PyTorch Tutorial-training-a-neural-network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cab4753a",
   "metadata": {},
   "source": [
    "# PyTorch Tutorial, Training a neural network:\n",
    "#### We use loss function and optimizer to train a model\n",
    "- Download the **MNIST** dataset and use DataLoader on them\n",
    "- Define a **neural network** (model)\n",
    "- Define loss function **MSE** for comparing the performance of the model \n",
    "- Define optimizer as **SGD** (Stochastic Gradient Descent), which is an optimization algorithm\n",
    "- Train our model (the neural network) with **training set**\n",
    "- Evaluate the model with **test set**\n",
    "\n",
    "https://github.com/ostad-ai/PyTorch-Tutorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "75354f9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing the necessary modules\n",
    "import torch\n",
    "import torch.nn as tnn\n",
    "from torchvision import datasets\n",
    "from torch.utils.data import DataLoader\n",
    "from torchvision.transforms import ToTensor, Lambda\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c5e5ce0",
   "metadata": {},
   "source": [
    "As we did before we download the MINST data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5ae0fc7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "training_set=datasets.MNIST(root='./MNIST',train=True, download=True, transform=ToTensor())\n",
    "test_set=datasets.MNIST(root='./MNIST',train=False,download=True,transform=ToTensor())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47462aff",
   "metadata": {},
   "source": [
    "Converting the class labels to one-hot vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "9ba42428",
   "metadata": {},
   "outputs": [],
   "source": [
    "one_hot_transform=Lambda(lambda y:torch.zeros(Nclasses,dtype=torch.float).index_put([torch.tensor(y)],\n",
    "                                                                         values=torch.tensor(1.)))\n",
    "training_set.target_transform=one_hot_transform\n",
    "test_set.target_transform=one_hot_transform"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2626bd63",
   "metadata": {},
   "source": [
    "Using **DataLoader** to make dataset iterable and in a form of batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "dad868ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "batchSize=16\n",
    "train_dataloader=DataLoader(training_set,batch_size=batchSize,shuffle=True)\n",
    "test_dataloader=DataLoader(test_set,batch_size=batchSize,shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "fded2a91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The device chosen is: cuda\n"
     ]
    }
   ],
   "source": [
    "device=torch.device('cuda' if torch.cuda.is_available()\n",
    "         else 'mps' if torch.backends.mps.is_available()\n",
    "         else 'cpu')\n",
    "print(f'The device chosen is: {device}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c9bede5",
   "metadata": {},
   "source": [
    "Defining a model, which we introduced it in some previous post, set the device of model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "354a4b66",
   "metadata": {},
   "outputs": [],
   "source": [
    "cin,cout,kernelSize,Nclasses=1,32,3,10\n",
    "model=tnn.Sequential(\n",
    "      tnn.Conv2d(cin,cout,kernel_size=kernelSize),\n",
    "      tnn.ReLU(),\n",
    "      tnn.MaxPool2d(kernel_size=2,stride=2),\n",
    "      tnn.Flatten(),\n",
    "      tnn.Linear(5408,Nclasses),\n",
    "      tnn.Softmax(dim=1)\n",
    ")\n",
    "model=model.to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c9c4fc5",
   "metadata": {},
   "source": [
    "Choose the loss function and optimizer:\n",
    " - Loss function is **Mean Squared Error** (MSE)\n",
    " - The optimzier is **Stochastic Gradient Descent** (SGD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e19b3c81",
   "metadata": {},
   "outputs": [],
   "source": [
    "learningRate=.001 # this is the learning rate in the SGD algorithm\n",
    "optimizer=torch.optim.SGD(model.parameters(),lr=learningRate)\n",
    "lossFn=tnn.MSELoss().to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8e05b45",
   "metadata": {},
   "source": [
    "We train the model with the training set.\n",
