187 lines
11 KiB
Plaintext
187 lines
11 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\nNeural Networks\n===============\n\nNeural networks can be constructed using the ``torch.nn`` package.\n\nNow that you had a glimpse of ``autograd``, ``nn`` depends on\n``autograd`` to define models and differentiate them.\nAn ``nn.Module`` contains layers, and a method ``forward(input)``\\ that\nreturns the ``output``.\n\nFor example, look at this network that classifies digit images:\n\n.. figure:: /_static/img/mnist.png\n :alt: convnet\n\n convnet\n\nIt is a simple feed-forward network. It takes the input, feeds it\nthrough several layers one after the other, and then finally gives the\noutput.\n\nA typical training procedure for a neural network is as follows:\n\n- Define the neural network that has some learnable parameters (or\n weights)\n- Iterate over a dataset of inputs\n- Process input through the network\n- Compute the loss (how far is the output from being correct)\n- Propagate gradients back into the network\u2019s parameters\n- Update the weights of the network, typically using a simple update rule:\n ``weight = weight - learning_rate * gradient``\n\nDefine the network\n------------------\n\nLet\u2019s define this network:\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\n\n\nclass Net(nn.Module):\n\n def __init__(self):\n super(Net, self).__init__()\n # 1 input image channel, 6 output channels, 5x5 square convolution\n # kernel\n self.conv1 = nn.Conv2d(1, 6, 5)\n self.conv2 = nn.Conv2d(6, 16, 5)\n # an affine operation: y = Wx + b\n self.fc1 = nn.Linear(16 * 5 * 5, 120)\n self.fc2 = nn.Linear(120, 84)\n self.fc3 = nn.Linear(84, 10)\n\n def forward(self, x):\n # Max pooling over a (2, 2) window\n x = F.max_pool2d(F.relu(self.conv1(x)), (2, 2))\n # If the size is a square you can only specify a single number\n x = F.max_pool2d(F.relu(self.conv2(x)), 2)\n x = x.view(-1, self.num_flat_features(x))\n x = F.relu(self.fc1(x))\n x = F.relu(self.fc2(x))\n x = self.fc3(x)\n return x\n\n def num_flat_features(self, x):\n size = x.size()[1:] # all dimensions except the batch dimension\n num_features = 1\n for s in size:\n num_features *= s\n return num_features\n\n\nnet = Net()\nprint(net)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"You just have to define the ``forward`` function, and the ``backward``\nfunction (where gradients are computed) is automatically defined for you\nusing ``autograd``.\nYou can use any of the Tensor operations in the ``forward`` function.\n\nThe learnable parameters of a model are returned by ``net.parameters()``\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"params = list(net.parameters())\nprint(len(params))\nprint(params[0].size()) # conv1's .weight"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let try a random 32x32 input\nNote: Expected input size to this net(LeNet) is 32x32. To use this net on\nMNIST dataset, please resize the images from the dataset to 32x32.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"input = torch.randn(1, 1, 32, 32)\nout = net(input)\nprint(out)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Zero the gradient buffers of all parameters and backprops with random\ngradients:\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"net.zero_grad()\nout.backward(torch.randn(1, 10))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<div class=\"alert alert-info\"><h4>Note</h4><p>``torch.nn`` only supports mini-batches. The entire ``torch.nn``\n package only supports inputs that are a mini-batch of samples, and not\n a single sample.\n\n For example, ``nn.Conv2d`` will take in a 4D Tensor of\n ``nSamples x nChannels x Height x Width``.\n\n If you have a single sample, just use ``input.unsqueeze(0)`` to add\n a fake batch dimension.</p></div>\n\nBefore proceeding further, let's recap all the classes you\u2019ve seen so far.\n\n**Recap:**\n - ``torch.Tensor`` - A *multi-dimensional array* with support for autograd\n operations like ``backward()``. Also *holds the gradient* w.r.t. the\n tensor.\n - ``nn.Module`` - Neural network module. *Convenient way of\n encapsulating parameters*, with helpers for moving them to GPU,\n exporting, loading, etc.\n - ``nn.Parameter`` - A kind of Tensor, that is *automatically\n registered as a parameter when assigned as an attribute to a*\n ``Module``.