Handwritten Digits Classifier - Explained.ipynb

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  "cells": [
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      "cell_type": "markdown",
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      "source": [
        "# Handwritten Digits Classifier\n",
        "Dataset: MNIST\n",
        "\n",
        "Model: LeNet-5\n",
        "\n",
        "This notebook contains helpful explainations (and some more code than the unexplained version) that help getting started in PyTorch. This also helps those who have started their Deep Learning journey.\n",
        "\n",
        "(Note how PyTorch uses \"minibatches\" and \"batches\" interchangeably. This holds true in the comments below.)\n",
        "\n",
        "### References:\n",
        "- [PyTorch Blitz](https://pytorch.org/tutorials/beginner/deep_learning_60min_blitz.html)\n",
        "- Official PyTorch Documentation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9KxRRY8380Z3"
      },
      "source": [
        "# Libraries\n",
        "Some packages are reimported to be able to refer to them more easily."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eSVI2guS80Z4"
      },
      "source": [
        "#Import libraries\n",
        "import torch #for tensors, GPU enabled.\n",
        "import torchvision #for Computer Vision\n",
        "import torchvision.transforms as transforms #for common image preprocessing. Inputs are PIL/Tensor image.\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import torch.nn as nn #for building NNs. Only supports inputs that are a mini-batch of samples, and not a single sample (In which case, use input.unsqueeze(0) to add a fake batch dimension)\n",
        "import torch.nn.functional as F #for common functions like ReLu, pooling, etc.\n",
        "import torch.optim as optim #a small package implementing various optimization algorithms. can use various different update rules such as SGD, Adam, etc."
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8bjkbpl980Z6"
      },
      "source": [
        "# Preparing the data\n",
        "In the MNIST dataset, each image has 1 channel (grayscale), is 28*28 pixels, and is accompanied with its target label.\n",
        "\n",
        "The train set has 60,000 images and the test set has 10,000 images.\n",
        "\n",
        "For other specifics, visit the [official website](http://yann.lecun.com/exdb/mnist/).\n",
        "\n",
        "You don't have to worry about navigating this page directly, as PyTorch has pre-loaded datasets.\n",
        "\n",
        "During the preprocessing, we resize to 32*32 px since the LeNet-5 architecture takes in images of those dimensions."
      ]
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        "id": "F4OpVD0h80aC",
        "outputId": "bc457102-9033-43c4-801b-b5ad76372965"
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      "source": [
        "#Prepare for preprocessing:\n",
        "transform = transforms.Compose([transforms.Resize(32), transforms.ToTensor(), transforms.Normalize((0.5), (0.5))])\n",
        "# ToTensor() converts a PIL Image or numpy.ndarray (H x W x C) to a torch.FloatTensor of shape (C x H x W), where C is the no. of channels\n",
        "# Normalize() takes parameters as the channel's mean and Standard Deviation. This is done so that each pixel is ensured the same Standard Normal data distribution, which makes convergence faster  \n",
        "\n",
        "#Load train dataset:\n",
        "trainset = torchvision.datasets.MNIST(root='~/.pytorch/MNIST_data/', train = True, download = True, transform = transform)  \n",
        "trainloader = torch.utils.data.DataLoader(trainset, batch_size=4, shuffle = True, num_workers = 2, drop_last = True) #Final iterable data that will be taken for training: shuffled in batches\n",
        "\n",
        "#Load test dataset:\n",
        "testset = torchvision.datasets.MNIST(root = '~/.pytorch/MNIST_data/', train = False, download = True, transform = transform)\n",
        "testloader = torch.utils.data.DataLoader(testset, batch_size=4, shuffle = False, num_workers=2, drop_last = True)\n",
        "\n",
        "classes = (\"Zero\", \"One\", \"Two\", \"Three\", \"Four\", \"Five\", \"Six\", \"Seven\", \"Eight\", \"Nine\") #Just labels, for our own printing use\n",
        "\n",
        "#Now, data is in the tensors trainset and testset as: no_of_images*2*1*32*32"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/train-images-idx3-ubyte.gz\n"
