Autograd mechanics

This note will present an overview of how autograd works and records the operations. It’s not strictly necessary to understand all this, but we recommend getting familiar with it, as it will help you write more efficient, cleaner programs, and can aid you in debugging.

Excluding subgraphs from backward

Every Variable has two flags: requires_grad and volatile. They both allow for fine grained exclusion of subgraphs from gradient computation and can increase efficiency.

requires_grad

If there’s a single input to an operation that requires gradient, its output will also require gradient. Conversely, only if all inputs don’t require gradient, the output also won’t require it. Backward computation is never performed in the subgraphs, where all Variables didn’t require gradients.

>>> x = Variable(torch.randn(5, 5))
>>> y = Variable(torch.randn(5, 5))
>>> z = Variable(torch.randn(5, 5), requires_grad=True)
>>> a = x + y
>>> a.requires_grad
False
>>> b = a + z
>>> b.requires_grad
True

This is especially useful when you want to freeze part of your model, or you know in advance that you’re not going to use gradients w.r.t. some parameters. For example if you want to finetune a pretrained CNN, it’s enough to switch the requires_grad flags in the frozen base, and no intermediate buffers will be saved, until the computation gets to the last layer, where the affine transform will use weights that require gradient, and the output of the network will also require them.

model = torchvision.models.resnet18(pretrained=True)
for param in model.parameters():
    param.requires_grad = False
# Replace the last fully-connected layer
# Parameters of newly constructed modules have requires_grad=True by default
model.fc = nn.Linear(512, 100)

# Optimize only the classifier
optimizer = optim.SGD(model.fc.parameters(), lr=1e-2, momentum=0.9)

volatile

Volatile is recommended for purely inference mode, when you’re sure you won’t be even calling .backward(). It’s more efficient than any other autograd setting - it will use the absolute minimal amount of memory to evaluate the model. volatile also determines that requires_grad is False.

Volatile differs from requires_grad in how the flag propagates. If there’s even a single volatile input to an operation, its output is also going to be volatile. Volatility spreads accross the graph much easier than non-requiring gradient - you only need a single volatile leaf to have a volatile output, while you need all leaves to not require gradient to have an output the doesn’t require gradient. Using volatile flag you don’t need to change any settings of your model parameters to use it for inference. It’s enough to create a volatile input, and this will ensure that no intermediate states are saved.

>>> regular_input = Variable(torch.randn(1, 3, 227, 227))
>>> volatile_input = Variable(torch.randn(1, 3, 227, 227), volatile=True)
>>> model = torchvision.models.resnet18(pretrained=True)
>>> model(regular_input).requires_grad
True
>>> model(volatile_input).requires_grad
False
>>> model(volatile_input).volatile
True
>>> model(volatile_input).creator is None
True

How autograd encodes the history

Autograd is reverse automatic differentiation system. Conceptually, autograd records a graph recording all of the operations that created the data as you execute operations, giving you a directed acyclic graph whose leaves are the input variables and roots are the output variables. By tracing this graph from roots to leaves, you can automatically compute the gradients using the chain rule.

Internally, autograd represents this graph as a graph of Function objects (really expressions), which can be apply() ed to compute the result of evaluating the graph. When computing the forwards pass, autograd simultaneously performs the requested computations and builds up a graph representing the function that computes the gradient (the .grad_fn attribute of each Variable is an entry point into this graph). When the forwards pass is completed, we evaluate this graph in the backwards pass to compute the gradients.

An important thing to note is that the graph is recreated from scratch at every iteration, and this is exactly what allows for using arbitrary Python control flow statements, that can change the overall shape and size of the graph at every iteration. You don’t have to encode all possible paths before you launch the training - what you run is what you differentiate.

In-place operations on Variables

Supporting in-place operations in autograd is a hard matter, and we discourage their use in most cases. Autograd’s aggressive buffer freeing and reuse makes it very efficient and there are very few occasions when in-place operations actually lower memory usage by any significant amount. Unless you’re operating under heavy memory pressure, you might never need to use them.

There are two main reasons that limit the applicability of in-place operations:

  1. Overwriting values required to compute gradients. This is why variables don’t support log_. Its gradient formula requires the original input, and while it is possible to recreate it by computing the inverse operation, it is numerically unstable, and requires additional work that often defeats the purpose of using these functions.
  2. Every in-place operation actually requires the implementation to rewrite the computational graph. Out-of-place versions simply allocate new objects and keep references to the old graph, while in-place operations, require changing the creator of all inputs to the Function representing this operation. This can be tricky, especially if there are many Variables that reference the same storage (e.g. created by indexing or transposing), and in-place functions will actually raise an error if the storage of modified inputs is referenced by any other Variable.

In-place correctness checks

Every variable keeps a version counter, that is incremented every time it’s marked dirty in any operation. When a Function saves any tensors for backward, a version counter of their containing Variable is saved as well. Once you access self.saved_tensors it is checked, and if it’s greater than the saved value an error is raised.