foundations/02_Intermediate/pytorch_cnn.ipynb

{
 "cells": [
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   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Basics of PyTorch - Convolutional Neural Networks (CNNs)\n",
    "### Date: 02/22/2025\n",
    "### by Malik N. Mohammed\n",
    "\n",
    "## Objectives\n",
    "- Build and train CNNs\n",
    "- Understand layers in the CNNs\n",
    "- Deep dive into each layer\n",
    "\n",
    "\n",
    "![Convolutional Neural Network](https://media.datacamp.com/legacy/v1700043905/image10_f8b261ebf1.png)\n",
    "\n",
    "*Image source: [An Introduction to Convolutional Neural Networks (CNNs)](https://media.datacamp.com/legacy/v1700043905/image10_f8b261ebf1.png)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b0297d5e-b561-4ef5-abde-a94c7000a9b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torchvision import datasets\n",
    "from torchvision.transforms import ToTensor\n",
    "from torch import nn\n",
    "from torch.utils.data import DataLoader\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0e60f95b-aaa6-493f-a3f2-a6eae0adc259",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.backends.cudnn.enabled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "969b572c-b2f6-49f6-896e-28d109304d2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "device(type='cuda')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the device\n",
    "device = torch.accelerator.current_accelerator() if torch.accelerator.is_available() else 'cpu'\n",
    "\n",
    "device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1aa751ab-bfd4-4169-86a7-80cdfe16a110",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_tensor(image, axes=None, size=None, cmap=None):\n",
    "\n",
    "    if size:\n",
    "        image = torch.reshape(image, size)\n",
    "\n",
    "    if axes:\n",
    "        axes.imshow(image, cmap=cmap)\n",
    "        axes.axis('off')\n",
    "    else:\n",
    "        plt.imshow(image, cmap=cmap)\n",
    "        plt.axis('off')\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "07713da2-2935-4ffb-9dd8-af329ba240d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 10000)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the training data for MNIST.\n",
    "training_data = datasets.MNIST(\n",
    "    'data',\n",
    "    train=True,\n",
    "    download=True,\n",
    "    transform=ToTensor(),\n",
    ")\n",
    "\n",
    "# Get the test data for MNIST.\n",
    "test_data = datasets.MNIST(\n",
    "    'data',\n",
    "    train=False,\n",
    "    download=True,\n",
    "    transform=ToTensor()\n",
    ")\n",
    "\n",
    "len(training_data), len(test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "351fea7d-a1ed-46f5-b9c3-a4657ec504b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training batches: 938\n",
      "Number of testing batches: 157\n"
     ]
    }
   ],
   "source": [
    "# Set the batch size.\n",
    "batch_size = 64\n",
    "\n",
    "# Get the dataloaders for training and test datasets.\n",
    "train_loader = DataLoader(training_data, shuffle=True, batch_size=batch_size)\n",
    "test_loader = DataLoader(test_data, shuffle=True, batch_size=batch_size)\n",
    "\n",
    "\n",
    "print(f'Number of training batches: {len(train_loader)}') # ceil(len(training_data) / batch_size)\n",
    "print(f'Number of testing batches: {len(test_loader)}') # ceil(len(test_data) / batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ce2005cf-624f-4076-8909-0f863825c7b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28, 28])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_data[0][0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4da9db1e-beee-40d9-b65a-c43742c8f4e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets build the Convolutional Neural Network.\n",
    "class ConvolutionalNN(nn.Module):\n",
    "\n",
