "  # These are images of shape 28x28 which have been flatten to shape 784\n",
        "  X_train, X_test, y_train, y_test = train_test_split(\n",
        "      images, labels, test_size=0.2, train_size=0.8, random_state=seed\n",
        "  )\n",
        "\n",
        "  train_dataset = (X_train, y_train)\n",
        "  test_dataset = (X_test, y_test)\n",
        "\n",
        "  return train_dataset, test_dataset\n",
        "\n",
        "training_data, val_data = load_dataset(32)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fcJMGW7HWkWI"
      },
      "source": [
        "**Tâche:**\n",
        "1. Construisez un réseau de neurones qui génère des logits pour chacune des 10 classes. <!--Build a neural network that outputs logits for each of the 10 classes.-->\n",
        "2. Initialisez votre modèle avec des entrées factice. <!--Initialise your model with some dummy input.-->\n",
        "3. Définissez votre fonction d'entropie croisée softmax. <!--Define your softmax cross entropy function.-->"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DBOzpb2YXzvR"
      },
      "outputs": [],
      "source": [
        "# @title Completez le code\n",
        "class Network(nn.Module):\n",
        "  hidden_size: int\n",
        "  output_size: int\n",
        "\n",
        "  @nn.compact\n",
        "  def __call__(self, x):\n",
        "    # First layer with ReLU activation\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Second layer\n",
        "    x = ...  # update me\n",
        "    x = ...  # update me\n",
        "\n",
        "    # Third (output) layer with no activation applied\n",
        "    x = nn.Dense(self.output_size)(x)\n",
        "\n",
        "    return x\n",
        "\n",
        "# transform and intialiase the model.\n",
        "seed = 32\n",
        "input_size = 784 # remember our features are images of shape 28x28 flatten\n",
        "hidden_size = ... # update me\n",
        "output_size = ... # update me (hint: number classes)\n",
        "\n",
        "# instantiate the model\n",
        "model = Network... # update me\n",
        "\n",
        "key = jax.random.PRNGKey(seed)\n",
        "dummy = jnp.zeros((1, input_size), dtype=float)\n",
        "initial_params = model.init(key, dummy)\n",
        "\n",
        "def softmax(logits):\n",
        "  exp_logits = jnp.exp(logits)\n",
        "  return exp_logits / jnp.sum(exp_logits, axis=-1, keepdims=True)\n",
        "\n",
        "\n",
        "def cross_entropy_softmax_loss(params, X, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        params: model parameters\n",
        "        X: features arrary (num_samples, num_features)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    # use the model to compute the predictions\n",
        "    preds = model.apply(params, X)\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = softmax(preds)\n",
        "\n",
        "    num_classes = preds.shape[-1]\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = jax.nn.one_hot(targets, num_classes)\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss_i = jnp.sum(-targets_one_hot*jnp.log(probs), axis=-1)\n",
        "\n",
        "    return jnp.mean(loss_i)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mBM7kwGjY4dr"
      },
      "outputs": [],
      "source": [
        "# @title Exemple de solution (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts !)\n",
        "class Network(nn.Module):\n",
        "  hidden_size: int\n",
        "  output_size: int\n",
        "\n",
        "  @nn.compact\n",
        "  def __call__(self, x):\n",
        "    # First layer with ReLU activation\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Second layer\n",
        "    x = nn.Dense(self.hidden_size)(x)\n",
        "    x = jax.nn.relu(x)\n",
        "\n",
        "    # Third (output) layer with no activation applied\n",
        "    x = nn.Dense(self.output_size)(x)\n",
        "\n",
        "    return x\n",
        "\n",
        "# transform and intialiase the model.\n",
        "seed = 67\n",
