# PYTORCH NEURAL NETWORKS

 Audio version of the article

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:

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)
```

Out:

```Net(
(conv1): Conv2d(1, 6, kernel_size=(3, 3), stride=(1, 1))
(conv2): Conv2d(6, 16, kernel_size=(3, 3), stride=(1, 1))
(fc1): Linear(in_features=576, 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
```

Out:

```10
torch.Size([6, 1, 3, 3])
```

Let try a random 32×32 input. Note: expected input size of this net (LeNet) is 32×32. To use this net on MNIST dataset, please resize the images from the dataset to 32×32.

```input = torch.randn(1, 1, 32, 32)
out = net(input)
print(out)
```

Out:

```tensor([[ 0.0522, -0.1175,  0.0718,  0.0602,  0.0790, -0.0436,  0.0198,  0.0458,
```

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)
```

Out:

```tensor(1.8860, grad_fn=<MseLossBackward>)
```

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
```

Out:

```<MseLossBackward object at 0x7f1465107ef0>
<AddmmBackward object at 0x7f1465107f98>
<AccumulateGrad object at 0x7f1465107f98>
```

## 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

loss.backward()

```

Out:

```conv1.bias.grad before backward
tensor([0., 0., 0., 0., 0., 0.])
tensor([-0.0189,  0.0574, -0.0527, -0.0099,  0.0280,  0.0115])
```

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():
```

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:
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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