# -*- coding: utf-8 -*- """ Neural Networks =============== Neural networks can be constructed using the ``torch.nn`` package. Now that you had a glimpse of ``autograd``, ``nn`` depends on ``autograd`` to define models and differentiate them. An ``nn.Module`` contains layers, and a method ``forward(input)`` that returns the ``output``. For example, look at this network that classifies digit images: .. figure:: /_static/img/mnist.png :alt: convnet convnet It is a simple feed-forward network. It takes the input, feeds it through several layers one after the other, and then finally gives the output. A typical training procedure for a neural network is as follows: - Define the neural network that has some learnable parameters (or weights) - Iterate over a dataset of inputs - Process input through the network - Compute the loss (how far is the output from being correct) - Propagate gradients back into the network’s parameters - Update the weights of the network, typically using a simple update rule: ``weight = weight - learning_rate * gradient`` Define the network ------------------ Let’s define this network: """ import torch import torch.nn as nn import torch.nn.functional as F class Net(nn.Module): def __init__(self): super(Net, self).__init__() # 1 input image channel, 6 output channels, 3x3 square convolution # kernel self.conv1 = nn.Conv2d(1, 6, 3) self.conv2 = nn.Conv2d(6, 16, 3) # an affine operation: y = Wx + b self.fc1 = nn.Linear(16 * 6 * 6, 120) # 6*6 from image dimension self.fc2 = nn.Linear(120, 84) self.fc3 = nn.Linear(84, 10) def forward(self, x): # Max pooling over a (2, 2) window x = F.max_pool2d(F.relu(self.conv1(x)), (2, 2)) # If the size is a square you can only specify a single number x = F.max_pool2d(F.relu(self.conv2(x)), 2) x = x.view(-1, self.num_flat_features(x)) x = F.relu(self.fc1(x)) x = F.relu(self.fc2(x)) x = self.fc3(x) return x def num_flat_features(self, x): size = x.size()[1:] # all dimensions except the batch dimension num_features = 1 for s in size: num_features *= s return num_features net = Net() print(net) ######################################################################## # You just have to define the ``forward`` function, and the ``backward`` # function (where gradients are computed) is automatically defined for you # using ``autograd``. # You can use any of the Tensor operations in the ``forward`` function. # # The learnable parameters of a model are returned by ``net.parameters()`` params = list(net.parameters()) print(len(params)) print(params[0].size()) # conv1's .weight ######################################################################## # Let's try a random 32x32 input. # Note: expected input size of this net (LeNet) is 32x32. To use this net on # the MNIST dataset, please resize the images from the dataset to 32x32. input = torch.randn(1, 1, 32, 32) out = net(input) print(out) ######################################################################## # Zero the gradient buffers of all parameters and backprops with random # gradients: net.zero_grad() out.backward(torch.randn(1, 10)) ######################################################################## # .. note:: # # ``torch.nn`` only supports mini-batches. The entire ``torch.nn`` # package only supports inputs that are a mini-batch of samples, and not # a single sample. # # For example, ``nn.Conv2d`` will take in a 4D Tensor of # ``nSamples x nChannels x Height x Width``. # # If you have a single sample, just use ``input.unsqueeze(0)`` to add # a fake batch dimension. # # Before proceeding further, let's recap all the classes you’ve seen so far. # # **Recap:** # - ``torch.Tensor`` - A *multi-dimensional array* with support for autograd # operations like ``backward()``. Also *holds the gradient* w.r.t. the # tensor. # - ``nn.Module`` - Neural network module. *Convenient way of # encapsulating parameters*, with helpers for moving them to GPU, # exporting, loading, etc. # - ``nn.Parameter`` - A kind of Tensor, that is *automatically # registered as a parameter when assigned as an attribute to a* # ``Module``. # - ``autograd.Function`` - Implements *forward and backward definitions # of an autograd operation*. Every ``Tensor`` operation creates at # least a single ``Function`` node that connects to functions that # created a ``Tensor`` and *encodes its history*. # # **At this point, we covered:** # - Defining a neural network # - Processing inputs and calling backward # # **Still Left:** # - Computing the loss # - Updating the weights of the network # # Loss Function # ------------- # A loss function takes the (output, target) pair of inputs, and computes a # value that estimates how far away the output is from the target. # # There are several different # `loss functions `_ under the # nn package . # A simple loss is: ``nn.MSELoss`` which computes the mean-squared error # between the input and the target. # # For example: output = net(input) target = torch.randn(10) # a dummy target, for example target = target.view(1, -1) # make it the same shape as output criterion = nn.MSELoss() loss = criterion(output, target) print(loss) ######################################################################## # Now, if you follow ``loss`` in the backward direction, using its # ``.grad_fn`` attribute, you will see a graph of computations that looks # like this: # # :: # # input -> conv2d -> relu -> maxpool2d -> conv2d -> relu -> maxpool2d # -> view -> linear -> relu -> linear -> relu -> linear # -> MSELoss # -> loss # # So, when we call ``loss.backward()``, the whole graph is differentiated # w.r.t. the loss, and all Tensors in the graph that has ``requires_grad=True`` # will have their ``.grad`` Tensor accumulated with the gradient. # # For illustration, let us follow a few steps backward: print(loss.grad_fn) # MSELoss print(loss.grad_fn.next_functions[0][0]) # Linear print(loss.grad_fn.next_functions[0][0].next_functions[0][0]) # ReLU ######################################################################## # Backprop # -------- # To backpropagate the error all we have to do is to ``loss.backward()``. # You need to clear the existing gradients though, else gradients will be # accumulated to existing gradients. # # # Now we shall call ``loss.backward()``, and have a look at conv1's bias # gradients before and after the backward. net.zero_grad() # zeroes the gradient buffers of all parameters print('conv1.bias.grad before backward') print(net.conv1.bias.grad) loss.backward() print('conv1.bias.grad after backward') print(net.conv1.bias.grad) ######################################################################## # Now, we have seen how to use loss functions. # # **Read Later:** # # The neural network package contains various modules and loss functions # that form the building blocks of deep neural networks. A full list with # documentation is `here `_. # # **The only thing left to learn is:** # # - Updating the weights of the network # # Update the weights # ------------------ # The simplest update rule used in practice is the Stochastic Gradient # Descent (SGD): # # ``weight = weight - learning_rate * gradient`` # # We can implement this using simple Python code: # # .. code:: python # # learning_rate = 0.01 # for f in net.parameters(): # f.data.sub_(f.grad.data * learning_rate) # # However, as you use neural networks, you want to use various different # update rules such as SGD, Nesterov-SGD, Adam, RMSProp, etc. # To enable this, we built a small package: ``torch.optim`` that # implements all these methods. Using it is very simple: import torch.optim as optim # create your optimizer optimizer = optim.SGD(net.parameters(), lr=0.01) # in your training loop: optimizer.zero_grad() # zero the gradient buffers output = net(input) loss = criterion(output, target) loss.backward() optimizer.step() # Does the update ############################################################### # .. Note:: # # Observe how gradient buffers had to be manually set to zero using # ``optimizer.zero_grad()``. This is because gradients are accumulated # as explained in the `Backprop`_ section.