        "input_size = 784\n",
        "hidden_size = 100\n",
        "output_size = 10\n",
        "\n",
        "# Instantiate the model\n",
        "model = Network(hidden_size, output_size)\n",
        "\n",
        "key = jax.random.PRNGKey(seed)\n",
        "dummy = jnp.zeros((1, input_size), dtype=float)\n",
        "initial_params = model.init(key, dummy)\n",
        "\n",
        "def softmax(logits):\n",
        "  exp_logits = jnp.exp(logits)\n",
        "  return exp_logits / jnp.sum(exp_logits, axis=-1, keepdims=True)\n",
        "\n",
        "def cross_entropy_softmax_loss(params, X, targets):\n",
        "    \"\"\"Compute the cross entropy softmax loss function\n",
        "\n",
        "      Args:\n",
        "        params: model params\n",
        "        X: (num_features, num_classes)\n",
        "        targets: (num_samples)\n",
        "    \"\"\"\n",
        "\n",
        "    preds = model.apply(params, X)\n",
        "\n",
        "    # Compute the softmax probabilities\n",
        "    probs = softmax(preds)\n",
        "\n",
        "    num_classes = preds.shape[-1]\n",
        "\n",
        "    # One-hot encode the targets\n",
        "    targets_one_hot = jax.nn.one_hot(targets, num_classes)\n",
        "\n",
        "    # Compute the cross-entropy loss\n",
        "    eps = 1e-15\n",
        "    probs += eps # to avoid calling log with 0 values\n",
        "\n",
        "    loss_i = jnp.sum(-targets_one_hot*jnp.log(probs), axis=-1)\n",
        "\n",
        "    return jnp.mean(loss_i)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GcSvlekHPWxW"
      },
      "source": [
        "#### Entraîner le modèle\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xed1mfr1cOzW"
      },
      "source": [
        "**Tâche:**\n",
        "  1. Utilisez la fonction `batch_gradient_descent` pour entraîner le modèle.\n",
        "  2. Variez le `learning_rate` et le `batch_size` et observez le changement de la fonction de perte."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lslWzLP0cciM"
      },
      "outputs": [],
      "source": [
        "params = batch_gradient_descent ... # update me"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WZGTHUrTdW2x"
      },
      "outputs": [],
      "source": [
        "# @title Exemple de solution (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts !)\n",
        "params = batch_gradient_descent(cross_entropy_softmax_loss, initial_params, training_data, val_data, learning_rate=0.01, num_epochs=10, batch_size=1000)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sGPvmGWkP1fT"
      },
      "source": [
        "#### Évaluation du modèle\n",
        "Jusqu'a présent nous n'avons vu qu'une seule méthode pour évaluer notre modèle: la fonction de coût.\n",
        "\n",
        "Par contre, lors de l'évaluation d'un modèle d'apprentissage automatique plusieurs méthodes peuvent être utiliser.  Les hyperparamètres sont selectionner en fonction de la métrique qu'on optimise. Voici quelques métriques que nous pouvons utilser pour nos tâches de classification.\n",
        "\n",
        "*   **Accuracy**:  c'est la métrique la plus importante pour les tâches de classification. Elle mésure la proportion des instances classifier correctment: $$ \\text{Accuracy} = \\frac{\\text{Nombre des prediction correctes}}{\\text{total nombres des predictions}}$$\n",
        "\n",
        "* **Precision**: c'est la mésure des prédictions positives, Par example si notre modèle prédit 100 points qui appartiennent à la classe 1, notre precision sera le pourcentage de ces 100 points qui appartiennent à la classe 1. Une grande précision est néccessaire pour un diagnostic des images. Nous ne voulons pas faire des précision inutiles qui pourons engendrer de traitement non neccessaire.\n",
        "\n",
