# -*- coding: utf-8 -*-
"""
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 `_ 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.arange(1, 11) # 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 `_.
#
# **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.