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# 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:

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, 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) # 5*5 from image dimension
self.fc2 = nn.Linear(120, 84)
self.fc3 = nn.Linear(84, 10)
def forward(self, input):
# Convolution layer C1: 1 input image channel, 6 output channels,
# 5x5 square convolution, it uses RELU activation function, and
# outputs a Tensor with size (N, 6, 28, 28), where N is the size of the batch
c1 = F.relu(self.conv1(input))
# Subsampling layer S2: 2x2 grid, purely functional,
# this layer does not have any parameter, and outputs a (N, 6, 14, 14) Tensor
s2 = F.max_pool2d(c1, (2, 2))
# Convolution layer C3: 6 input channels, 16 output channels,
# 5x5 square convolution, it uses RELU activation function, and
# outputs a (N, 16, 10, 10) Tensor
c3 = F.relu(self.conv2(s2))
# Subsampling layer S4: 2x2 grid, purely functional,
# this layer does not have any parameter, and outputs a (N, 16, 5, 5) Tensor
s4 = F.max_pool2d(c3, 2)
# Flatten operation: purely functional, outputs a (N, 400) Tensor
s4 = torch.flatten(s4, 1)
# Fully connected layer F5: (N, 400) Tensor input,
# and outputs a (N, 120) Tensor, it uses RELU activation function
f5 = F.relu(self.fc1(s4))
# Fully connected layer F6: (N, 120) Tensor input,
# and outputs a (N, 84) Tensor, it uses RELU activation function
f6 = F.relu(self.fc2(f5))
# Gaussian layer OUTPUT: (N, 84) Tensor input, and
# outputs a (N, 10) Tensor
output = self.fc3(f6)
return output
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, bias=True)
(fc2): Linear(in_features=120, out_features=84, bias=True)
(fc3): Linear(in_features=84, out_features=10, bias=True)
)
```

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
```

```
10
torch.Size([6, 1, 5, 5])
```

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)
```

```
tensor([[ 0.1453, -0.0590, -0.0065, 0.0905, 0.0146, -0.0805, -0.1211, -0.0394,
-0.0181, -0.0136]], grad_fn=<AddmmBackward0>)
```

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 output and the target.

For example:

```
tensor(1.3619, grad_fn=<MseLossBackward0>)
```

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
-> flatten -> linear -> relu -> linear -> relu -> linear
-> MSELoss
-> loss
```

So, when we call `loss.backward()`

, the whole graph is differentiated
w.r.t. the neural net parameters, and all Tensors in the graph that have
`requires_grad=True`

will have their `.grad`

Tensor accumulated with the
gradient.

For illustration, let us follow a few steps backward:

```
<MseLossBackward0 object at 0x7f3f6b17efb0>
<AddmmBackward0 object at 0x7f3f6b17f010>
<AccumulateGrad object at 0x7f3f6b17cee0>
```

## 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)
```

```
conv1.bias.grad before backward
None
conv1.bias.grad after backward
tensor([ 0.0081, -0.0080, -0.0039, 0.0150, 0.0003, -0.0105])
```

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:

```
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.

**Total running time of the script:** ( 0 minutes 0.065 seconds)