        "* **Recall**: Il s'agit d'une mésure de la capacité du modèle à identifier de manière efficiente toutes les instances positives. Par exemple, si l'ensemble de données comporte 100 points de données appartenant à la classe 1, combien sont effectivement classifiés comme appartenant à la classe 1 ? Le rappel revêt une importance primordiale dans les scénarios où l'omission d'une seule instance positive n'est pas souhaitée. Prenons l'exemple d'une entreprise de sécurité : nous ne souhaitons pas attribuer à tort la classification \"sûr\" à un signal émis par un utilisateur alors qu'il est en réalité en situation de danger."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-0htEsSspFQN"
      },
      "source": [
        "<!--**Let's use accuracy to evaluate the performance of our trained classifier.**-->\n",
        "**Utilisons l'`accuracy` pour évaluer la performance du classificateur**\n",
        "\n",
        "Tout d'abord, définissons une fonction de prédiction qui transforme la sortie du modèle en classe. Rappelons que la sortie du classificateur est composée de logits, correspondant à des probabilités non normalisées pour chaque classe. Ainsi, la classe prédite est celle avec la probabilité la plus élevée.\n",
        "  \n",
        "\n",
        "**Tâche**\n",
        "  1. Implémentez une fonction appelée \"model_predict\" qui sélectionne la classe appropriée à partir de la sortie du modèle."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tWMMpYSDhAhE"
      },
      "outputs": [],
      "source": [
        "# @title Completez ce code\n",
        "def model_predict(params, X):\n",
        "    \"\"\"Use the model for predicition\n",
        "\n",
        "      args:\n",
        "        params: model parameters\n",
        "        X: features array (num_samples, num_features)\n",
        "\n",
        "      return\n",
        "        pred: predicted class (num_samples, 1)\n",
        "    \"\"\"\n",
        "\n",
        "    # call the model to compute the logits\n",
        "    logits = model... # update me\n",
        "    preds = ... # update me: hint use jnp.argmax\n",
        "\n",
        "    return preds"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3u3PzTGmxENi"
      },
      "outputs": [],
      "source": [
        "# @title Executez cette cellule pour tester votre code\n",
        "def test_model_predict():\n",
        "    features = val_data[0][0:10]\n",
        "    preds = model_predict(params, features)\n",
        "    expected = jnp.argmax(model.apply(params, features), axis=-1)\n",
        "    assert jnp.array_equal(preds, expected), \"Failed! try again\"\n",
        "    print(\"Nice! Your answer looks correct.\")\n",
        "\n",
        "test_model_predict()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xhJbRdW8DsHS"
      },
      "outputs": [],
      "source": [
        "# @title Exemple de solution: model_predict (Essayez de ne pas tricher avant d'avoir fait de sérieux efforts!)\n",
        "def model_predict(params, X):\n",
        "    \"\"\"Use the model for predicition\n",
        "\n",
        "      args:\n",
        "        params: model parameters\n",
        "        X: features array (num_samples, num_features)\n",
        "\n",
        "      return\n",
        "        pred: predicted class (num_samples, 1)\n",
        "    \"\"\"\n",
        "\n",
        "    # call the model to compute the logits\n",
        "    logits = model.apply(params, X)\n",
        "    preds = jnp.argmax(logits, axis=-1)\n",
        "\n",
        "    return preds"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "k-rRiOD2z5ks"
      },
      "outputs": [],
      "source": [
        "# @title Evaluez l'accuracy de votre modèle\n",
        "def compute_accuracy(data):\n",
        "  \"\"\"Compute the accuracy of the model\"\"\"\n",
        "\n",
        "  X, y_true = data\n",
        "  y_pred = model_predict(params, X).squeeze()\n",
        "\n",
        "  acc = sum(y_pred==y_true)/len(y_true)\n",
        "\n",
        "  return acc\n",
        "\n",
        "train_acc = compute_accuracy(training_data)\n",
        "val_acc = compute_accuracy(val_data)\n",
        "print(f\"The training accuracy is {train_acc} while the validation accuracy is {val_acc}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r5-yxk9e19q4"
