tutorials/beginner_source/pytorch_with_examples.rst

Learning PyTorch with Examples
******************************
**Author**: `Justin Johnson <https://github.com/jcjohnson/pytorch-examples>`_

This tutorial introduces the fundamental concepts of
`PyTorch <https://github.com/pytorch/pytorch>`__ through self-contained
examples.

At its core, PyTorch provides two main features:

- An n-dimensional Tensor, similar to numpy but can run on GPUs
- Automatic differentiation for building and training neural networks

We will use a fully-connected ReLU network as our running example. The
network will have a single hidden layer, and will be trained with
gradient descent to fit random data by minimizing the Euclidean distance
between the network output and the true output.

.. Note::
	You can browse the individual examples at the
	:ref:`end of this page <examples-download>`.

.. contents:: Table of Contents
	:local:

Tensors
=======

Warm-up: numpy
--------------

Before introducing PyTorch, we will first implement the network using
numpy.

Numpy provides an n-dimensional array object, and many functions for
manipulating these arrays. Numpy is a generic framework for scientific
computing; it does not know anything about computation graphs, or deep
learning, or gradients. However we can easily use numpy to fit a
two-layer network to random data by manually implementing the forward
and backward passes through the network using numpy operations:

.. includenodoc:: /beginner/examples_tensor/two_layer_net_numpy.py


PyTorch: Tensors
----------------

Numpy is a great framework, but it cannot utilize GPUs to accelerate its
numerical computations. For modern deep neural networks, GPUs often
provide speedups of `50x or
greater <https://github.com/jcjohnson/cnn-benchmarks>`__, so
unfortunately numpy won't be enough for modern deep learning.

Here we introduce the most fundamental PyTorch concept: the **Tensor**.
A PyTorch Tensor is conceptually identical to a numpy array: a Tensor is
an n-dimensional array, and PyTorch provides many functions for
operating on these Tensors. Behind the scenes, Tensors can keep track of
a computational graph and gradients, but they're also useful as a
generic tool for scientific computing.

Also unlike numpy, PyTorch Tensors can utilize GPUs to accelerate
their numeric computations. To run a PyTorch Tensor on GPU, you simply
need to cast it to a new datatype.

Here we use PyTorch Tensors to fit a two-layer network to random data.
Like the numpy example above we need to manually implement the forward
and backward passes through the network:

.. includenodoc:: /beginner/examples_tensor/two_layer_net_tensor.py


Autograd
========

PyTorch: Tensors and autograd
-------------------------------

In the above examples, we had to manually implement both the forward and
backward passes of our neural network. Manually implementing the
backward pass is not a big deal for a small two-layer network, but can
quickly get very hairy for large complex networks.

Thankfully, we can use `automatic
differentiation <https://en.wikipedia.org/wiki/Automatic_differentiation>`__
to automate the computation of backward passes in neural networks. The
**autograd** package in PyTorch provides exactly this functionality.
When using autograd, the forward pass of your network will define a
**computational graph**; nodes in the graph will be Tensors, and edges
will be functions that produce output Tensors from input Tensors.
Backpropagating through this graph then allows you to easily compute
gradients.

This sounds complicated, it's pretty simple to use in practice. Each Tensor
represents a node in a computational graph. If ``x`` is a Tensor that has
``x.requires_grad=True`` then ``x.grad`` is another Tensor holding the
gradient of ``x`` with respect to some scalar value.

Here we use PyTorch Tensors and autograd to implement our two-layer
network; now we no longer need to manually implement the backward pass
through the network:

.. includenodoc:: /beginner/examples_autograd/two_layer_net_autograd.py

PyTorch: Defining new autograd functions
----------------------------------------

Under the hood, each primitive autograd operator is really two functions
that operate on Tensors. The **forward** function computes output
Tensors from input Tensors. The **backward** function receives the
gradient of the output Tensors with respect to some scalar value, and
computes the gradient of the input Tensors with respect to that same
scalar value.

In PyTorch we can easily define our own autograd operator by defining a
subclass of ``torch.autograd.Function`` and implementing the ``forward``
and ``backward`` functions. We can then use our new autograd operator by
constructing an instance and calling it like a function, passing
Tensors containing input data.

In this example we define our own custom autograd function for
performing the ReLU nonlinearity, and use it to implement our two-layer
network:

.. includenodoc:: /beginner/examples_autograd/two_layer_net_custom_function.py

`nn` module
===========

PyTorch: nn
-----------

Computational graphs and autograd are a very powerful paradigm for
defining complex operators and automatically taking derivatives; however
for large neural networks raw autograd can be a bit too low-level.

