.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_beginner_blitz_neural_networks_tutorial.py:
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:
.. code-block:: default
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)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
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()``
.. code-block:: default
params = list(net.parameters())
print(len(params))
print(params[0].size()) # conv1's .weight
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
10
torch.Size([6, 1, 3, 3])
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.
.. code-block:: default
input = torch.randn(1, 1, 32, 32)
out = net(input)
print(out)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
tensor([[-0.0705, -0.0309, -0.0288, -0.1339, 0.0382, 0.1188, -0.0436, 0.0081,
-0.0757, 0.1149]], grad_fn=)
Zero the gradient buffers of all parameters and backprops with random
gradients:
.. code-block:: default
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:
.. code-block:: default
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)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
tensor(1.4709, grad_fn=)
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:
.. code-block:: default
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
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
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.
.. code-block:: default
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)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
conv1.bias.grad before backward
tensor([0., 0., 0., 0., 0., 0.])
conv1.bias.grad after backward
tensor([ 3.7201e-03, 1.2418e-02, -8.0362e-05, 2.8057e-02, 1.7011e-02,
7.6589e-03])
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:
.. 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:
.. code-block:: default
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.
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 3.473 seconds)
.. _sphx_glr_download_beginner_blitz_neural_networks_tutorial.py:
.. only :: html
.. container:: sphx-glr-footer
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.. container:: sphx-glr-download
:download:`Download Python source code: neural_networks_tutorial.py `
.. container:: sphx-glr-download
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