    "    def __init__(self):\n",
    "        \"\"\"\n",
    "        Initialize the CNN model with:\n",
    "            1. Convolution Layers\n",
    "            2. Batch Normalization\n",
    "            3. Max pooling layers\n",
    "            4. LeakyReLU, and\n",
    "            5. Linear layers\n",
    "        \"\"\"\n",
    "        \n",
    "        super().__init__()\n",
    "        self.conv1 = nn.Conv2d(in_channels=1, out_channels=16, stride=2, kernel_size=(5,  5))\n",
    "        self.maxpool = nn.MaxPool2d(kernel_size=(2, 2), stride=1)\n",
    "        self.bn1 = nn.BatchNorm2d(16)\n",
    "        self.relu = nn.LeakyReLU()\n",
    "        self.conv2 = nn.Conv2d(in_channels=16, out_channels=64, stride=2, kernel_size=(5, 5))\n",
    "        self.bn2 = nn.BatchNorm2d(64)\n",
    "        self.linear1 = nn.Linear(64 * 3 * 3, 256)\n",
    "        self.bn3 = nn.BatchNorm1d(256)\n",
    "        self.linear2 = nn.Linear(256, 128)\n",
    "        self.bn4 = nn.BatchNorm1d(128)\n",
    "        self.linear3 = nn.Linear(128, 10)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.relu(self.bn1(self.conv1(x)))\n",
    "        x = self.maxpool(x)\n",
    "        x = self.relu(self.bn2(self.conv2(x)))\n",
    "        x = self.maxpool(x)\n",
    "        x = torch.flatten(x, 1)\n",
    "        x = self.relu(self.linear1(x))\n",
    "        x = self.bn3(x)\n",
    "        x = self.relu(self.linear2(x))\n",
    "        x = self.bn4(x)\n",
    "        logits = self.relu(self.linear3(x))\n",
    "        \n",
    "        return logits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "938cecee-f686-4bd9-9fd2-9581b66f6a77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------------------------------------\n",
      "        Layer (type)               Output Shape         Param #\n",
      "================================================================\n",
      "            Conv2d-1           [-1, 16, 12, 12]             416\n",
      "       BatchNorm2d-2           [-1, 16, 12, 12]              32\n",
      "         LeakyReLU-3           [-1, 16, 12, 12]               0\n",
      "         MaxPool2d-4           [-1, 16, 11, 11]               0\n",
      "            Conv2d-5             [-1, 64, 4, 4]          25,664\n",
      "       BatchNorm2d-6             [-1, 64, 4, 4]             128\n",
      "         LeakyReLU-7             [-1, 64, 4, 4]               0\n",
      "         MaxPool2d-8             [-1, 64, 3, 3]               0\n",
      "            Linear-9                  [-1, 256]         147,712\n",
      "        LeakyReLU-10                  [-1, 256]               0\n",
      "      BatchNorm1d-11                  [-1, 256]             512\n",
      "           Linear-12                  [-1, 128]          32,896\n",
      "        LeakyReLU-13                  [-1, 128]               0\n",
      "      BatchNorm1d-14                  [-1, 128]             256\n",
      "           Linear-15                   [-1, 10]           1,290\n",
      "        LeakyReLU-16                   [-1, 10]               0\n",
      "================================================================\n",
      "Total params: 208,906\n",
      "Trainable params: 208,906\n",
      "Non-trainable params: 0\n",
      "----------------------------------------------------------------\n",
      "Input size (MB): 0.00\n",
      "Forward/backward pass size (MB): 0.10\n",
      "Params size (MB): 0.80\n",
      "Estimated Total Size (MB): 0.90\n",
      "----------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "from torchsummary import summary\n",
    "\n",
    "# Instantiate the model and move to device and print the summary.\n",
    "model = ConvolutionalNN().to(device)\n",
    "summary(model, (1, 28, 28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "10f63c94-73b9-4974-98cb-9fa0009a6f35",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_loop(dataloader, model, loss_fn, optimizer):\n",