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          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/train-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ]
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          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/train-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ]
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        {
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          "metadata": {}
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/t10k-images-idx3-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
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        {
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              "version_major": 2
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting /root/.pytorch/MNIST_data/MNIST/raw/t10k-labels-idx1-ubyte.gz to /root/.pytorch/MNIST_data/MNIST/raw\n",
            "\n"
          ]
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NM0d8ujj80aF"
      },
      "source": [
        "## Peeking into the dataset\n",
        "View images in 1 minibatch."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 156
        },
        "id": "cxPUnj_I80aH",
        "outputId": "dfd6ee86-6d34-4ed7-a7fd-740523c4a61d"
      },
      "source": [
        "#Check how the image is loaded finally\n",
        "def imshow(img): #A function to plot image(s)\n",
        "  #we first undo some of the preprocessing to see how the actual image is\n",
        "  img = img/2 + 0.5 #un-normalize (remember the parameters we passed to Normalize for preprocessing)\n",
        "  npimg = img.numpy() #convert from Tensor back to numpy's ndarray (needed for the transpose() below)\n",
        "  plt.imshow(np.transpose(npimg, (1,2,0))) #to plot H vs W, the axes are thus specified\n",
        "  plt.show() \n",
        "  \n",
        "dataiter = iter(trainloader) #An iterator that enumerates over batches \n",
        "images, labels = dataiter.next() #A batch of 4 samples is loaded. Each sample is it's [image, label]. Since we are loading only 1 batch, we won't need a loop\n",
        "imshow(torchvision.utils.make_grid(images)) \n",
        "print(' '.join('%5s' % classes[labels[j]] for j in range(4) )) #Remember: List comprehensions are more efficient than explicit loops!"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " Zero  Zero  Nine  Zero\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m5MaQ1j780aI"
      },
      "source": [
        "# Defining the model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVv9fEGR80aJ"
      },
      "source": [
        "## The network class\n",
        "The layers and their parameters below are all taken from LeNet-5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "otzcbo-G80aM",
        "outputId": "2adca461-2fdf-474e-9548-459c505747b3"
      },
      "source": [
        "#A class to encapsulate the network architecture\n",
        "class Net(nn.Module): #Must inherit \"Module\", a base class for all NN modules\n",
        "  \n",
        "  def __init__(self): #constructor to define the network's layers.\n",
        "    super(Net, self).__init__() \n",
        "    self.conv1 = nn.Conv2d(1,6,5) #Valid convolution (no padding). Args: 1 input image channel, 6 output channels (/no. of filters), 5x5 square size of the convolving kernel.\n",
        "                                  #Striding assumed 1, bias is assumed added. Output is again the 4D Tensor - no.of.samples(batch size)*C*H*W\n",
        "    self.pool = nn.MaxPool2d(2,2) #Args: kernel size, stride\n",
        "    self.conv2 = nn.Conv2d(6,16,5) \n",
        "    self.fc1 = nn.Linear(16*5*5,120) #Args: input, output features. Bias set true. 16*5*5 = 400\n",
        "    self.fc2 = nn.Linear(120,84)\n",
        "    self.fc3 = nn.Linear(84,10) \n",
        "  \n",
        "  def forward(self, x): #Forward prop on x, the actual image vector \n",
        "    x = self.pool(F.relu(self.conv1(x))) \n",
        "    x = self.pool(F.relu(self.conv2(x)))\n",
        "    x = x.view(-1, 16*5*5) #reshaping\n",
        "    x = F.relu(self.fc1(x))\n",
        "    x = F.relu(self.fc2(x))\n",
        "    x = self.fc3(x) #The softmax activation isn't done here as combining it with loss calculations will make it more computationally efficient. Hence, this will automatically be taken care of by the loss criterion that we chose later\n",
        "    return x\n",
        "\n",
        "net = Net() \n",
        "\n",
        "#Just for info:\n",
        "print(net) \n",
        "params = list(net.parameters()) #shows the learnable parameters of our model\n",