      },
      "source": [
        "\n",
        "\n",
        "Félicitations, nous venons d'entraîner un modèle d'apprentissage automatique pour la classification en utilisant le dataset populaire mnist digit.\n",
        "\n",
        "**Excercice**:\n",
        "- Etes-vous satisfait de la precision de votre modèle?\n",
        "- Que pouvez vous faire pour améliorer la précision de votre modèle?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fV3YG7QOZD-B"
      },
      "source": [
        "\n",
        "\n",
        "## Resumé\n",
        "\n",
        "- L'apprentissage automatique est la science de l'utilisation des données pour construire des systèmes intelligents.\n",
        "- L'apprentissage profond est le sous-ensemble des méthodes d'apprentissage automatique qui utilise des réseaux de neurones.\n",
        "- L'optimisation est le procéssus de recherche des paramètres qui rendent la fonction de perte aussi petite que possible.\n",
        "- JAX est un nouveau framework populaire qui peut être utilisé pour calculer les dérivées et former des modèles d'apprentissage automatique.\n",
        "\n",
        "**Prochaines étapes:**\n",
        " - Participez à d'autres tutoriels comme Math for Machine Learning, pour lequel nous avons également une version française.\n",
        "\n",
        "**Références:**\n",
        "\n",
        "\n",
        "1. https://d2l.ai/chapter_linear-networks/linear-regression.html\n",
        "2. https://jax.readthedocs.io/en/latest/notebooks/quickstart.html\n",
        "3. https://www.simplilearn.com/tutorials/artificial-intelligence-tutorial/ai-vs-machine-learning-vs-deep-learning\n",
        "4. https://www.javatpoint.com/machine-learning\n",
        "5. Aurelien Genon, Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, 2nd Edition, O'Reilly Media, 2019."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "742JhcnAxTof"
      },
      "source": [
        "### Appendix\n",
        "\n",
        "#### Base de JAX [OPTIONAL]\n",
        "\n",
        "Pendant ce tutoriel, nous avons utilisé le framework [JAX](https://jax.readthedocs.io/en/latest/) pour illustrer les différents concepts discutés. Jax est similaire à numpy mais il existe quelques differences qui doivent être mentionnés."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T221aJAVyjvj"
      },
      "source": [
        "Similarités entre JAX et Numpy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Co610zXhygak"
      },
      "outputs": [],
      "source": [
        "# Create NumPy arrays\n",
        "np_array1 = np.array([1, 2, 3])\n",
        "np_array2 = np.array([4, 5, 6])\n",
        "\n",
        "# Create JAX arrays\n",
        "jax_array1 = jnp.array([1, 2, 3])\n",
        "jax_array2 = jnp.array([4, 5, 6])\n",
        "\n",
        "# Element-wise addition using NumPy\n",
        "np_result = np_array1 + np_array2\n",
        "print(\"NumPy result:\", np_result)\n",
        "\n",
        "# Element-wise addition using JAX\n",
        "jax_result = jax_array1 + jax_array2\n",
        "print(\"JAX result:\", jax_result)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "o5i-RM66zYz7"
      },
      "outputs": [],
      "source": [
        "# Array concatenation using NumPy\n",
        "np_array1 = np.array([1, 2, 3])\n",
        "np_array2 = np.array([4, 5, 6])\n",
        "np_concatenated = np.concatenate([np_array1, np_array2])\n",
        "\n",
        "# Array concatenation using JAX\n",
        "jax_array1 = jnp.array([1, 2, 3])\n",
        "jax_array2 = jnp.array([4, 5, 6])\n",
        "jax_concatenated = jnp.concatenate([jax_array1, jax_array2])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fz73kSvDzojV"
      },
      "outputs": [],
      "source": [
        "# Element-wise functions using NumPy\n",
        "np_array = np.array([0, np.pi/2, np.pi])\n",
        "np_sin = np.sin(np_array)\n",
        "\n",
        "# Element-wise functions using JAX\n",
        "jax_array = jnp.array([0, jnp.pi/2, jnp.pi])\n",