    "    \"\"\"\n",
    "    Define the training loop.\n",
    "    \"\"\"\n",
    "\n",
    "    # Set the model in training mode.\n",
    "    model.train()\n",
    "    for batch, (X, y) in enumerate(dataloader):\n",
    "\n",
    "        # Get the input and labels and move to device.\n",
    "        X, y = X.to(device), y.to(device)\n",
    "\n",
    "        # Make predictions\n",
    "        pred = model(X)\n",
    "\n",
    "        # Compute the loss.\n",
    "        loss = loss_fn(pred, y)\n",
    "\n",
    "        # Perfom backward propagation.\n",
    "        loss.backward()\n",
    "\n",
    "        # Update the model parameters with the updated weights.\n",
    "        optimizer.step()\n",
    "\n",
    "        # Reset the gradients.\n",
    "        optimizer.zero_grad()\n",
    "\n",
    "\n",
    "        # Print the loss.\n",
    "        if batch % 64 == 63:\n",
    "            print(f\"Loss: {loss.item()}.  Current: {batch * batch_size}/{len(dataloader.dataset)}\")\n",
    "\n",
    "    print(\"Done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "862cb793-85ba-4ebc-a174-368f889fe020",
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_loop(dataloader, model, loss_fn):\n",
    "    \"\"\"\n",
    "    Define the test loop.\n",
    "    \"\"\"\n",
    "\n",
    "    # Set the model in evaluation mode.\n",
    "    model.eval()\n",
    "\n",
    "    correct = 0\n",
    "    total_loss = 0.0\n",
    "    for X, y in dataloader:\n",
    "        X, y = X.to(device), y.to(device)\n",
    "\n",
    "        # Disable gradient tracking.\n",
    "        with torch.no_grad():\n",
    "            pred = model(X)\n",
    "            loss = loss_fn(pred, y)\n",
    "\n",
    "            # Compute the correct predictions.\n",
    "            correct += (torch.argmax(pred, dim=1) == y).sum().item()\n",
    "\n",
    "            # Add to the total loss.\n",
    "            total_loss += loss.item()\n",
    "\n",
    "    avg_loss = total_loss / (len(dataloader) * batch_size)\n",
    "\n",
    "    # Print the accuracy.\n",
    "    print(f\"Average Loss: {avg_loss:>.8f}, Accuracy: {100*correct/len(dataloader.dataset)}%\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "05844dfd-ec70-46bf-9beb-d03dc7ff452d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGD (\n",
       "Parameter Group 0\n",
       "    dampening: 0\n",
       "    differentiable: False\n",
       "    foreach: None\n",
       "    fused: None\n",
       "    lr: 0.05\n",
       "    maximize: False\n",
       "    momentum: 0\n",
       "    nesterov: False\n",
       "    weight_decay: 0\n",
       ")"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initialize the loss function, and optimizer.\n",
    "learning_rate = 0.05\n",
    "\n",
    "loss_fn = nn.CrossEntropyLoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)\n",
    "optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1d4a2dcd-9361-40e0-96a6-c90f86c74532",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1:\n",
      "Loss: 0.1769426316022873.  Current: 4032/60000\n",
      "Loss: 0.18626275658607483.  Current: 8128/60000\n",
      "Loss: 0.08170099556446075.  Current: 12224/60000\n",
      "Loss: 0.08379678428173065.  Current: 16320/60000\n",
      "Loss: 0.17252153158187866.  Current: 20416/60000\n",
      "Loss: 0.1402389407157898.  Current: 24512/60000\n",
      "Loss: 0.07699812203645706.  Current: 28608/60000\n",
      "Loss: 0.10723704099655151.  Current: 32704/60000\n",
      "Loss: 0.1224956139922142.  Current: 36800/60000\n",
      "Loss: 0.04031235724687576.  Current: 40896/60000\n",
      "Loss: 0.02244812250137329.  Current: 44992/60000\n",
      "Loss: 0.030163556337356567.  Current: 49088/60000\n",
