{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notebook entrainement d'une IA à résoudre le XOR\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/git/http%3A%2F%2Fgitea.louisgallet.fr%2FCours-particulier%2FNotebooks/master?urlpath=%2Fdoc%2Ftree%2FNotebook_IA_Training.ipynb)\n",
    "\n",
    "La table de veritée du XOR est la suivante:\n",
    "> x: entrée 1 ; y: entrée 2 ; r: sortie\n",
    "\n",
    "x = 0 ; y = 0 ; r = 0  \n",
    "x = 1 ; y = 0 ; r = 1  \n",
    "x = 0 ; y = 1 ; r = 1  \n",
    "x = 1 ; y = 1 ; r = 0  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "xwVyblbIKSYS",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "!pip install numpy\n",
    "!pip install matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "wgVHhV0zKeOV",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def sigmoid_derivative(x):\n",
    "    return x * (1 - x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "Bv03so9jKhZH",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "# Entrées et sorties du XOR\n",
    "X = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
    "y = np.array([[0],[1],[1],[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "-utexs_vKjws",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "# 2 neurones en entrée, 3 neurones cachés, 1 neurone en sortie\n",
    "w1 = np.random.randn(2, 4)\n",
    "b1 = np.zeros((1, 4))\n",
    "\n",
    "w2 = np.random.randn(4, 1)\n",
    "b2 = np.zeros((1, 1))\n",
    "\n",
    "# Pour enregistrer la perte au fil des époques\n",
    "loss_history = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "AGlpWtKdKmcZ",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.1\n",
    "epochs = 10000\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    # Forward pass\n",
    "    z1 = np.dot(X, w1) + b1\n",
    "    a1 = sigmoid(z1)\n",
    "\n",
    "    z2 = np.dot(a1, w2) + b2\n",
    "    a2 = sigmoid(z2)\n",
    "\n",
    "    # Calcul de l'erreur\n",
    "    loss = np.mean((y - a2) ** 2)\n",
    "    loss_history.append(loss)\n",
    "\n",
    "    # Backpropagation\n",
    "    d_a2 = (a2 - y)\n",
    "    d_z2 = d_a2 * sigmoid_derivative(a2)\n",
    "\n",
    "    d_w2 = np.dot(a1.T, d_z2)\n",
    "    d_b2 = np.sum(d_z2, axis=0, keepdims=True)\n",
    "\n",
    "    d_a1 = np.dot(d_z2, w2.T)\n",
    "    d_z1 = d_a1 * sigmoid_derivative(a1)\n",
    "\n",
    "    d_w1 = np.dot(X.T, d_z1)\n",
    "    d_b1 = np.sum(d_z1, axis=0, keepdims=True)\n",
    "\n",
    "    # Mise à jour des poids\n",
    "    w2 -= learning_rate * d_w2\n",
    "    b2 -= learning_rate * d_b2\n",
    "    w1 -= learning_rate * d_w1\n",
    "    b1 -= learning_rate * d_b1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 474
    },
    "id": "m60PeuYnKoie",
    "outputId": "d5e217cf-a0b9-49a8-a01b-d9575b7f797f",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "plt.plot(loss_history)\n",
    "plt.title(\"Perte d'erreurs au fil des époques\")\n",
    "plt.xlabel(\"Époques\")\n",
    "plt.ylabel(\"Taux d'erreur moyen\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "A2sN1_fHKrh8",
    "outputId": "fa906657-126c-4e13-cb6e-c6e7afd9bfd7",
    "trusted": true
   },
   "outputs": [],
   "source": [
    "print(\"Sortie finale après entraînement :\")\n",
    "a1 = sigmoid(np.dot(X, w1) + b1)\n",
    "a2 = sigmoid(np.dot(a1, w2) + b2)\n",
    "for i in range(4):\n",
    "    print(f\"Entrée : {X[i]} → Prédit : {a2[i][0]:.4f} → Arrondi : {round(a2[i][0])}\")"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}