Learning PyTorch with Examples ****************************** **Author**: `Justin Johnson `_ This tutorial 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:: You can browse the individual examples at the :ref:`end of this page `. .. 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 `__, 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. Like numpy arrays, PyTorch Tensors do not know anything about deep learning or computational graphs or gradients; they are 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 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: Variables 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 `__ 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. We wrap our PyTorch Tensors in **Variable** objects; a Variable represents a node in a computational graph. If ``x`` is a Variable then ``x.data`` is a Tensor, and ``x.grad`` is another Variable holding the gradient of ``x`` with respect to some scalar value. PyTorch Variables have the same API as PyTorch Tensors: (almost) any operation that you can perform on a Tensor also works on Variables; the difference is that using Variables defines a computational graph, allowing you to automatically compute gradients. Here we use PyTorch Variables 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 Variables 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 TensorFlow: Static Graphs ------------------------- PyTorch 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: .. includenodoc:: /beginner/examples_autograd/tf_two_layer_net.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 `__, `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 Variables and computes output Variables, but may also hold internal state such as Variables 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 ``.data`` member for Variables 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 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 Variables and produces output Variables using other modules or other autograd operations on Variables. 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
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
`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