# Automatic differentiation package - torch.autograd¶

torch.autograd provides classes and functions implementing automatic differentiation of arbitrary scalar valued functions. It requires minimal changes to the existing code - you only need to declare Tensor s for which gradients should be computed with the requires_grad=True keyword.

torch.autograd.backward(tensors, grad_tensors=None, retain_graph=None, create_graph=False, grad_variables=None)[source]

Computes the sum of gradients of given tensors w.r.t. graph leaves.

The graph is differentiated using the chain rule. If any of tensors are non-scalar (i.e. their data has more than one element) and require gradient, the function additionally requires specifying grad_tensors. It should be a sequence of matching length, that contains gradient of the differentiated function w.r.t. corresponding tensors (None is an acceptable value for all tensors that don’t need gradient tensors).

This function accumulates gradients in the leaves - you might need to zero them before calling it.

Parameters: tensors (sequence of Tensor) – Tensors of which the derivative will be computed. grad_tensors (sequence of (Tensor or None)) – Gradients w.r.t. each element of corresponding tensors. None values can be specified for scalar Tensors or ones that don’t require grad. If a None value would be acceptable for all grad_tensors, then this argument is optional. retain_graph (bool, optional) – If False, the graph used to compute the grad will be freed. Note that in nearly all cases setting this option to True is not needed and often can be worked around in a much more efficient way. Defaults to the value of create_graph. create_graph (bool, optional) – If True, graph of the derivative will be constructed, allowing to compute higher order derivative products. Defaults to False.
torch.autograd.grad(outputs, inputs, grad_outputs=None, retain_graph=None, create_graph=False, only_inputs=True, allow_unused=False)[source]

Computes and returns the sum of gradients of outputs w.r.t. the inputs.

grad_outputs should be a sequence of length matching output containing the pre-computed gradients w.r.t. each of the outputs. If an output doesn’t require_grad, then the gradient can be None).

If only_inputs is True, the function will only return a list of gradients w.r.t the specified inputs. If it’s False, then gradient w.r.t. all remaining leaves will still be computed, and will be accumulated into their .grad attribute.

Parameters: outputs (sequence of Tensor) – outputs of the differentiated function. inputs (sequence of Tensor) – Inputs w.r.t. which the gradient will be returned (and not accumulated into .grad). grad_outputs (sequence of Tensor) – Gradients w.r.t. each output. None values can be specified for scalar Tensors or ones that don’t require grad. If a None value would be acceptable for all grad_tensors, then this argument is optional. Default: None. retain_graph (bool, optional) – If False, the graph used to compute the grad will be freed. Note that in nearly all cases setting this option to True is not needed and often can be worked around in a much more efficient way. Defaults to the value of create_graph. create_graph (bool, optional) – If True, graph of the derivative will be constructed, allowing to compute higher order derivative products. Default: False. allow_unused (bool, optional) – If False, specifying inputs that were not used when computing outputs (and therefore their grad is always zero) is an error. Defaults to False.

class torch.autograd.no_grad[source]

Disabling gradient calculation is useful for inference, when you are sure that you will not call Tensor.backward(). It will reduce memory consumption for computations that would otherwise have requires_grad=True. In this mode, the result of every computation will have requires_grad=False, even when the inputs have requires_grad=True.

Example:

>>> x = torch.tensor([1], requires_grad=True)
...   y = x * 2
False

class torch.autograd.enable_grad[source]

Enables gradient calculation inside a no_grad context. This has no effect outside of no_grad.

Example:

>>> x = torch.tensor([1], requires_grad=True)
...     y = x * 2
True
>>> y.backward()

class torch.autograd.set_grad_enabled(mode)[source]

Context-manager that sets gradient calculation to on or off.

set_grad_enabled will enable or disable grads based on its argument mode. It can be used as a context-manager or as a function.

Parameters: mode (bool) – Flag whether to enable grad (True), or disable (False). This can be used to conditionally enable gradients.

Example:

>>> x = torch.tensor([1], requires_grad=True)
>>> is_train = False
...   y = x * 2
False
>>> y = x * 2
True
>>> y = x * 2
True


## In-place operations on Tensors¶

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.

### In-place correctness checks¶

All Tensor s keep track of in-place operations applied to them, and if the implementation detects that a tensor was saved for backward in one of the functions, but it was modified in-place afterwards, an error will be raised once backward pass is started. This ensures that if you’re using in-place functions and not seeing any errors, you can be sure that the computed gradients are correct.

## Variable (deprecated)¶

Warning

The Variable API has been deprecated: Variables are no longer necessary to use autograd with tensors. Autograd automatically supports Tensors with requires_grad set to True. Below please find a quick guide on what has changed:

• Variable(tensor) and Variable(tensor, requires_grad) still work as expected, but they return Tensors instead of Variables.
• var.data is the same thing as tensor.data.
• Methods such as var.backward(), var.detach(), var.register_hook() now work on tensors with the same method names.

In addition, one can now create tensors with requires_grad=True using factory methods such as torch.randn(), torch.zeros(), torch.ones(), and others like the following:

autograd_tensor = torch.randn((2, 3, 4), requires_grad=True)

class torch.Tensor
backward(gradient=None, retain_graph=None, create_graph=False)[source]

Computes the gradient of current tensor w.r.t. graph leaves.

The graph is differentiated using the chain rule. If the tensor is non-scalar (i.e. its data has more than one element) and requires gradient, the function additionally requires specifying gradient. It should be a tensor of matching type and location, that contains the gradient of the differentiated function w.r.t. self.

This function accumulates gradients in the leaves - you might need to zero them before calling it.

