neural_network/CNN_Pytorch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wq_TKqjUmILg"
   },
   "source": [
    "# Convolutional Neural Network (CNN)\n",
    "\n",
    "## Resources\n",
    "\n",
    "    CNN : https://en.wikipedia.org/wiki/Convolutional_neural_network\n",
    "    Pytorch : https://pytorch.org/tutorials/beginner/basics/intro.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start by importing both the training and testing MNIST datasets using DataLoaders and the torchvision provided datasets. You can set both the training and testing batch size to be whatever you feel is best."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "qGEvJYHnmILh"
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torchvision import datasets, transforms\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from torch.utils.data.dataloader import DataLoader\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437,
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    },
    "id": "N_61-p6ymILj",
    "outputId": "765b9e09-2ce2-47ab-eac2-6978fa820170"
   },
   "outputs": [],
   "source": [
    "# Downloading MNIST dataset from Pytorch\n",
    "dataset = datasets.MNIST(\n",
    "    root=\"./data\",\n",
    "    download=True,\n",
    "    train=True,\n",
    "    transform=transforms.ToTensor(),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "UlRAhZOpmILk"
   },
   "outputs": [],
   "source": [
    "# Splitting the dataset into training and testing set\n",
    "train_dataset, test_dataset = torch.utils.data.random_split(dataset, [50000, 10000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 332
    },
    "id": "iQWzZCRFmILl",
    "outputId": "d2992c28-d667-4653-bbc2-9b323c82def0"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.8/site-packages/torchvision/datasets/mnist.py:52: UserWarning: train_labels has been renamed targets\n",
      "  warnings.warn(\"train_labels has been renamed targets\")\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Label : 3')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing a sample from dataset\n",
    "plt.imshow(train_dataset.dataset.data[10])\n",
    "plt.title(\"Label : \" + str(train_dataset.dataset.train_labels[10].item()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "9WhgIZF0mILl"
   },
   "outputs": [],
   "source": [
    "# Creating a DataLoader for training and testing\n",
    "train = DataLoader(train_dataset, batch_size=32, shuffle=True)\n",
    "test = DataLoader(test_dataset, batch_size=1, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pWhZXmm6mILm"
   },
   "source": [
    "Define a network with the following architecture:\n",
    "\n",
    "Conv2d (input channels=1, output channels = 15,kernel size = 5)\n",
    "$\\rightarrow$\n",
    "MaxPool (kernel size = 2)\n",
    "$\\rightarrow$\n",
    "ReLU\n",
    "$\\rightarrow$\n",
    "Conv2d (input channels=15, output channels = 30,kernel size = 5)\n",
    "$\\rightarrow$\n",
    "Dropout2d (p = 0.5)\n",
    "$\\rightarrow$\n",
    "MaxPool (kernel size = 2)\n",
    "$\\rightarrow$\n",
    "ReLU\n",
    "$\\rightarrow$\n",
    "Linear(input dimension = 480, hidden units = 64)\n",
    "$\\rightarrow$\n",
    "ReLU\n",
    "$\\rightarrow$\n",
    "Dropout (p=0.5)\n",
    "$\\rightarrow$\n",
    "Linear(input dimension = 64, hidden units = 10)\n",
    "$\\rightarrow$\n",
    "LogSoftMax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "_-RTFbeKmILn"
   },
   "outputs": [],
   "source": [
    "class CNN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.cnn = nn.Sequential(\n",
    "            nn.Conv2d(1, 15, kernel_size=5),\n",
    "            nn.MaxPool2d(2, 2),\n",
    "            nn.ReLU(),\n",
    "            nn.Conv2d(15, 30, kernel_size=5),\n",
    "            nn.Dropout2d(0.5),\n",
    "            nn.MaxPool2d(2, 2),\n",
    "            nn.ReLU(),\n",
    "            nn.Flatten(),\n",
    "            nn.Linear(480, 64),\n",
    "            nn.ReLU(),\n",
    "            nn.Dropout(0.5),\n",
    "            nn.Linear(64, 10),\n",
    "            nn.LogSoftmax(dim=1),\n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.cnn(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jzwFIYidmILo"
   },
   "source": [
    "Train the network you defined in the previous question on MNIST, using the optimizer and the number of training epochs you deem appropriate. Use a cross-entropy loss. Each epoch test your model on the testing dataset and print the value of the accuracy that you achieve. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "-hdIBNSzmILp",