When building neural networks we frequently think of arranging the
computation into **layers**, some of which have **learnable parameters**
which will be optimized during learning.

In TensorFlow, packages like
`Keras <https://github.com/fchollet/keras>`__,
`TensorFlow-Slim <https://github.com/tensorflow/tensorflow/tree/master/tensorflow/contrib/slim>`__,
and `TFLearn <http://tflearn.org/>`__ provide higher-level abstractions
over raw computational graphs that are useful for building neural
networks.

In PyTorch, the ``nn`` package serves this same purpose. The ``nn``
package defines a set of **Modules**, which are roughly equivalent to
neural network layers. A Module receives input Tensors and computes
output Tensors, but may also hold internal state such as Tensors
containing learnable parameters. The ``nn`` package also defines a set
of useful loss functions that are commonly used when training neural
networks.

In this example we use the ``nn`` package to implement our two-layer
network:

.. includenodoc:: /beginner/examples_nn/two_layer_net_nn.py

PyTorch: optim
--------------

Up to this point we have updated the weights of our models by manually
mutating the Tensors holding learnable parameters (with ``torch.no_grad()``
or ``.data`` to avoid tracking history in autograd). This is not a huge
burden for simple optimization algorithms like stochastic gradient descent,
but in practice we often train neural networks using more sophisticated
optimizers like AdaGrad, RMSProp, Adam, etc.

The ``optim`` package in PyTorch abstracts the idea of an optimization
algorithm and provides implementations of commonly used optimization
algorithms.

In this example we will use the ``nn`` package to define our model as
before, but we will optimize the model using the Adam algorithm provided
by the ``optim`` package:

.. includenodoc:: /beginner/examples_nn/two_layer_net_optim.py

PyTorch: Custom nn Modules
--------------------------

Sometimes you will want to specify models that are more complex than a
sequence of existing Modules; for these cases you can define your own
Modules by subclassing ``nn.Module`` and defining a ``forward`` which
receives input Tensors and produces output Tensors using other
modules or other autograd operations on Tensors.

In this example we implement our two-layer network as a custom Module
subclass:

.. includenodoc:: /beginner/examples_nn/two_layer_net_module.py

PyTorch: Control Flow + Weight Sharing
--------------------------------------

As an example of dynamic graphs and weight sharing, we implement a very
strange model: a fully-connected ReLU network that on each forward pass
chooses a random number between 1 and 4 and uses that many hidden
layers, reusing the same weights multiple times to compute the innermost
hidden layers.

For this model we can use normal Python flow control to implement the loop,
and we can implement weight sharing among the innermost layers by simply
reusing the same Module multiple times when defining the forward pass.

We can easily implement this model as a Module subclass:

.. includenodoc:: /beginner/examples_nn/dynamic_net.py


.. _examples-download:

Examples
========

You can browse the above examples here.

Tensors
-------

.. toctree::
   :maxdepth: 2
   :hidden:

   /beginner/examples_tensor/two_layer_net_numpy
   /beginner/examples_tensor/two_layer_net_tensor

.. galleryitem:: /beginner/examples_tensor/two_layer_net_numpy.py

.. galleryitem:: /beginner/examples_tensor/two_layer_net_tensor.py

.. raw:: html

    <div style='clear:both'></div>

Autograd
--------

.. toctree::
   :maxdepth: 2
   :hidden:

   /beginner/examples_autograd/two_layer_net_autograd
   /beginner/examples_autograd/two_layer_net_custom_function
   /beginner/examples_autograd/tf_two_layer_net


.. galleryitem:: /beginner/examples_autograd/two_layer_net_autograd.py

.. galleryitem:: /beginner/examples_autograd/two_layer_net_custom_function.py

.. galleryitem:: /beginner/examples_autograd/tf_two_layer_net.py

.. raw:: html

    <div style='clear:both'></div>

`nn` module
-----------

.. toctree::
   :maxdepth: 2
   :hidden:

   /beginner/examples_nn/two_layer_net_nn
   /beginner/examples_nn/two_layer_net_optim
   /beginner/examples_nn/two_layer_net_module
   /beginner/examples_nn/dynamic_net


.. galleryitem:: /beginner/examples_nn/two_layer_net_nn.py

.. galleryitem:: /beginner/examples_nn/two_layer_net_optim.py

.. galleryitem:: /beginner/examples_nn/two_layer_net_module.py

.. galleryitem:: /beginner/examples_nn/dynamic_net.py

.. raw:: html

    <div style='clear:both'></div>