```
%matplotlib inline
```

# 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, 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)
```

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 try a random 32x32 input 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 = 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 <https://pytorch.org/docs/nn.html#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 <https://pytorch.org/docs/nn>`

_.

**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 `Backprop`_ section.
```