{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "hD9BWJyeDmio"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from tensorflow.keras.datasets import mnist\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(X_train, _), (_, _) = mnist.load_data()\n",
        "X_train = X_train.reshape(-1, 784) / 255.0\n",
        "X_train = (X_train > 0.5).astype(np.float32)"
      ],
      "metadata": {
        "id": "TSqsfNzrDnOx"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class RBM:\n",
        "    def __init__(self, n_visible, n_hidden, lr=0.01):\n",
        "        self.n_visible = n_visible\n",
        "        self.n_hidden = n_hidden\n",
        "        self.lr = lr\n",
        "        self.W = np.random.normal(0, 0.01, (n_visible, n_hidden))\n",
        "        self.bv = np.zeros(n_visible)\n",
        "        self.bh = np.zeros(n_hidden)\n",
        "\n",
        "    def sigmoid(self, x):\n",
        "        return 1 / (1 + np.exp(-x))\n",
        "\n",
        "    def sample_prob(self, probs):\n",
        "        return np.random.binomial(1, probs)\n",
        "\n",
        "    def forward(self, v):\n",
        "        h_prob = self.sigmoid(np.dot(v, self.W) + self.bh)\n",
        "        h_sample = self.sample_prob(h_prob)\n",
        "        return h_prob, h_sample\n",
        "\n",
        "    def backward(self, h):\n",
        "        v_prob = self.sigmoid(np.dot(h, self.W.T) + self.bv)\n",
        "        v_sample = self.sample_prob(v_prob)\n",
        "        return v_prob, v_sample\n",
        "\n",
        "    def train(self, X, epochs=10, batch_size=64):\n",
        "        n_samples = X.shape[0]\n",
        "        for epoch in range(epochs):\n",
        "            np.random.shuffle(X)\n",
        "            epoch_error = 0\n",
        "            for i in range(0, n_samples, batch_size):\n",
        "                v0 = X[i:i+batch_size]\n",
        "                h0_prob, h0 = self.forward(v0)\n",
        "                v1_prob, v1 = self.backward(h0)\n",
        "                h1_prob, _ = self.forward(v1)\n",
        "                self.W += self.lr * (np.dot(v0.T, h0_prob) - np.dot(v1.T, h1_prob)) / batch_size\n",
        "                self.bv += self.lr * np.mean(v0 - v1, axis=0)\n",
        "                self.bh += self.lr * np.mean(h0_prob - h1_prob, axis=0)\n",
        "                epoch_error += np.mean((v0 - v1) ** 2)\n",
        "            print(f\"Epoch {epoch+1}/{epochs}, Reconstruction Error: {epoch_error:.4f}\")"
      ],
      "metadata": {
        "id": "Xl4fHUBYDnRg"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "rbm = RBM(n_visible=784, n_hidden=256, lr=0.1)\n",
        "rbm.train(X_train, epochs=60, batch_size=128)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "collapsed": true,
        "id": "NX34UejwDnUg",
        "outputId": "897b01ac-7d22-4b27-8d5a-48e16b226ccf"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/60, Reconstruction Error: 50.7778\n",
            "Epoch 2/60, Reconstruction Error: 34.2624\n",
            "Epoch 3/60, Reconstruction Error: 29.6647\n",
            "Epoch 4/60, Reconstruction Error: 27.0522\n",
            "Epoch 5/60, Reconstruction Error: 25.2470\n",
            "Epoch 6/60, Reconstruction Error: 23.8840\n",
            "Epoch 7/60, Reconstruction Error: 22.7969\n",
            "Epoch 8/60, Reconstruction Error: 21.9367\n",
            "Epoch 9/60, Reconstruction Error: 21.1854\n",
            "Epoch 10/60, Reconstruction Error: 20.5688\n",
            "Epoch 11/60, Reconstruction Error: 20.0177\n",
            "Epoch 12/60, Reconstruction Error: 19.5278\n",
            "Epoch 13/60, Reconstruction Error: 19.0854\n",
            "Epoch 14/60, Reconstruction Error: 18.7511\n",
            "Epoch 15/60, Reconstruction Error: 18.3978\n",
            "Epoch 16/60, Reconstruction Error: 18.0871\n",
            "Epoch 17/60, Reconstruction Error: 17.8307\n",
            "Epoch 18/60, Reconstruction Error: 17.5827\n",
            "Epoch 19/60, Reconstruction Error: 17.3631\n",
            "Epoch 20/60, Reconstruction Error: 17.1510\n",
            "Epoch 21/60, Reconstruction Error: 16.9438\n",