        "print(len(params)) #no. of parameter tensors (arrays) = no.of.layers*2, as each layer has 1 Weight and 1 Bias array \n",
        "for s in range(len(params)): #show the actual no. of weights and biases for each layer\n",
        "  print(s, \":\", params[s].size()) #(W,b)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Net(\n",
            "  (conv1): Conv2d(1, 6, kernel_size=(5, 5), stride=(1, 1))\n",
            "  (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False)\n",
            "  (conv2): Conv2d(6, 16, kernel_size=(5, 5), stride=(1, 1))\n",
            "  (fc1): Linear(in_features=400, out_features=120, bias=True)\n",
            "  (fc2): Linear(in_features=120, out_features=84, bias=True)\n",
            "  (fc3): Linear(in_features=84, out_features=10, bias=True)\n",
            ")\n",
            "10\n",
            "0 : torch.Size([6, 1, 5, 5])\n",
            "1 : torch.Size([6])\n",
            "2 : torch.Size([16, 6, 5, 5])\n",
            "3 : torch.Size([16])\n",
            "4 : torch.Size([120, 400])\n",
            "5 : torch.Size([120])\n",
            "6 : torch.Size([84, 120])\n",
            "7 : torch.Size([84])\n",
            "8 : torch.Size([10, 84])\n",
            "9 : torch.Size([10])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eRwD9z1Z80aN"
      },
      "source": [
        "## The loss function and the update rule\n",
        "The negative log likelihood loss is apt for multi-class training.\n",
        "\n",
        "The SGD is a pretty introductory update rule, that a beginner may be familiar with. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6-Zs3OiN80aN"
      },
      "source": [
        "#Deciding the Loss function and Optimizer\n",
        "criterion = nn.CrossEntropyLoss()  #an optimizer object, that will hold the current state and will update the parameters by step() after gradients are computed by backward().\n",
        "# This criterion combines nn.LogSoftmax() (hence did not apply activn in the NN Model itself) and nn.NLLLoss() in one single class.\n",
        "# Input: raw, unnormalized scores for each class (i.e the final layer output of our model) of Tensor dims (minibatch, C classes), along with their Target labels.\n",
        "# FINAL output is the SCALAR cost (averaged over the minibatch)\n",
        "\n",
        "optimizer = optim.SGD(net.parameters(), lr = 0.001, momentum = 0.9)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H7900m1a80aO"
      },
      "source": [
        "# Training the model\n",
        "Loop over our data iterator, feeding the inputs to the network, and optimize."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4AAUSzI_80aO",
        "outputId": "1afdfa23-41a2-4463-c43a-6d3f194d83dd"
      },
      "source": [
        "x_minibatches=[] #x and y for plotting the training curve later\n",
        "y_loss=[]\n",
        "optimizer.zero_grad() #initializes gradients to 0\n",
        "running_loss = 0.0\n",
        "\n",
        "for epoch in range(3): \n",
        "  print(\"Epoch loss:\", running_loss/1000) #The inner loop runs 15k times, where the loss is reset every 2000th batch. This leaves space for 1000 batches' loss to be recorded, as statistics for every epoch.   \n",
        "  running_loss = 0.0\n",
        "  for i, data in enumerate(trainloader, 0): #as said before, the DataLoader enumerates over batches, so i is also the no. of minibatches\n",
        "     inputs, labels = data\n",
        "     optimizer.zero_grad() #Zero the existing gradient buffers of all parameters, else gradients will be accumulated (i.e summed) to existing gradients (from the previous batch).\n",
        "     outputs = net(inputs) #Forward prop. This syntax works (instead of directly calling forward()) because the base Module class allows it (similarly for the next line)\n",
        "     loss = criterion(outputs, labels) #The scalar loss is held in this object\n",
        "     loss.backward()  #Backward prop. This is when accumulation of grads happen. \n",
        "     optimizer.step()  #Optimizer finally updates the parameters\n",
        "    \n",
        "     #Record some statistics:\n",
        "     running_loss += loss.item()  #Torch.Tensor.item() retrieves the scalar value, rather than a tensor\n",
        "     if i%2000 == 1999: #For every 2000 minibatches (or 8k images)\n",
        "       print('[%d, %d] loss: %.3f' %(epoch+1, i+1, running_loss/2000)) \n",
        "       x_minibatches.append((i+1)*4+(epoch*60000)) #Record at which stage of the data...\n",
        "       y_loss.append(running_loss/2000)            #...the loss was recorded. Helps in plotting a graph.\n",