    "outputId": "101815c2-c1c6-441b-bd05-ce08b702c044"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.8/site-packages/torch/nn/functional.py:718: UserWarning: Named tensors and all their associated APIs are an experimental feature and subject to change. Please do not use them for anything important until they are released as stable. (Triggered internally at  ../c10/core/TensorImpl.h:1156.)\n",
      "  return torch.max_pool2d(input, kernel_size, stride, padding, dilation, ceil_mode)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch :0 Loss : 0.44618519723548844 Train Accuracy:0.8599048256874084 Test Accuracy : 0.9340000152587891\n",
      "Epoch :1 Loss : 0.20212347584169404 Train Accuracy:0.9430182576179504 Test Accuracy : 0.9490000009536743\n",
      "Epoch :2 Loss : 0.16394136824853056 Train Accuracy:0.952215313911438 Test Accuracy : 0.9531000256538391\n",
      "Epoch :3 Loss : 0.14257464571382256 Train Accuracy:0.9595929384231567 Test Accuracy : 0.9588000178337097\n",
      "Epoch :4 Loss : 0.12598471959617277 Train Accuracy:0.9644113779067993 Test Accuracy : 0.9648000001907349\n",
      "Epoch :5 Loss : 0.11733871379403024 Train Accuracy:0.9659308791160583 Test Accuracy : 0.9660000205039978\n",
      "Epoch :6 Loss : 0.11000267015220401 Train Accuracy:0.9681901931762695 Test Accuracy : 0.9664999842643738\n",
      "Epoch :7 Loss : 0.10582590816269605 Train Accuracy:0.9684301018714905 Test Accuracy : 0.9631999731063843\n",
      "Epoch :8 Loss : 0.09624670598793283 Train Accuracy:0.9711892008781433 Test Accuracy : 0.9706000089645386\n",
      "Epoch :9 Loss : 0.09422491162643551 Train Accuracy:0.9726687669754028 Test Accuracy : 0.9679999947547913\n"
     ]
    }
   ],
   "source": [
    "batch_size = 32\n",
    "\n",
    "model = CNN()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.001)\n",
    "\n",
    "# Running the model on GPU if available\n",
    "## Refer pytorch documentation for more details about copying model and data onto the device\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "model.to(device)\n",
    "\n",
    "cost = []\n",
    "epochs = 10\n",
    "\n",
    "# Training the model\n",
    "for epoch in range(epochs):\n",
    "\n",
    "    loss_epoch = []\n",
    "    train_acc = []\n",
    "\n",
    "    for x, y in train:\n",
    "\n",
    "        # Predicting the output\n",
    "        y_pred = model(x.to(device))\n",
    "\n",
    "        # Converting the predicted output from one hot encoding to a single number\n",
    "        _, t_preds = torch.max(y_pred, dim=1)\n",
    "\n",
    "        # Calculating the training accuracy\n",
    "        train_acc.append(\n",
    "            torch.tensor(torch.sum(t_preds == y.to(device)).item() / len(t_preds))\n",
    "        )\n",
    "\n",
    "        # Calculating the loss\n",
    "        loss = F.cross_entropy(y_pred, y.type(torch.LongTensor).to(device))\n",
    "\n",
    "        # Backpropagation\n",
    "\n",
    "        # Zeroing the gradients\n",
    "        optimizer.zero_grad()\n",
    "\n",
    "        # Calculating the gradients\n",
    "        loss.backward()\n",
    "\n",
    "        # Updating the weights\n",
    "        optimizer.step()\n",
    "\n",
    "        # Appending the loss of each batch to the epoch loss\n",
    "        loss_epoch.append(loss.item())\n",
    "\n",
    "    # Calculating test accuracy\n",
    "    with torch.no_grad():\n",
    "        if epoch % 1 == 0:\n",
    "            test_acc = []\n",
    "            for x, y in test:\n",
    "                y_pred = model(x.to(device))\n",
    "                _, t_preds = torch.max(y_pred, dim=1)\n",
    "                test_acc.append(\n",
    "                    torch.tensor(\n",
    "                        torch.sum(t_preds == y.to(device)).item() / len(t_preds)\n",
    "                    )\n",
    "                )\n",
    "\n",
    "            print(\n",
    "                \"Epoch :{} Loss : {} Train Accuracy:{} Test Accuracy : {}\".format(\n",
    "                    epoch,\n",
    "                    sum(loss_epoch) / len(loss_epoch),\n",
    "                    sum(train_acc) / len(train_acc),\n",
    "                    sum(test_acc) / len(test_acc),\n",
    "                )\n",
    "            )\n",
    "\n",
    "    cost.append(sum(loss_epoch) / len(loss_epoch))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 337
    },
    "id": "J7ecIEspmILq",
    "outputId": "5ec70ca4-45b0-4cf3-fedc-4f57daf7a8fa"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa94052aa00>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Plotting the cost vs epochs\n",
    "fig, ax = plt.subplots(figsize=(15, 5))\n",
    "plt.plot(np.array(cost))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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