        "jax_sin = jnp.sin(jax_array)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yVj6HoN4z5KZ"
      },
      "outputs": [],
      "source": [
        "# Reduction operations using NumPy\n",
        "np_array = np.array([1, 2, 3])\n",
        "np_sum = np.sum(np_array)\n",
        "np_mean = np.mean(np_array)\n",
        "\n",
        "# Reduction operations using JAX\n",
        "jax_array = jnp.array([1, 2, 3])\n",
        "jax_sum = jnp.sum(jax_array)\n",
        "jax_mean = jnp.mean(jax_array)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "etSsvtmQz9L9"
      },
      "source": [
        "Différence entre JAX et NumPy - ❌\n",
        "\n",
        "Malgré leurs similarité JAX et NumPy ont d'importantes différences:\n",
        "- Les tableaux de Jax sont **immuable** (they can't be modified after they are created).\n",
        "- La la façon dont le hasard  est traité **randomness** -- JAX handles randomness explicitly.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mgu5mHNZ1Esn"
      },
      "source": [
        "Les tableaux JAX sont immuable mais ceux de NumPy arrays ne le sont pas.\n",
        "\n",
        "Les tableaux JAX et NumPy sont souvent interchangeables, **mais** les tableaux Jax sont **immuables** (ils ne peuvent pas être modifiés après leur création).\n",
        "<!--JAX and NumPy arrays are often interchangeable, **but** Jax arrays are **immutable** (they can't be modified after they are created).-->\n",
        "L'autorisation des mutations rend les transformations difficiles et viole les conditions des [fonctions pures](https://en.wikipedia.org/wiki/Pure_function)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rf2bVtWr1QYX"
      },
      "source": [
        "Voyons cela en pratique en changeant le nombre au début d'un tableau."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aonuiSN81Ok5"
      },
      "outputs": [],
      "source": [
        "# NumPy: mutable arrays\n",
        "x = np.arange(10)\n",
        "x[0] = 10\n",
        "print(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_bikd7W91eQf"
      },
      "source": [
        "Essayons avec JAX."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Kt9yRXan1mMO"
      },
      "outputs": [],
      "source": [
        "# JAX: immutable arrays\n",
        "# Should raise an error.\n",
        "try:\n",
        "    x = jnp.arange(10)\n",
        "    x[0] = 10\n",
        "except Exception as e:\n",
        "    print(\"Exception {}\".format(e))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YHRr6uKH1sQ0"
      },
      "source": [
        "<!--So it fails! We can't mutate a JAX array once it has been created. To update JAX arrays, we need to use [helper functions](https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.ndarray.at.html) that return an updated copy of the JAX array.-->\n",
        "\n",
        "Erreur! Nous ne pouvons pas muter un tableau JAX une fois qu'il a été créé. Pour mettre à jour les tableaux JAX, nous devons utiliser des fonctions d'assistance qui renvoient une copie mise à jour du tableau JAX.\n",
        "\n",
        "Au lieu de faire ceci `x[idx] = y`, on doit faire `x = x.at[idx].set(y)`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XLL6d2p81xue"
      },
      "outputs": [],
      "source": [
        "x = jnp.arange(10)\n",
        "new_x = x.at[0].set(10)\n",
        "print(f\" new_x: {new_x} original x: {x}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w6ibwTBj14gw"
      },
      "source": [
        "<!--Note here that `new_x` is a copy and that the original `x` is unchanged.-->\n",
        "On note que `new_x` is une copie et que la valeur originale de `x` est nonchangé."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ik_8oN9m1_zS"
      },
      "source": [
        "Randomness in NumPy vs JAX\n",
        "\n",