Parameters: gradient (Tensor or None) – Gradient w.r.t. the tensor. If it is a tensor, it will be automatically converted to a Tensor that does not require grad unless create_graph is True. None values can be specified for scalar Tensors or ones that don’t require grad. If a None value would be acceptable then this argument is optional. retain_graph (bool, optional) – If False, the graph used to compute the grads will be freed. Note that in nearly all cases setting this option to True is not needed and often can be worked around in a much more efficient way. Defaults to the value of create_graph. create_graph (bool, optional) – If True, graph of the derivative will be constructed, allowing to compute higher order derivative products. Defaults to False.
detach()

Returns a new Tensor, detached from the current graph.

The result will never require gradient.

Note

Returned Tensor uses the same data tensor as the original one. In-place modifications on either of them will be seen, and may trigger errors in correctness checks.

detach_()

Detaches the Tensor from the graph that created it, making it a leaf. Views cannot be detached in-place.

register_hook(hook)[source]

Registers a backward hook.

The hook will be called every time a gradient with respect to the Tensor is computed. The hook should have the following signature:

hook(grad) -> Tensor or None


The hook should not modify its argument, but it can optionally return a new gradient which will be used in place of grad.

This function returns a handle with a method handle.remove() that removes the hook from the module.

Example

>>> v = torch.tensor([0., 0., 0.], requires_grad=True)
>>> v.backward(torch.tensor([1., 2., 3.]))

2 4 6

[torch.FloatTensor of size (3,)]

>>> h.remove()  # removes the hook

retain_grad()[source]

Enables .grad attribute for non-leaf Tensors.

## Function¶

class torch.autograd.Function[source]

Records operation history and defines formulas for differentiating ops.

Every operation performed on Tensor s creates a new function object, that performs the computation, and records that it happened. The history is retained in the form of a DAG of functions, with edges denoting data dependencies (input <- output). Then, when backward is called, the graph is processed in the topological ordering, by calling backward() methods of each Function object, and passing returned gradients on to next Function s.

Normally, the only way users interact with functions is by creating subclasses and defining new operations. This is a recommended way of extending torch.autograd.

Each function object is meant to be used only once (in the forward pass).

Variables: requires_grad – Boolean indicating whether the backward() will ever need to be called.

Examples:

>>> class Exp(Function):
>>>
>>>     @staticmethod
>>>     def forward(ctx, i):
>>>         result = i.exp()
>>>         ctx.save_for_backward(result)
>>>         return result
>>>
>>>     @staticmethod
>>>         result, = ctx.saved_tensors

static backward(ctx, *grad_outputs)[source]

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs did forward() return, and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input.

The context can be used to retrieve tensors saved during the forward pass.

static forward(ctx, *args, **kwargs)[source]

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store tensors that can be then retrieved during the backward pass.

## Profiler¶

Autograd includes a profiler that lets you inspect the cost of different operators inside your model - both on the CPU and GPU. There are two modes implemented at the moment - CPU-only using profile. and nvprof based (registers both CPU and GPU activity) using emit_nvtx.

class torch.autograd.profiler.profile(enabled=True, use_cuda=False)[source]

Context manager that manages autograd profiler state and holds a summary of results.

Parameters: enabled (bool, optional) – Setting this to False makes this context manager a no-op. Default: True. use_cuda (bool, optional) – Enables timing of CUDA events as well using the cudaEvent API. Adds approximately 4us of overhead to each tensor operation. Default: False

Example

>>> x = torch.randn((1, 1), requires_grad=True)
...     y = x ** 2
...     y.backward()
>>> # NOTE: some columns were removed for brevity
... print(prof)
-------------------------------------  ---------------  ---------------
Name                                          CPU time        CUDA time
-------------------------------------  ---------------  ---------------
PowConstant                                  142.036us          0.000us
PowConstantBackward                          184.228us          0.000us
MulConstant                                   50.288us          0.000us
PowConstant                                   28.439us          0.000us
Mul                                           20.154us          0.000us

export_chrome_trace(path)[source]

Exports an EventList as a Chrome tracing tools file.

The checkpoint can be later loaded and inspected under chrome://tracing URL.

Parameters: path (str) – Path where the trace will be written.
key_averages()[source]

Averages all function events over their keys.

Returns: An EventList containing FunctionEventAvg objects.
table(sort_by=None)[source]

Prints an EventList as a nicely formatted table.

Parameters: sort_by (str, optional) – Attribute used to sort entries. By default they are printed in the same order as they were registered. Valid keys include: cpu_time, cuda_time, cpu_time_total, cuda_time_total, count. A string containing the table.
total_average()[source]

Averages all events.

Returns: A FunctionEventAvg object.
class torch.autograd.profiler.emit_nvtx(enabled=True)[source]

Context manager that makes every autograd operation emit an NVTX range.

It is useful when running the program under nvprof:

nvprof --profile-from-start off -o trace_name.prof -- <regular command here>


Unfortunately, there’s no way to force nvprof to flush the data it collected to disk, so for CUDA profiling one has to use this context manager to annotate nvprof traces and wait for the process to exit before inspecting them. Then, either NVIDIA Visual Profiler (nvvp) can be used to visualize the timeline, or torch.autograd.profiler.load_nvprof() can load the results for inspection e.g. in Python REPL.

Parameters: enabled (bool, optional) – Setting this to False makes this context manager a no-op. Default: True.

Example

>>> with torch.cuda.profiler.profile():
...     model(x) # Warmup CUDA memory allocator and profiler

torch.autograd.profiler.load_nvprof(path)[source]