    "<br>Each run over the whole training set is called an **epoch**. We train the model over several epochs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "367566fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch0, loss:335.575509570539; Epoch1, loss:328.4970253407955; Epoch2, loss:320.0231431648135; Epoch3, loss:309.1276605427265; Epoch4, loss:294.767256423831; Epoch5, loss:276.2438206486404; Epoch6, loss:253.74232186377048; Epoch7, loss:228.81281803548336; Epoch8, loss:203.90042934380472; Epoch9, loss:181.17672333680093; Epoch10, loss:161.4360462296754; Epoch11, loss:144.61633023340255; Epoch12, loss:130.8293473208323; Epoch13, loss:119.68307584896684; Epoch14, loss:110.71886868029833; Epoch15, loss:103.48504076292738; Epoch16, loss:97.63002575421706; "
     ]
    }
   ],
   "source": [
    "Nepochs=17\n",
    "loss_epochs=[]\n",
    "model.train()\n",
    "for i in range(Nepochs):\n",
    "    losses=0.\n",
    "    for x,y in train_dataloader:\n",
    "        x,y=x.to(device),y.to(device)\n",
    "        output=model(x)\n",
    "        loss=lossFn(output,y)\n",
    "        losses+=loss.item()\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "    print(f'Epoch{i}, loss:{losses}', end='; ')\n",
    "    loss_epochs.append(losses)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4ad51a9",
   "metadata": {},
   "source": [
    "At this step, we  show the curve of training loss of each epoch as epoch advances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "f13860c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss_epochs)\n",
    "plt.title('Training loss versus epoch')\n",
    "plt.xlabel('epochs')\n",
    "plt.ylabel('Training loss of an epoch')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "358be4ab",
   "metadata": {},
   "source": [
    "As we see above, during training phase, the loss value is reduced after each epoch.\n",
    "<br>Let's evaluate the trained model with unseen dataset, called **test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "e4fb8ae3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total test loss : 15.109585538506508\n",
      "Accuracy(%): 87.71\n"
     ]
    }
   ],
   "source": [
    "model.eval()\n",
    "test_loss=0.\n",
    "accuracy=0.\n",
    "#Nbatches=len(test_dataloader)\n",
    "NtestSamples=len(test_dataloader.dataset)\n",
    "with torch.no_grad():\n",
    "    for x,y in test_dataloader:\n",
    "        x,y=x.to(device),y.to(device)\n",
    "        output=model(x)\n",
    "        predicted=torch.argmax(output,axis=1)\n",
    "        ydesired=torch.argmax(y,axis=1)\n",
    "        accuracy+=(predicted==ydesired).type(torch.float).sum().item()\n",
    "        loss=lossFn(output,y)\n",
    "        test_loss+=loss.item()\n",
    "print(f'Total test loss : {test_loss}')\n",
    "print(f'Accuracy(%): {100*accuracy/NtestSamples}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dacb43cf",
   "metadata": {},
   "source": [
    "Now, we actually give a batch of test images to the model, and observe the predicted labels. \n",
    "<br>We compare the predicated labels with the true labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "7f7bbd9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The accuracy of a test batch (%): 93.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x1600 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "accuracy_batch=0.\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    x,y=next(iter(test_dataloader))\n",
    "    x,y=x.to(device),y.to(device)\n",
    "    output=model(x)\n",
    "    y=y.argmax(1)\n",
    "    predicted=output.argmax(1)\n",
    "    accuracy_batch+=(y==predicted).type(torch.float).sum().item()\n",
    "    accuracy_batch/=batchSize\n",
    "    print(f'The accuracy of a test batch (%): {100*accuracy_batch}')\n",
    "    #plt.title(f'correct number is: {true_label.item()}, predicted number: {predicted_label}')\n",
    "plt.figure(figsize=(15,16))\n",
    "for i in range(batchSize):\n",
    "    plt.subplot(4,4,i+1)\n",
    "    plt.title(f'true: {y[i].item()}, predicted:{predicted[i].item()}')\n",
    "    plt.imshow(x[i].cpu().numpy()[0],cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "469b10fc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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