        "JAX est plus explicite dans la génération de nombres pseudo-aléatoires (PRNG) que NumPy et d'autres bibliothèques (telles que TensorFlow ou PyTorch). [PRNG](https://en.wikipedia.org/wiki/Pseudorandom_number_generator) est le processus de génération algorithmique d'une séquence de nombres, qui *se rapproche* des propriétés d'une séquence de nombres aléatoires. <!--is the process of algorithmically generating a sequence of numbers, which *approximate* the properties of a sequence of random numbers.-->\n",
        "\n",
        "Voyons les différences dans la façon dont JAX et NumPy génèrent des nombres aléatoires."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jaWE-uiW2G4p"
      },
      "source": [
        "<!--##### In Numpy, PRNG is based on a global `state`.\n",
        "\n",
        "Let's set the initial seed.-->\n",
        "\n",
        "Dans Numpy, PRNG est basé sur un état global.\n",
        "\n",
        "Définissons la graine initiale."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wa5e2_gb2Jl9"
      },
      "outputs": [],
      "source": [
        "# Set random seed\n",
        "np.random.seed(42)\n",
        "prng_state = np.random.get_state()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-9X10jhocGaS"
      },
      "outputs": [],
      "source": [
        "# @title Function d'aide pour comparer les clés prng (Exécuter la cellule)\n",
        "def is_prng_state_the_same(prng_1, prng_2):\n",
        "    \"\"\"Helper function to compare two prng keys.\"\"\"\n",
        "    # concat all elements in prng tuple\n",
        "    list_prng_data_equal = [(a == b) for a, b in zip(prng_1, prng_2)]\n",
        "    # stack all elements together\n",
        "    list_prng_data_equal = np.hstack(list_prng_data_equal)\n",
        "    # check if all elements are the same\n",
        "    is_prng_equal = all(list_prng_data_equal)\n",
        "    return is_prng_equal"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yCHvH8DZ3Aro"
      },
      "source": [
        "<!--Let's take a few samples from a Gaussian (normal) Distribution and check if PRNG keys/global state change.-->\n",
        "Prenons quelques échantillons d'une distribution gaussienne (normale) et vérifions si les clés PRNG/l'état global changent"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KSixAoOQ2QU9"
      },
      "outputs": [],
      "source": [
        "print(\n",
        "    f\"sample 1 = {np.random.normal()} Did prng state change: {not is_prng_state_the_same(prng_state,np.random.get_state())}\"\n",
        ")\n",
        "prng_state = np.random.get_state()\n",
        "print(\n",
        "    f\"sample 2 = {np.random.normal()} Did prng state change: {not is_prng_state_the_same(prng_state,np.random.get_state())}\"\n",
        ")\n",
        "prng_state = np.random.get_state()\n",
        "print(\n",
        "    f\"sample 3 = {np.random.normal()} Did prng state change: {not is_prng_state_the_same(prng_state,np.random.get_state())}\"\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dlwT1pZH4M7C"
      },
      "source": [
        "L'état aléatoire global de Numpy est mis à jour chaque fois qu'un nombre aléatoire est généré, donc *l'échantillon 1 != l'échantillon 2 != l'échantillon 3*.\n",
        "\n",
        "La mise à jour automatique de l'état rend difficile la gestion du caractère aléatoire de manière **reprodutible** sur différents threads, processus et appareils.\n",
        "\n",
        "<!--Having the state automatically updated, makes it difficult to handle randomness in a **reproducible** way across different threads, processes and devices.-->"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eNQW9JwK4Yp6"
      },
      "source": [
        "Pour JAX, PRNG est explicite\n",
        "<!--In JAX, PRNG is explicit-->\n",
        "\n",
        "Dans JAX, pour chaque génération de nombres aléatoires, vous devez transmettre explicitement une clé/un état aléatoire.\n",
        "\n",
        "Passer le même état/clé entraîne la génération du même numéro. Ceci n’est généralement pas souhaitable."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Qd0PAWvf4KtX"
      },
      "outputs": [],
      "source": [
        "from jax import random\n",
        "\n",
        "key = random.PRNGKey(42)\n",