            "Epoch 22/60, Reconstruction Error: 16.7869\n",
            "Epoch 23/60, Reconstruction Error: 16.6315\n",
            "Epoch 24/60, Reconstruction Error: 16.4813\n",
            "Epoch 25/60, Reconstruction Error: 16.3419\n",
            "Epoch 26/60, Reconstruction Error: 16.1979\n",
            "Epoch 27/60, Reconstruction Error: 16.0870\n",
            "Epoch 28/60, Reconstruction Error: 15.9579\n",
            "Epoch 29/60, Reconstruction Error: 15.8518\n",
            "Epoch 30/60, Reconstruction Error: 15.7397\n",
            "Epoch 31/60, Reconstruction Error: 15.6652\n",
            "Epoch 32/60, Reconstruction Error: 15.5647\n",
            "Epoch 33/60, Reconstruction Error: 15.4705\n",
            "Epoch 34/60, Reconstruction Error: 15.3722\n",
            "Epoch 35/60, Reconstruction Error: 15.2998\n",
            "Epoch 36/60, Reconstruction Error: 15.2197\n",
            "Epoch 37/60, Reconstruction Error: 15.1477\n",
            "Epoch 38/60, Reconstruction Error: 15.0694\n",
            "Epoch 39/60, Reconstruction Error: 14.9979\n",
            "Epoch 40/60, Reconstruction Error: 14.9407\n",
            "Epoch 41/60, Reconstruction Error: 14.9027\n",
            "Epoch 42/60, Reconstruction Error: 14.8197\n",
            "Epoch 43/60, Reconstruction Error: 14.7481\n",
            "Epoch 44/60, Reconstruction Error: 14.6960\n",
            "Epoch 45/60, Reconstruction Error: 14.6505\n",
            "Epoch 46/60, Reconstruction Error: 14.5926\n",
            "Epoch 47/60, Reconstruction Error: 14.5419\n",
            "Epoch 48/60, Reconstruction Error: 14.5012\n",
            "Epoch 49/60, Reconstruction Error: 14.4494\n",
            "Epoch 50/60, Reconstruction Error: 14.3994\n",
            "Epoch 51/60, Reconstruction Error: 14.3694\n",
            "Epoch 52/60, Reconstruction Error: 14.3164\n",
            "Epoch 53/60, Reconstruction Error: 14.2764\n",
            "Epoch 54/60, Reconstruction Error: 14.2339\n",
            "Epoch 55/60, Reconstruction Error: 14.2021\n",
            "Epoch 56/60, Reconstruction Error: 14.1647\n",
            "Epoch 57/60, Reconstruction Error: 14.1274\n",
            "Epoch 58/60, Reconstruction Error: 14.0711\n",
            "Epoch 59/60, Reconstruction Error: 14.0677\n",
            "Epoch 60/60, Reconstruction Error: 14.0242\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_reconstruction(rbm, X, n=10):\n",
        "    v = X[:n]\n",
        "    _, h = rbm.forward(v)\n",
        "    v_recon, _ = rbm.backward(h)\n",
        "    plt.figure(figsize=(10, 4))\n",
        "    for i in range(n):\n",
        "        plt.subplot(2, n, i+1)\n",
        "        plt.imshow(v[i].reshape(28,28), cmap='gray')\n",
        "        plt.axis('off')\n",
        "        plt.subplot(2, n, i+n+1)\n",
        "        plt.imshow(v_recon[i].reshape(28,28), cmap='gray')\n",
        "        plt.axis('off')\n",
        "    plt.show()\n",
        "\n",
        "plot_reconstruction(rbm, X_train)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "id": "MIL2BVMaDnYp",
        "outputId": "a8df1e1a-f647-42b4-afd1-5d50f14203b7"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x400 with 20 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def generate_samples(rbm, steps=5000, n_samples=10):\n",
        "    v = np.random.binomial(1, 0.5, (n_samples, rbm.n_visible))\n",
        "    for _ in range(steps):\n",
        "        _, h = rbm.forward(v)\n",
        "        _, v = rbm.backward(h)\n",
        "    plt.figure(figsize=(10,2))\n",
        "    for i in range(n_samples):\n",
        "        plt.subplot(1, n_samples, i+1)\n",
        "        plt.imshow(v[i].reshape(28,28), cmap='gray')\n",
        "        plt.axis('off')\n",
        "    plt.show()\n",
        "\n",
        "generate_samples(rbm)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "id": "N1JdwR8WD8tD",
        "outputId": "1fccaaa3-8a85-480b-8d88-d93bea744a5a"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x200 with 10 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "iAy0_HhfD8v4"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "RvRS2qy-D8zJ"
      },
      "execution_count": 6,
      "outputs": []
    }
  ]
}