# 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, then the Jacobian-vector product would be computed, in this case the function additionally requires specifying grad_tensors. It should be a sequence of matching length, that contains the “vector” in the Jacobian-vector product, usually the 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)) – The “vector” in the Jacobian-vector product, usually 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 “vector” in Jacobian-vector product, usually 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) – The “vector” in the Jacobian-vector product. Usually 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.

Also functions as a decorator.

Example:

>>> x = torch.tensor([1], requires_grad=True)
...   y = x * 2
False
... def doubler(x):
...     return x * 2
>>> z = doubler(x)
False

class torch.autograd.enable_grad[source]

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

Also functions as a decorator.

Example:

>>> x = torch.tensor([1], requires_grad=True)
...     y = x * 2
True
>>> y.backward()
... def doubler(x):
...     return x * 2
...     z = doubler(x)
True

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
False


## 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 shares the same storage with the original one. In-place modifications on either of them will be seen, and may trigger errors in correctness checks. IMPORTANT NOTE: Previously, in-place size / stride / storage changes (such as resize_ / resize_as_ / set_ / transpose_) to the returned tensor also update the original tensor. Now, these in-place changes will not update the original tensor anymore, and will instead trigger an error. For sparse tensors: In-place indices / values changes (such as zero_ / copy_ / add_) to the returned tensor will not update the original tensor anymore, and will instead trigger an error.

detach_()

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

grad

This attribute is None by default and becomes a Tensor the first time a call to backward() computes gradients for self. The attribute will then contain the gradients computed and future calls to backward() will accumulate (add) gradients into it.

is_leaf

All Tensors that have requires_grad which is False will be leaf Tensors by convention.

For Tensors that have requires_grad which is True, they will be leaf Tensors if they were created by the user. This means that they are not the result of an operation and so grad_fn is None.

Only leaf Tensors will have their grad populated during a call to backward(). To get grad populated for non-leaf Tensors, you can use retain_grad().

Example:

>>> a = torch.rand(10, requires_grad=True)
>>> a.is_leaf
True
>>> b.is_leaf
False
# b was created by the operation that cast a cpu Tensor into a cuda Tensor
>>> c = torch.rand(10, requires_grad=True) + 2
>>> c.is_leaf
False
# c was created by the addition operation
>>> d = torch.rand(10).cuda()
>>> d.is_leaf
True
# d does not require gradients and so has no operation creating it (that is tracked by the autograd engine)
>>> e.is_leaf
True
# e requires gradients and has no operations creating it
>>> f = torch.rand(10, requires_grad=True, device="cuda")
>>> f.is_leaf
True
# f requires grad, has no operation creating it

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

requires_grad

Is True if gradients need to be computed for this Tensor, False otherwise.

Note

The fact that gradients need to be computed for a Tensor do not mean that the grad attribute will be populated, see is_leaf for more details.

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).

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. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

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.

torch.autograd.gradcheck(func, inputs, eps=1e-06, atol=1e-05, rtol=0.001, raise_exception=True, check_sparse_nnz=False)[source]

Check gradients computed via small finite differences against analytical gradients w.r.t. tensors in inputs that are of floating point type and with requires_grad=True.

The check between numerical and analytical gradients uses allclose().

Note

The default values are designed for input of double precision. This check will likely fail if input is of less precision, e.g., FloatTensor.

Warning

If any checked tensor in input has overlapping memory, i.e., different indices pointing to the same memory address (e.g., from torch.expand()), this check will likely fail because the numerical gradients computed by point perturbation at such indices will change values at all other indices that share the same memory address.

Parameters
• func (function) – a Python function that takes Tensor inputs and returns a Tensor or a tuple of Tensors

• inputs (tuple of Tensor or Tensor) – inputs to the function

• eps (float, optional) – perturbation for finite differences

• atol (float, optional) – absolute tolerance

• rtol (float, optional) – relative tolerance

• raise_exception (bool, optional) – indicating whether to raise an exception if the check fails. The exception gives more information about the exact nature of the failure. This is helpful when debugging gradchecks.

• check_sparse_nnz (bool, optional) – if True, gradcheck allows for SparseTensor input, and for any SparseTensor at input, gradcheck will perform check at nnz positions only.

Returns

True if all differences satisfy allclose condition

torch.autograd.gradgradcheck(func, inputs, grad_outputs=None, eps=1e-06, atol=1e-05, rtol=0.001, gen_non_contig_grad_outputs=False, raise_exception=True)[source]

Check gradients of gradients computed via small finite differences against analytical gradients w.r.t. tensors in inputs and grad_outputs that are of floating point type and with requires_grad=True.

This function checks that backpropagating through the gradients computed to the given grad_outputs are correct.

The check between numerical and analytical gradients uses allclose().

Note

The default values are designed for input and grad_outputs of double precision. This check will likely fail if they are of less precision, e.g., FloatTensor.

Warning

If any checked tensor in input and grad_outputs has overlapping memory, i.e., different indices pointing to the same memory address (e.g., from torch.expand()), this check will likely fail because the numerical gradients computed by point perturbation at such indices will change values at all other indices that share the same memory address.