      "Loss: 0.11711115390062332.  Current: 53184/60000\n",
      "Loss: 0.040313296020030975.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00070634, Accuracy: 98.65%\n",
      "=========\n",
      "Epoch 2:\n",
      "Loss: 0.02336859703063965.  Current: 4032/60000\n",
      "Loss: 0.01881936378777027.  Current: 8128/60000\n",
      "Loss: 0.01624634675681591.  Current: 12224/60000\n",
      "Loss: 0.04149604216217995.  Current: 16320/60000\n",
      "Loss: 0.09228809922933578.  Current: 20416/60000\n",
      "Loss: 0.1138325035572052.  Current: 24512/60000\n",
      "Loss: 0.04926512390375137.  Current: 28608/60000\n",
      "Loss: 0.012557308189570904.  Current: 32704/60000\n",
      "Loss: 0.045757170766592026.  Current: 36800/60000\n",
      "Loss: 0.012029441073536873.  Current: 40896/60000\n",
      "Loss: 0.023237142711877823.  Current: 44992/60000\n",
      "Loss: 0.012106086127460003.  Current: 49088/60000\n",
      "Loss: 0.029018208384513855.  Current: 53184/60000\n",
      "Loss: 0.04590524360537529.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00062832, Accuracy: 98.8%\n",
      "=========\n",
      "Epoch 3:\n",
      "Loss: 0.006652869749814272.  Current: 4032/60000\n",
      "Loss: 0.08422740548849106.  Current: 8128/60000\n",
      "Loss: 0.004882033448666334.  Current: 12224/60000\n",
      "Loss: 0.005373609252274036.  Current: 16320/60000\n",
      "Loss: 0.00653875432908535.  Current: 20416/60000\n",
      "Loss: 0.022139819338917732.  Current: 24512/60000\n",
      "Loss: 0.012273832224309444.  Current: 28608/60000\n",
      "Loss: 0.025449378415942192.  Current: 32704/60000\n",
      "Loss: 0.01603904739022255.  Current: 36800/60000\n",
      "Loss: 0.03693719580769539.  Current: 40896/60000\n",
      "Loss: 0.02540045604109764.  Current: 44992/60000\n",
      "Loss: 0.01647198386490345.  Current: 49088/60000\n",
      "Loss: 0.0610705129802227.  Current: 53184/60000\n",
      "Loss: 0.021100740879774094.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00068608, Accuracy: 98.67%\n",
      "=========\n",
      "Epoch 4:\n",
      "Loss: 0.0033214115537703037.  Current: 4032/60000\n",
      "Loss: 0.023244410753250122.  Current: 8128/60000\n",
      "Loss: 0.00988948717713356.  Current: 12224/60000\n",
      "Loss: 0.00721649918705225.  Current: 16320/60000\n",
      "Loss: 0.008124185726046562.  Current: 20416/60000\n",
      "Loss: 0.005461432971060276.  Current: 24512/60000\n",
      "Loss: 0.09701761603355408.  Current: 28608/60000\n",
      "Loss: 0.035062115639448166.  Current: 32704/60000\n",
      "Loss: 0.09527350962162018.  Current: 36800/60000\n",
      "Loss: 0.011409969069063663.  Current: 40896/60000\n",
      "Loss: 0.001518746605142951.  Current: 44992/60000\n",
      "Loss: 0.014118844643235207.  Current: 49088/60000\n",
      "Loss: 0.03702551871538162.  Current: 53184/60000\n",
      "Loss: 0.01942933164536953.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00049630, Accuracy: 99.03%\n",
      "=========\n",
      "Epoch 5:\n",
      "Loss: 0.0076421936973929405.  Current: 4032/60000\n",
      "Loss: 0.019913597032427788.  Current: 8128/60000\n",
      "Loss: 0.004327340517193079.  Current: 12224/60000\n",
      "Loss: 0.005988575518131256.  Current: 16320/60000\n",
      "Loss: 0.04171706363558769.  Current: 20416/60000\n",
      "Loss: 0.002248138887807727.  Current: 24512/60000\n",
      "Loss: 0.010110623203217983.  Current: 28608/60000\n",
      "Loss: 0.001411470933817327.  Current: 32704/60000\n",
      "Loss: 0.0025157106574624777.  Current: 36800/60000\n",
      "Loss: 0.010537663474678993.  Current: 40896/60000\n",
      "Loss: 0.013231804594397545.  Current: 44992/60000\n",
      "Loss: 0.04055314138531685.  Current: 49088/60000\n",
      "Loss: 0.010136566124856472.  Current: 53184/60000\n",
      "Loss: 0.05637117102742195.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00045102, Accuracy: 99.17%\n",
