Neural networks can be constructed using the
Now that you had a glimpse of
nn depends on
autograd to define models and differentiate them.
nn.Module contains layers, and a method
For example, look at this network that classfies digit images:
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 from torch.autograd import Variable 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, 5x5 square convolution # kernel self.conv1 = nn.Conv2d(1, 6, 5) self.conv2 = nn.Conv2d(6, 16, 5) # an affine operation: y = Wx + b self.fc1 = nn.Linear(16 * 5 * 5, 120) 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)
Net( (conv1): Conv2d (1, 6, kernel_size=(5, 5), stride=(1, 1)) (conv2): Conv2d (6, 16, kernel_size=(5, 5), stride=(1, 1)) (fc1): Linear(in_features=400, out_features=120) (fc2): Linear(in_features=120, out_features=84) (fc3): Linear(in_features=84, out_features=10) )
You just have to define the
forward function, and the
function (where gradients are computed) is automatically defined for you
You can use any of the Tensor operations in the
The learnable parameters of a model are returned by
params = list(net.parameters()) print(len(params)) print(params.size()) # conv1's .weight
10 torch.Size([6, 1, 5, 5])
The input to the forward is an
autograd.Variable, and so is the output.
Note: Expected input size to this net(LeNet) is 32x32. To use this net on
MNIST dataset,please resize the images from the dataset to 32x32.
input = Variable(torch.randn(1, 1, 32, 32)) out = net(input) print(out)
Variable containing: 0.0490 0.0798 0.0189 -0.0231 0.0577 -0.0843 -0.0357 -0.0950 0.0220 -0.1126 [torch.FloatTensor of size 1x10]
Zero the gradient buffers of all parameters and backprops with random gradients:
net.zero_grad() out.backward(torch.randn(1, 10))
torch.nn only supports mini-batches The entire
package only supports inputs that are a mini-batch of samples, and not
a single sample.
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.
torch.Tensor- A multi-dimensional array.
autograd.Variable- Wraps a Tensor and records the history of operations applied to it. Has the same API as a
Tensor, with some additions 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 Variable, that is automatically registered as a parameter when assigned as an attribute to a
autograd.Function- Implements forward and backward definitions of an autograd operation. Every
Variableoperation, creates at least a single
Functionnode, that connects to functions that created a
Variableand 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
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.
output = net(input) target = Variable(torch.arange(1, 11)) # a dummy target, for example criterion = nn.MSELoss() loss = criterion(output, target) print(loss)
Variable containing: 38.9008 [torch.FloatTensor of size 1]
Now, if you follow
loss in the backward direction, using it’s
.grad_fn attribute, you will see a graph of computations that looks
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 Variables in the graph will have their
.grad Variable accumulated with the gradient.
For illustration, let us follow a few steps backward:
print(loss.grad_fn) # MSELoss print(loss.grad_fn.next_functions) # Linear print(loss.grad_fn.next_functions.next_functions) # ReLU
<MseLossBackward object at 0x7ff91efb6ba8> <AddmmBackward object at 0x7ff91efb6860> <ExpandBackward object at 0x7ff91efb6860>
To backpropagate the error all we have to do is to
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)
conv1.bias.grad before backward Variable containing: 0 0 0 0 0 0 [torch.FloatTensor of size 6] conv1.bias.grad after backward Variable containing: -0.0474 -0.0176 0.0885 0.1813 -0.0705 -0.1154 [torch.FloatTensor of size 6]
Now, we have seen how to use loss functions.
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:
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:
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
Total running time of the script: ( 0 minutes 0.192 seconds)