# 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 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)
```

Out:

```
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 `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
```

Out:

```
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)
```

Out:

```
Variable containing:
0.0023 -0.0613 -0.0397 -0.1123 -0.0397 0.0330 -0.0656 -0.1231 0.0412 0.0162
[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))
```

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*.`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*`Module`

.`autograd.Function`

- Implements*forward and backward definitions of an autograd operation*. Every`Variable`

operation, creates at least a single`Function`

node, that connects to functions that created a`Variable`

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 = Variable(torch.arange(1, 11)) # a dummy target, for example
criterion = nn.MSELoss()
loss = criterion(output, target)
print(loss)
```

Out:

```
Variable containing:
38.8243
[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
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 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[0][0]) # Linear
print(loss.grad_fn.next_functions[0][0].next_functions[0][0]) # ReLU
```

Out:

```
<MseLossBackward object at 0x7fe4c18539e8>
<AddmmBackward object at 0x7fe3f5498550>
<ExpandBackward object at 0x7fe4c18539e8>
```

## 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)
```

Out:

```
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:
1.00000e-02 *
7.4571
-0.4714
-5.5774
-6.2058
6.6810
3.1632
[torch.FloatTensor of size 6]
```

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 Backprop section.

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