      "=========\n",
      "Epoch 6:\n",
      "Loss: 0.0005198753788135946.  Current: 4032/60000\n",
      "Loss: 0.0008072713389992714.  Current: 8128/60000\n",
      "Loss: 0.01344691775739193.  Current: 12224/60000\n",
      "Loss: 0.012442420236766338.  Current: 16320/60000\n",
      "Loss: 0.032818760722875595.  Current: 20416/60000\n",
      "Loss: 0.02034093625843525.  Current: 24512/60000\n",
      "Loss: 0.050087448209524155.  Current: 28608/60000\n",
      "Loss: 0.001609618659131229.  Current: 32704/60000\n",
      "Loss: 0.007246875204145908.  Current: 36800/60000\n",
      "Loss: 0.00402261083945632.  Current: 40896/60000\n",
      "Loss: 0.007635957095772028.  Current: 44992/60000\n",
      "Loss: 0.002326701069250703.  Current: 49088/60000\n",
      "Loss: 0.001986436080187559.  Current: 53184/60000\n",
      "Loss: 0.005829004570841789.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00079091, Accuracy: 98.49%\n",
      "=========\n",
      "Epoch 7:\n",
      "Loss: 0.002594569930806756.  Current: 4032/60000\n",
      "Loss: 0.0035098474472761154.  Current: 8128/60000\n",
      "Loss: 0.003332257503643632.  Current: 12224/60000\n",
      "Loss: 0.007904964499175549.  Current: 16320/60000\n",
      "Loss: 0.005527996923774481.  Current: 20416/60000\n",
      "Loss: 0.00308916624635458.  Current: 24512/60000\n",
      "Loss: 0.15297573804855347.  Current: 28608/60000\n",
      "Loss: 0.000930069072637707.  Current: 32704/60000\n",
      "Loss: 0.001500538783147931.  Current: 36800/60000\n",
      "Loss: 0.0019475541776046157.  Current: 40896/60000\n",
      "Loss: 0.030944911763072014.  Current: 44992/60000\n",
      "Loss: 0.0018028123304247856.  Current: 49088/60000\n",
      "Loss: 0.005440311506390572.  Current: 53184/60000\n",
      "Loss: 0.010909250006079674.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00058643, Accuracy: 98.9%\n",
      "=========\n",
      "Epoch 8:\n",
      "Loss: 0.0029536995571106672.  Current: 4032/60000\n",
      "Loss: 0.00447015929967165.  Current: 8128/60000\n",
      "Loss: 0.016484109684824944.  Current: 12224/60000\n",
      "Loss: 0.0038551711477339268.  Current: 16320/60000\n",
      "Loss: 0.007230805233120918.  Current: 20416/60000\n",
      "Loss: 0.005824634339660406.  Current: 24512/60000\n",
      "Loss: 0.0042272391729056835.  Current: 28608/60000\n",
      "Loss: 0.03424232080578804.  Current: 32704/60000\n",
      "Loss: 0.006988720037043095.  Current: 36800/60000\n",
      "Loss: 0.009675886482000351.  Current: 40896/60000\n",
      "Loss: 0.000690857763402164.  Current: 44992/60000\n",
      "Loss: 0.0027122970204800367.  Current: 49088/60000\n",
      "Loss: 0.07306861877441406.  Current: 53184/60000\n",
      "Loss: 0.0010721557773649693.  Current: 57280/60000\n",
      "Done\n",
      "---\n",
      "Test metrics:\n",
      "Average Loss: 0.00051958, Accuracy: 98.94%\n",
      "=========\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(8):\n",
    "    print(f'Epoch {epoch + 1}:')\n",
    "    train_loop(train_loader, model, loss_fn, optimizer)\n",
    "    print('---')\n",
    "    print('Test metrics:')\n",
    "    test_loop(test_loader, model, loss_fn)\n",
    "    print(\"=========\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b30463b2-ac11-406f-9fd5-5257eb158f13",
   "metadata": {},
   "source": [
    "### Visualizing the output at each layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "17a5765b-1759-4c03-810c-e9654ee05278",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ConvolutionalNN(\n",
       "  (conv1): Conv2d(1, 16, kernel_size=(5, 5), stride=(2, 2))\n",
       "  (maxpool): MaxPool2d(kernel_size=(2, 2), stride=1, padding=0, dilation=1, ceil_mode=False)\n",
       "  (bn1): BatchNorm2d(16, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (relu): LeakyReLU(negative_slope=0.01)\n",
