This repository introduces the fundamental concepts of 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: These examples have been update for PyTorch 0.4, which made several major changes to the core PyTorch API. Most notably, prior to 0.4 Tensors had to be wrapped in Variable objects to use autograd; this functionality has now been added directly to Tensors, and Variables are now deprecated.
- Warm-up: numpy
- PyTorch: Tensors
- PyTorch: Autograd
- PyTorch: Defining new autograd functions
- TensorFlow: Static Graphs
- PyTorch: nn
- PyTorch: optim
- PyTorch: Custom nn Modules
- PyTorch: Control Flow and Weight Sharing
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:
:INCLUDE tensor/two_layer_net_numpy.pyNumpy 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, 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. Any computation you might want to perform with numpy can also be accomplished with PyTorch Tensors; you should think of them as a generic tool for scientific computing.
However unlike numpy, PyTorch Tensors can utilize GPUs to accelerate their
numeric computations. To run a PyTorch Tensor on GPU, you use the device
argument when constructing a Tensor to place the Tensor on a GPU.
Here we use PyTorch Tensors to fit a two-layer network to random data. Like the numpy example above we manually implement the forward and backward passes through the network, using operations on PyTorch Tensors:
:INCLUDE tensor/two_layer_net_tensor.pyIn 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 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. If we want to
compute gradients with respect to some Tensor, then we set requires_grad=True
when constructing that Tensor. Any PyTorch operations on that Tensor will cause
a computational graph to be constructed, allowing us to later perform backpropagation
through the graph. If x is a Tensor with requires_grad=True, then after
backpropagation x.grad will be another Tensor holding the gradient of x with
respect to some scalar value.
Sometimes you may wish to prevent PyTorch from building computational graphs when
performing certain operations on Tensors with requires_grad=True; for example
we usually don't want to backpropagate through the weight update steps when
training a neural network. In such scenarios we can use the torch.no_grad()
context manager to prevent the construction of a computational graph.
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:
:INCLUDE autograd/two_layer_net_autograd.pyUnder 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:
:INCLUDE autograd/two_layer_net_custom_function.pyPyTorch autograd looks a lot like TensorFlow: in both frameworks we define a computational graph, and use automatic differentiation to compute gradients. The biggest difference between the two is that TensorFlow's computational graphs are static and PyTorch uses dynamic computational graphs.
In TensorFlow, we define the computational graph once and then execute the same graph over and over again, possibly feeding different input data to the graph. In PyTorch, each forward pass defines a new computational graph.
Static graphs are nice because you can optimize the graph up front; for example a framework might decide to fuse some graph operations for efficiency, or to come up with a strategy for distributing the graph across many GPUs or many machines. If you are reusing the same graph over and over, then this potentially costly up-front optimization can be amortized as the same graph is rerun over and over.
One aspect where static and dynamic graphs differ is control flow. For some models
we may wish to perform different computation for each data point; for example a
recurrent network might be unrolled for different numbers of time steps for each
data point; this unrolling can be implemented as a loop. With a static graph the
loop construct needs to be a part of the graph; for this reason TensorFlow
provides operators such as tf.scan for embedding loops into the graph. With
dynamic graphs the situation is simpler: since we build graphs on-the-fly for
each example, we can use normal imperative flow control to perform computation
that differs for each input.
To contrast with the PyTorch autograd example above, here we use TensorFlow to fit a simple two-layer net:
:INCLUDE autograd/tf_two_layer_net.pyComputational 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, TensorFlow-Slim, and TFLearn 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:
:INCLUDE nn/two_layer_net_nn.pyUp to this point we have updated the weights of our models by manually mutating Tensors holding learnable parameters. This is not a huge burden for simple optimization algorithms like stochastic gradient descent, but in practice we often train neural networks using more sophisiticated 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:
:INCLUDE nn/two_layer_net_optim.pySometimes 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:
:INCLUDE nn/two_layer_net_module.pyAs 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 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:
:INCLUDE nn/dynamic_net.py