Parameters
• func (function) – a Python function that takes Tensor inputs and returns a Tensor or a tuple of Tensors

• inputs (tuple of Tensor or Tensor) – inputs to the function

• grad_outputs (tuple of Tensor or Tensor, optional) – The gradients with respect to the function’s outputs.

• eps (float, optional) – perturbation for finite differences

• atol (float, optional) – absolute tolerance

• rtol (float, optional) – relative tolerance

• gen_non_contig_grad_outputs (bool, optional) – if grad_outputs is None and gen_non_contig_grad_outputs is True, the randomly generated gradient outputs are made to be noncontiguous

• raise_exception (bool, optional) – indicating whether to raise an exception if the check fails. The exception gives more information about the exact nature of the failure. This is helpful when debugging gradchecks.

Returns

True if all differences satisfy allclose condition

## 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.

self_cpu_time_total

Returns total time spent on CPU obtained as a sum of all self times across all the events.

table(sort_by=None, row_limit=100)[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.

Returns

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
...         model(x)


Forward-backward correlation

When viewing a profile created using emit_nvtx in the Nvidia Visual Profiler, correlating each backward-pass op with the corresponding forward-pass op can be difficult. To ease this task, emit_nvtx appends sequence number information to the ranges it generates.

During the forward pass, each function range is decorated with seq=<N>. seq is a running counter, incremented each time a new backward Function object is created and stashed for backward. Thus, the seq=<N> annotation associated with each forward function range tells you that if a backward Function object is created by this forward function, the backward object will receive sequence number N. During the backward pass, the top-level range wrapping each C++ backward Function’s apply() call is decorated with stashed seq=<M>. M is the sequence number that the backward object was created with. By comparing stashed seq numbers in backward with seq numbers in forward, you can track down which forward op created each backward Function.

Any functions executed during the backward pass are also decorated with seq=<N>. During default backward (with create_graph=False) this information is irrelevant, and in fact, N may simply be 0 for all such functions. Only the top-level ranges associated with backward Function objects’ apply() methods are useful, as a way to correlate these Function objects with the earlier forward pass.

Double-backward

If, on the other hand, a backward pass with create_graph=True is underway (in other words, if you are setting up for a double-backward), each function’s execution during backward is given a nonzero, useful seq=<N>. Those functions may themselves create Function objects to be executed later during double-backward, just as the original functions in the forward pass did. The relationship between backward and double-backward is conceptually the same as the relationship between forward and backward: The functions still emit current-sequence-number-tagged ranges, the Function objects they create still stash those sequence numbers, and during the eventual double-backward, the Function objects’ apply() ranges are still tagged with stashed seq numbers, which can be compared to seq numbers from the backward pass.

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

Opens an nvprof trace file and parses autograd annotations.

Parameters

path (str) – path to nvprof trace

## Anomaly detection¶

class torch.autograd.detect_anomaly[source]

Context-manager that enable anomaly detection for the autograd engine.

This does two things: - Running the forward pass with detection enabled will allow the backward pass to print the traceback of the forward operation that created the failing backward function. - Any backward computation that generate “nan” value will raise an error.

Example

>>> import torch
...     @staticmethod
...     def forward(ctx, inp):
...         return inp.clone()
...     @staticmethod
...     def backward(ctx, gO):
...         # Error during the backward pass
...         raise RuntimeError("Some error in backward")
...         return gO.clone()
>>> def run_fn(a):
...     out = MyFunc.apply(a)
...     return out.sum()
>>> inp = torch.rand(10, 10, requires_grad=True)
>>> out = run_fn(inp)
>>> out.backward()
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/your/pytorch/install/torch/tensor.py", line 93, in backward
File "/your/pytorch/install/torch/autograd/__init__.py", line 90, in backward
allow_unreachable=True)  # allow_unreachable flag
File "/your/pytorch/install/torch/autograd/function.py", line 76, in apply
return self._forward_cls.backward(self, *args)
File "<stdin>", line 8, in backward
RuntimeError: Some error in backward
...     inp = torch.rand(10, 10, requires_grad=True)
...     out = run_fn(inp)
...     out.backward()
Traceback of forward call that caused the error:
File "tmp.py", line 53, in <module>
out = run_fn(inp)
File "tmp.py", line 44, in run_fn
out = MyFunc.apply(a)
Traceback (most recent call last):
File "<stdin>", line 4, in <module>
File "/your/pytorch/install/torch/tensor.py", line 93, in backward
File "/your/pytorch/install/torch/autograd/__init__.py", line 90, in backward
allow_unreachable=True)  # allow_unreachable flag
File "/your/pytorch/install/torch/autograd/function.py", line 76, in apply
return self._forward_cls.backward(self, *args)
File "<stdin>", line 8, in backward
RuntimeError: Some error in backward

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

Context-manager that sets the anomaly detection for the autograd engine on or off.

set_detect_anomaly will enable or disable the autograd anomaly detection based on its argument mode. It can be used as a context-manager or as a function.

See detect_anomaly above for details of the anomaly detection behaviour.

Parameters

mode (bool) – Flag whether to enable anomaly detection (True), or disable (False).