IDLCV_Exercise_1_1_NNs.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IgdHnzSnzZs2"
      },
      "source": [
        "# # Exercise 1.1\n",
        "\n",
        "## Classification of MNIST digits with a fully-connected neural network\n",
        "\n",
        "In this exercise we will classify [MNIST digits](https://en.wikipedia.org/wiki/MNIST_database) using a fully-connected neural network\n",
        "\n",
        "We start by importing the modules that we need"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "n6YTUAAlzZs5"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from tqdm.notebook import tqdm\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torchvision.datasets as datasets\n",
        "from torch.utils.data import DataLoader\n",
        "import torchvision.transforms as transforms\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sOeRq_xHzZtC"
      },
      "source": [
        "We check that we have a GPU available"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "eRKroSgizZtC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8e3f661c-97d5-42a2-97c9-2d1873dba4ff"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The code will run on GPU.\n"
          ]
        }
      ],
      "source": [
        "if torch.cuda.is_available():\n",
        "    print(\"The code will run on GPU.\")\n",
        "else:\n",
        "    print(\"The code will run on CPU. Go to Edit->Notebook Settings and choose GPU as the hardware accelerator\")\n",
        "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hf5kG-RszZtG"
      },
      "source": [
        "The MNIST dataset is a built-in dataset in PyTorch (it is a very common dataset to test algorithms on).\n",
        "\n",
        "We import it, and set our minibatch size"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "lzZHxNsgzZtH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5e6be83a-1a6a-4af6-a74e-c67719d7f6d4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz to ./data/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 9912422/9912422 [00:01<00:00, 5970184.09it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/train-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz to ./data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 28881/28881 [00:00<00:00, 445157.06it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1648877/1648877 [00:00<00:00, 3991490.19it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 4542/4542 [00:00<00:00, 2382805.35it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "batch_size = 64\n",
        "trainset = datasets.MNIST('./data', train=True, download=True, transform=transforms.ToTensor())\n",
        "train_loader = DataLoader(trainset, batch_size=batch_size, shuffle=True, num_workers=1)\n",
        "testset = datasets.MNIST('./data', train=False, download=True, transform=transforms.ToTensor())\n",
        "test_loader = DataLoader(testset, batch_size=batch_size, shuffle=False, num_workers=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7xoF9GRL25jq"
      },
      "source": [
        "First, we plot the images to get an idea of what data we're working with. MNIST images are $28\\times28$ images of handwritten digits (0-9)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "mjeITqYf1itt",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "outputId": "259dcdf4-4569-4db3-acf8-dc780c7981e0"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2000x1000 with 21 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "images, labels = next(iter(train_loader))\n",
        "plt.figure(figsize=(20,10))\n",
        "\n",
        "for i in range(21):\n",
        "    plt.subplot(5,7,i+1)\n",
        "    plt.imshow(images[i].numpy()[0], 'gray')\n",
        "    plt.title(labels[i].item())\n",
        "    plt.axis('off')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hGuvRy0zzZtP"
      },
      "source": [
        "You should implement a fully-connected network to classify the digits. It should contain 1 hidden layer with 100 units. Don't forget the ReLU activation function after the hidden layer."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "kkWvoY__zZtQ"
      },
      "outputs": [],
      "source": [
        "class Network(nn.Module):\n",
        "    def __init__(self):\n",
        "        super(Network, self).__init__()\n",
        "        self.fully_connected1 = nn.Sequential(\n",
        "            nn.Linear(784, 200),\n",
        "            nn.ReLU()\n",
        "            )\n",
        "\n",
        "        self.fully_connected2 = nn.Sequential(\n",
        "            nn.Linear(200,10),\n",
        "            nn.Softmax(dim = 1)\n",
        "            )\n",
        "\n",
        "    def forward(self, x):\n",
        "      #reshaping x so it becomes flat, except for the first dimension (which is the minibatch)\n",
        "        x = x.view(x.size(0),-1)\n",
        "        x = self.fully_connected1(x)\n",
        "        x = self.fully_connected2(x)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_i2qWBsNzZtU"
      },
      "source": [
        "We instantiate a copy of our network and transfer it to the GPU if it's available"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "VJVToX8hzZtV"
      },
      "outputs": [],
      "source": [
        "model = Network()\n",
        "model.to(device)\n",
        "#Initialize the optimer\n",
        "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ky-KOYBA3i4R"
      },
      "source": [
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              "  0%|          | 0/5 [00:00<?, ?epoch/s]"
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            "Accuracy train: 96.6%\t test: 96.4%\n"
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        "num_epochs = 5\n",
        "\n",
        "for epoch in tqdm(range(num_epochs), unit='epoch'):\n",
        "    #For each epoch\n",
        "    train_correct = 0\n",
        "    for minibatch_no, (data, target) in tqdm(enumerate(train_loader), total=len(train_loader)):\n",
        "        data, target = data.to(device), target.to(device)\n",
        "        #Zero the gradients computed for each weight\n",
        "        optimizer.zero_grad()\n",
        "        #Forward pass your image through the network\n",
        "        output = model(data)\n",
        "        #Compute the loss\n",
        "        loss = F.nll_loss(torch.log(output), target)\n",
        "        #Backward pass through the network\n",
        "        loss.backward()\n",
        "        #Update the weights\n",
        "        optimizer.step()\n",
        "\n",
        "        #Compute how many were correctly classified\n",
        "        predicted = output.argmax(1)\n",
        "        train_correct += (target==predicted).sum().cpu().item()\n",
        "    #Comput the test accuracy\n",
        "    test_correct = 0\n",
        "    for data, target in test_loader:\n",
        "        data = data.to(device)\n",
        "        with torch.no_grad():\n",
        "            output = model(data)\n",
        "        predicted = output.argmax(1).cpu()\n",
        "        test_correct += (target==predicted).sum().item()\n",
        "    train_acc = train_correct/len(trainset)\n",
        "    test_acc = test_correct/len(testset)\n",
        "    print(\"Accuracy train: {train:.1f}%\\t test: {test:.1f}%\".format(test=100*test_acc, train=100*train_acc))"
      ]
    },
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        "You should now have a model that has about 96% accuracy on the test set.\n",
        "Try to get an even better accuracy. You can\n",
        "* Change the number of hidden layers\n",
        "* Change the number of units in the hidden layers\n",
        "* Try changing the learning rate by factors of 10. What happens if it is too high or too low?\n",
        "* Try using sigmoid instead of ReLU activation. What happens?\n",
        "\n",
        "How large accuracy can you get?\n",
        "\n",
        "Try showing the classification output (probabilities) from the model alongside the ground truth.\n",
        "\n",
        "* Which are classified correctly/incorrectly?\n",
        "* If it's incorrect, what is the second most likely class?\n",
        "* Do the misclassifications you see make sense? Why/why not?"
      ]
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