        "print(f\"sample 1 = {random.normal(key)}\")\n",
        "print(f\"sample 2 = {random.normal(key)}\")\n",
        "print(f\"sample 3 = {random.normal(key)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iUpdRj074oYO"
      },
      "source": [
        "Pour générer des échantillons différents et indépendants, vous devez  manuellement diviser les clés."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "82xoxsrF4vls"
      },
      "outputs": [],
      "source": [
        "from jax import random\n",
        "\n",
        "key = random.PRNGKey(42)\n",
        "print(f\"sample 1 = {random.normal(key)}\")\n",
        "\n",
        "# We split the key -> new key and subkey\n",
        "new_key, subkey = random.split(key)\n",
        "\n",
        "# We use the subkey immediately and keep the new key for future splits.\n",
        "# It doesn't really matter which key we keep and which one we use immediately.\n",
        "print(f\"sample 2 = {random.normal(subkey)}\")\n",
        "\n",
        "# We split the new key -> new key2 and subkey\n",
        "new_key2, subkey = random.split(new_key)\n",
        "print(f\"sample 3 = {random.normal(subkey)}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C2wiRBEo5OQb"
      },
      "source": [
        "<!--By using JAX, we can more easily reproduce random number generation in parallel across threads, processes, or even devices by explicitly passing and keeping track of the prng key (without relying on a global state that automatically gets updated).-->\n",
        "\n",
        "En utilisant JAX, nous pouvons reproduire plus facilement la génération de nombres aléatoires en parallèle sur des threads, des processus ou même des périphériques en transmettant et en gardant explicitement la clé prng (sans compter sur un état global automatiquement mis à jour)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kh_8f4gKyufu"
      },
      "source": [
        "### Derivation of partial derivatives for exercise 2 [OPTIONAL]\n",
        "Derive $\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}}$:\n",
        "\\begin{aligned}\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{ \\partial}{\\partial \\mathbf{w}} (\\frac{1}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Definition of $\\mathcal{L}$} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\frac{ \\partial }{\\partial \\mathbf{w}} ( \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Constant multiple rule} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\sum_{i=1}^m \\frac{ \\partial }{\\partial \\mathbf{w}} (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2 \\quad \\text{: Sum Rule - derivative of sum is sum of derivatives.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) \\frac{ \\partial }{\\partial \\mathbf{w}}(y_i -(\\mathbf{w}^T \\mathbf{x}_i + b))  \\quad \\text{: Power Rule + Chain Rule.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-\\mathbf{x}_i)  \\quad \\text{: Compute derative.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{2}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-\\mathbf{x}_i)  \\quad \\text{: Factor constant out of summation.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial \\mathbf{w}} & = \\frac{2}{m} \\sum_{i=1}^m \\mathbf{x}_i((\\mathbf{w}^T \\mathbf{x}_i + b) -y_i ) \\quad \\text{: Rearrange.} \\\\  \n",
        "\\end{aligned}\n",
        "\n",
        "Derive $\\frac{\\partial \\mathcal{L}}{\\partial b}$:\n",
        "\\begin{aligned}\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{ \\partial}{\\partial b} (\\frac{1}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Definition of $\\mathcal{L}$} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\frac{ \\partial }{\\partial b} ( \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2) \\quad \\text{: Constant multiple rule} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\sum_{i=1}^m \\frac{ \\partial }{\\partial b} (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b))^2 \\quad \\text{: Sum Rule - derivative of sum is sum of derivatives.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) \\frac{ \\partial }{\\partial b}(y_i -(\\mathbf{w}^T \\mathbf{x}_i + b))  \\quad \\text{: Power Rule + Chain Rule.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{1}{m} \\sum_{i=1}^m 2 (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-1)  \\quad \\text{: Compute derative.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{2}{m} \\sum_{i=1}^m (y_i - (\\mathbf{w}^T \\mathbf{x}_i + b)) (-1)  \\quad \\text{: Factor constant out of summation.} \\\\\n",