       "  (conv2): Conv2d(16, 64, kernel_size=(5, 5), stride=(2, 2))\n",
       "  (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (linear1): Linear(in_features=576, out_features=256, bias=True)\n",
       "  (bn3): BatchNorm1d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (linear2): Linear(in_features=256, out_features=128, bias=True)\n",
       "  (bn4): BatchNorm1d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (linear3): Linear(in_features=128, out_features=10, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set the model in evaluation mode.\n",
    "model.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1624494d-7c65-4a68-af8f-6bfbbb366b21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([64, 1, 28, 28]), torch.Size([64]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the test sample.\n",
    "test_sample = next(iter(test_loader))\n",
    "tx, ty = test_sample[0].to(device), test_sample[1].to(device)\n",
    "\n",
    "tx.shape, ty.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fb2ea01f-8628-4f1d-a58c-9ffb5f693711",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(5, device='cuda:0')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets analyze the network flow of this image.\n",
    "\n",
    "draw_tensor(tx[0].cpu(), cmap='gray', size=(28, 28))\n",
    "\n",
    "ty[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f09ebf3b-2c3a-43e0-af2c-55acfb3e79e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8610e809-6dd5-4ee6-af5a-5729ce57ec4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2080x200 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2080x200 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4160x200 with 32 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4160x200 with 32 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# In this section we print out the convoluted image, and downsampled image at each layer \n",
    "# of the CNNs that we defined up until the flatten layer.\n",
    "\n",
    "with torch.no_grad():\n",
    "    sample_image = tx[0].reshape(1, 1, 28, 28)\n",
    "    layers = []\n",
    "\n",
    "    x = model.relu(model.bn1(model.conv1(sample_image)))\n",
    "    \n",
    "    layers.append((x, 'ReLU(BN(Convolution(Image)))'))\n",
    "    x = model.maxpool(x)\n",
    "    layers.append((x, 'Max Pooling'))\n",
    "    x = model.relu(model.bn2(model.conv2(x)))\n",
    "    layers.append((x, 'ReLU(BN(Convolution(Feature_map)))'))\n",
    "    x = model.maxpool(x)\n",
    "    layers.append((x, 'Max Pooling'))\n",
    "\n",
    "    for i, (layer, label) in enumerate(layers):\n",
    "\n",
    "        size = layer.shape\n",
    "\n",
    "        if size[1] > 20:\n",
    "            layer = layer[:, :32, :, :]\n",
    "        channels = layer.shape[1]\n",
    "        # print(layer.shape)\n",
    "        fig, axes = plt.subplots(nrows=1, ncols=channels, figsize=(channels*1.3, 2))\n",
    "    \n",
    "        for i in range(layer.size()[1]):\n",
    "            draw_tensor(layer[0][i].cpu(), axes=axes[i], size=layer[0][i].shape, cmap='gray')\n",
    "\n",
    "            \n",
    "        fig.suptitle(f'{label} with {size[1]} channels and HxW: {size[2]}x{size[3]}', fontsize=24)\n",
    "\n",
    "        plt.tight_layout()\n",
    "        display(fig)\n",
    "        plt.close(fig)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c088145b-1809-45f2-a7dd-99a83263607b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Loss: 0.00052281, Accuracy: 98.94%\n"
     ]
    }
   ],
   "source": [
    "test_loop(test_loader, model, loss_fn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eaec4497-757b-4cc0-b298-a72acc8bb2f3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "machine-learning-malik",
   "language": "python",
   "name": "machine-learning-malik"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}