        "       running_loss = 0.0 #Reset the loss, so we know how the loss changes within a reasonable frame (an average loss from the beginning would be meaningless)\n",
        "\n",
        "print('Finished training')\n",
        "\n",
        "#Demo: We will be showing how to save the trained model params and load them back in. However, this isn't a necessary step and one could directly pass the test set to the model class, like we did during training.  \n",
        "PATH = './MNIST_net.pth' #By convention, PyTorch files have pt/pth extension\n",
        "torch.save(net.state_dict(), PATH) #recommended to save state dict rather than module for compatibility\n",
        "# A module’s state dict contains all of its parameters and persistent buffers. (even optims have this, also having hyperparas)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch loss: 0.0\n",
            "[1, 2000] loss: 1.044\n",
            "[1, 4000] loss: 0.209\n",
            "[1, 6000] loss: 0.141\n",
            "[1, 8000] loss: 0.109\n",
            "[1, 10000] loss: 0.090\n",
            "[1, 12000] loss: 0.081\n",
            "[1, 14000] loss: 0.081\n",
            "Epoch loss: 0.08143176434358156\n",
            "[2, 2000] loss: 0.064\n",
            "[2, 4000] loss: 0.060\n",
            "[2, 6000] loss: 0.058\n",
            "[2, 8000] loss: 0.058\n",
            "[2, 10000] loss: 0.054\n",
            "[2, 12000] loss: 0.049\n",
            "[2, 14000] loss: 0.057\n",
            "Epoch loss: 0.05984801999468891\n",
            "[3, 2000] loss: 0.038\n",
            "[3, 4000] loss: 0.040\n",
            "[3, 6000] loss: 0.042\n",
            "[3, 8000] loss: 0.037\n",
            "[3, 10000] loss: 0.040\n",
            "[3, 12000] loss: 0.044\n",
            "[3, 14000] loss: 0.042\n",
            "Finished training\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1nsf9pxO80ab"
      },
      "source": [
        "# Peeking into the trained model "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "zyUG3ZBk80ac",
        "outputId": "9c43488f-fb48-45a8-84b4-1ecf3d219659"
      },
      "source": [
        "#We can directly see the grads and params of any layer:\n",
        "print('Sample Grads: ', net.conv1.bias.grad) \n",
        "print('Sample Paras: ', net.conv1.bias)\n",
        "# print(params) prints all params, each W and b. print(net.parameters()) only shows an object in memory. \n",
        "\n",
        "#Plot a graph for the loss throughout the training:\n",
        "plt.plot(x_minibatches, y_loss, marker='.', markerfacecolor='g') \n",
        "for i in range(len(x_minibatches)):\n",
        "    if i%7==0:\n",
        "        plt.annotate(\"Epoch \" + str(int(i/7)+1), (x_minibatches[i], y_loss[i]))\n",
        "plt.xlabel(\"Total no. of images progressed through\")\n",
        "plt.ylabel(\"Avg. Loss\")\n",
        "plt.title('Avg. Loss for every 8k images')\n",
        "plt.show()\n",
        "\n",
        "#From previous graph we see that the scale of just the first plot point makes it imopssible to see the actual progress in later epochs \n",
        "#So, zoom in, depending on the first point, while still maintaing a perspective of the 1st-to-2nd points' slope.\n",
        "plt.ylim(top=0.225)\n",
        "plt.plot(x_minibatches, y_loss, marker='.', markerfacecolor='g') \n",
        "for i in range(len(x_minibatches)):\n",
        "    if i%7==0:\n",
        "        plt.annotate(\"Epoch \" + str(int(i/7)+1), (x_minibatches[i], y_loss[i]))\n",
        "plt.xlabel(\"Total no. of images progressed through\")\n",
        "plt.ylabel(\"Avg. Loss\")\n",
        "plt.title('Avg. Loss for every 8k images')\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sample Grads:  tensor([-0.0160,  0.0146,  0.0086, -0.0092, -0.0126, -0.0002])\n",
            "Sample Paras:  Parameter containing:\n",
            "tensor([ 0.2372,  0.1222,  0.1215, -0.4027, -0.6526,  0.1432],\n",
            "       requires_grad=True)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jqTkmyeD80ap"
      },
      "source": [
        "## A live sample test of the predictions made by the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        },
        "id": "C_zX7dcW80aq",
        "outputId": "02bb711f-cc8a-4105-d963-e7c8b5120436"
      },
      "source": [
        "dataiter = iter(testloader)\n",
        "images, labels = dataiter.next() \n",
        "imshow(torchvision.utils.make_grid(images)) #Print images...\n",
        "print('Target labels: ', ' '.join('%5s' % classes[labels[j]] for j in range(4))) #...and their actual target labels\n",