        "\\frac{\\partial \\mathcal{L}}{\\partial b} & = \\frac{2}{m} \\sum_{i=1}^m ((\\mathbf{w}^T \\mathbf{x}_i + b) -y_i ) \\quad \\text{: Rearrange.} \\\\  \n",
        "\\end{aligned}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fRYbQvz01Zlm"
      },
      "source": [
        "### Intuition pour la function cout avec l'entropie croisée multi-classes.: exercise 3 [OPTIONAL]\n",
        "\n",
        "Pour la classification binaire, nous utilisons la formule suivante pour la perte d'entropie croisée\n",
        "\n",
        " $$ -y_i \\log(p_i) - (1-y_i) \\log (1-p_i).$$\n",
        "\n",
        "Rappelez-vous qu'en classe binaire, nous avons une classe, donc la sortie de notre modèle est la probabilité, $p$, d'appartenir à cette classe. Au lieu de cela, nous pouvons traiter notre classificateur binaire comme deux classes définies comme suit\n",
        "\n",
        "  - Class 1: Appartient à la classe en question.\n",
        "  - Class 2: N'appartient pas à la classe en question.\n",
        "\n",
        "Si la probabilité pour le point de données $y$_i d'appartenir à la classe 1 est $p$_i, cela signifie que sa probabilité de ne pas appartenir à la classe 1, ce qui équivaut à appartenir à la classe 2, est $(1-p_i)$.\n",
        "\n",
        "Puisque les valeurs cibles sont codées à chaud (one-hot) pour une classification multi-classe, si $y_i$ est l'étiquette qui indique si le point de données appartient à la classe 1 ou non, l'étiquette correspondante pour l'appartenance à la classe 2 sera $(1 - y_i) $. Nous pouvons donc écrire notre perte d'entropie croisée sous forme compacte comme suit\n",
        "\n",
        "$$ \\sum_c -y^c_i \\log(p^c_i).$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s75zkKGJ9QRn"
      },
      "source": [
        "**References:**\n",
        "\n",
        "1. https://d2l.ai/chapter_linear-networks/linear-regression.html\n",
        "2. https://jax.readthedocs.io/en/latest/notebooks/quickstart.html\n",
        "3. https://www.simplilearn.com/tutorials/artificial-intelligence-tutorial/ai-vs-machine-learning-vs-deep-learning\n",
        "\n",
        "\n",
        "Pour d'autres travaux pratiques du Deep Learning Indaba, veuillez visiter [ici](https://github.com/deep-learning-indaba/indaba-pracs-2023)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o1ndpYE50BpG"
      },
      "source": [
        "## Feedback\n",
        "\n",
        "<!--Please provide feedback that we can use to improve our practicals in the future.-->\n",
        "Veuillez fournir des commentaires que nous pouvons utiliser pour améliorer nos travaux pratiques à l'avenir."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bMk4EcMcUUPd"
      },
      "outputs": [],
      "source": [
        "# @title Générer un formulaire de commentaires. (Run Cell)\n",
        "from IPython.display import HTML\n",
        "\n",
        "HTML(\n",
        "    \"\"\"\n",
        "<iframe\n",
        "\tsrc=\"https://forms.gle/Cg9aoa7czoZCYqxF7\",\n",
        "  width=\"80%\"\n",
        "\theight=\"1200px\" >\n",
        "\tLoading...\n",
        "</iframe>\n",
        "\"\"\"\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oglV4kHMWnIN"
      },
      "source": [
        "<img src=\"https://baobab.deeplearningindaba.com/static/media/indaba-logo-dark.d5a6196d.png\" width=\"50%\" />"
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.8.5"
    },
    "vscode": {
      "interpreter": {
        "hash": "145833166d986a8417df3c7acb65d917d84b716b5a452e57fcacdc66f1a168c9"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}