\n - ``autograd.Function`` - Implements *forward and backward definitions\n of an autograd operation*. Every ``Tensor`` operation, creates at\n least a single ``Function`` node, that connects to functions that\n created a ``Tensor`` and *encodes its history*.\n\n**At this point, we covered:**\n - Defining a neural network\n - Processing inputs and calling backward\n\n**Still Left:**\n - Computing the loss\n - Updating the weights of the network\n\nLoss Function\n-------------\nA loss function takes the (output, target) pair of inputs, and computes a\nvalue that estimates how far away the output is from the target.\n\nThere are several different\n`loss functions <https://pytorch.org/docs/nn.html#loss-functions>`_ under the\nnn package .\nA simple loss is: ``nn.MSELoss`` which computes the mean-squared error\nbetween the input and the target.\n\nFor example:\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"output = net(input)\ntarget = torch.randn(10) # a dummy target, for example\ntarget = target.view(1, -1) # make it the same shape as output\ncriterion = nn.MSELoss()\n\nloss = criterion(output, target)\nprint(loss)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now, if you follow ``loss`` in the backward direction, using its\n``.grad_fn`` attribute, you will see a graph of computations that looks\nlike this:\n\n::\n\n input -> conv2d -> relu -> maxpool2d -> conv2d -> relu -> maxpool2d\n -> view -> linear -> relu -> linear -> relu -> linear\n -> MSELoss\n -> loss\n\nSo, when we call ``loss.backward()``, the whole graph is differentiated\nw.r.t. the loss, and all Tensors in the graph that has ``requires_grad=True``\nwill have their ``.grad`` Tensor accumulated with the gradient.\n\nFor illustration, let us follow a few steps backward:\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"print(loss.grad_fn) # MSELoss\nprint(loss.grad_fn.next_functions[0][0]) # Linear\nprint(loss.grad_fn.next_functions[0][0].next_functions[0][0]) # ReLU"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Backprop\n--------\nTo backpropagate the error all we have to do is to ``loss.backward()``.\nYou need to clear the existing gradients though, else gradients will be\naccumulated to existing gradients.\n\n\nNow we shall call ``loss.backward()``, and have a look at conv1's bias\ngradients before and after the backward.\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"net.zero_grad() # zeroes the gradient buffers of all parameters\n\nprint('conv1.bias.grad before backward')\nprint(net.conv1.bias.grad)\n\nloss.backward()\n\nprint('conv1.bias.grad after backward')\nprint(net.conv1.bias.grad)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now, we have seen how to use loss functions.\n\n**Read Later:**\n\n The neural network package contains various modules and loss functions\n that form the building blocks of deep neural networks. A full list with\n documentation is `here <https://pytorch.org/docs/nn>`_.\n\n**The only thing left to learn is:**\n\n - Updating the weights of the network\n\nUpdate the weights\n------------------\nThe simplest update rule used in practice is the Stochastic Gradient\nDescent (SGD):\n\n ``weight = weight - learning_rate * gradient``\n\nWe can implement this using simple python code:\n\n.. code:: python\n\n learning_rate = 0.01\n for f in net.parameters():\n f.data.sub_(f.grad.data * learning_rate)\n\nHowever, as you use neural networks, you want to use various different\nupdate rules such as SGD, Nesterov-SGD, Adam, RMSProp, etc.\nTo enable this, we built a small package: ``torch.optim`` that\nimplements all these methods. Using it is very simple:\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import torch.optim as optim\n\n# create your optimizer\noptimizer = optim.SGD(net.parameters(), lr=0.01)\n\n# in your training loop:\noptimizer.zero_grad() # zero the gradient buffers\noutput = net(input)\nloss = criterion(output, target)\nloss.backward()\noptimizer.step() # Does the update"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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".. Note::\n\n Observe how gradient buffers had to be manually set to zero using\n ``optimizer.zero_grad()``. This is because gradients are accumulated\n as explained in `Backprop`_ section.\n\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.7"
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"nbformat": 4,
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"nbformat_minor": 0
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