        "net = Net()  \n",
        "net.load_state_dict(torch.load(PATH)) # So we first saved, then load the trained state_dict, then put it in the required module's state_dict\n",
        "outputs = net(images) #The actual testing. As said before, we can skip all the saving-and-loading and directly do this for the testset\n",
        "_, predicted = torch.max(outputs, 1) #Second argument tells that we want to vary the column index in search of the max (\"outputs\" is of 4*10 dims). This gives us the max for each row (image)  \n",
        "#max() returns 2 things: 1st the actual max value (which we don't need, so '_' is just a placeholder), and 2nd the index where the max elem was found, which also corresponds to the class (which we need)  \n",
        "#Notice how we didn't have to apply the last activation layer. This saves us from doing an unnecesary layer on the testset\n",
        "\n",
        "print('Predicted labels: ', ' '.join('%5s' % classes[predicted[j]] for j in range(4)))"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Target labels:  Seven   Two   One  Zero\n",
            "Predicted labels:  Seven   Two   One  Zero\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i_FC8NYQ80ar"
      },
      "source": [
        "# Testing the model\n",
        "Putting the model through both the test and train sets to see how well it performs.\n",
        "\n",
        "We add aditional metrics to see how well it's recognizing each class."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "p67PkGY680a2",
        "outputId": "60e50aea-1135-407e-bdc3-cb8e2a212e19"
      },
      "source": [
        "#Test set:\n",
        "correct = 0.0\n",
        "total = 0.0 \n",
        "class_correct = list(0. for i in range(10))\n",
        "class_total = list(0. for i in range(10))\n",
        "with torch.no_grad(): #no_grad() is a context-manager that disables gradient calculation, use when you are sure you wont do T.backward(). It will reduce memory consumption for computations.\n",
        "  for data in testloader:\n",
        "    images, labels = data\n",
        "    outputs = net(images)\n",
        "    _, predicted = torch.max(outputs.data, 1) #the .data just specifies not to keep track of changes in the parameters, so use it only if you won't need its grads again. \n",
        "    # Though it doesn't make a difference in the code, I mentioned .data here as you might see it elsewhere. It's safer to use .detach() though.\n",
        "    total+=labels.size(0) \n",
        "    correct += (predicted==labels).sum().item() #this 'construct' counts number of same entries across 2 tensors\n",
        "    # For accuracy per class:\n",
        "    c = (predicted == labels).squeeze()\n",
        "    for i in range(4):\n",
        "      label = labels[i]\n",
        "      class_correct[label] += c[i].item() #since True is 1 and False is just 0. \n",
        "      class_total[label] += 1\n",
        "print('Test set accuracy: %f %%' %(100.0*correct/total)) \n",
        "\n",
        "# Similarly, for the train set:\n",
        "correct = 0.0\n",
        "total = 0.0\n",
        "with torch.no_grad():\n",
        "  for data in trainloader:\n",
        "    images, labels = data\n",
        "    outputs = net(images)\n",
        "    _, predicted = torch.max(outputs.data, 1)\n",
        "    total+=labels.size(0) \n",
        "    correct += (predicted==labels).sum().item() \n",
        "print('Train set accuracy: %f %%' %(100.0*correct/total))\n",
        "\n",
        "#Print accuracy per class:\n",
        "avg_acc = 0.0\n",
        "for i in range(10):\n",
        "    x = 100.0 * class_correct[i] / class_total[i]\n",
        "    avg_acc +=x\n",
        "    print('Accuracy of %5s : %f %%' % (classes[i], x))\n",
        "avg_acc/=10\n",
        "print(\"Average class accuracy: \", avg_acc)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Test set accuracy: 98.750000 %\n",
            "Train set accuracy: 99.145000 %\n",
            "Accuracy of  Zero : 99.591837 %\n",
            "Accuracy of   One : 99.823789 %\n",
            "Accuracy of   Two : 98.546512 %\n",
            "Accuracy of Three : 98.910891 %\n",
            "Accuracy of  Four : 98.167006 %\n",
            "Accuracy of  Five : 98.766816 %\n",
            "Accuracy of   Six : 98.434238 %\n",
            "Accuracy of Seven : 98.346304 %\n",
            "Accuracy of Eight : 99.178645 %\n",
            "Accuracy of  Nine : 97.621407 %\n",
            "Average class accuracy:  98.73874438470673\n"
          ]
        }
      ]
    }
  ]
}