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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. As of now, we only support autograd for floating point Tensor types ( half, float, double and bfloat16) and complex Tensor types (cfloat, cdouble).


Computes the sum of gradients of given tensors with respect to graph leaves.


Computes and returns the sum of gradients of outputs with respect to the inputs.

Forward-mode Automatic Differentiation


This API is in beta. Even though the function signatures are very unlikely to change, improved operator coverage is planned before we consider this stable.

Please see the forward-mode AD tutorial for detailed steps on how to use this API.


Context-manager that enables forward AD.


Associates a tensor value with a forward gradient, the tangent, to create a “dual tensor”, which is used to compute forward AD gradients.


Unpacks a “dual tensor” to get both its Tensor value and its forward AD gradient.

Functional higher level API


This API is in beta. Even though the function signatures are very unlikely to change, major improvements to performances are planned before we consider this stable.

This section contains the higher level API for the autograd that builds on the basic API above and allows you to compute jacobians, hessians, etc.

This API works with user-provided functions that take only Tensors as input and return only Tensors. If your function takes other arguments that are not Tensors or Tensors that don’t have requires_grad set, you can use a lambda to capture them. For example, for a function f that takes three inputs, a Tensor for which we want the jacobian, another tensor that should be considered constant and a boolean flag as f(input, constant, flag=flag) you can use it as functional.jacobian(lambda x: f(x, constant, flag=flag), input).


Function that computes the Jacobian of a given function.


Function that computes the Hessian of a given scalar function.


Function that computes the dot product between a vector v and the Jacobian of the given function at the point given by the inputs.


Function that computes the dot product between the Jacobian of the given function at the point given by the inputs and a vector v.


Function that computes the dot product between a vector v and the Hessian of a given scalar function at the point given by the inputs.


Function that computes the dot product between the Hessian of a given scalar function and a vector v at the point given by the inputs.

Locally disabling gradient computation

See Locally disabling gradient computation for more information on the differences between no-grad and inference mode as well as other related mechanisms that may be confused with the two.


Context-manager that disabled gradient calculation.


Context-manager that enables gradient calculation.


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


Context-manager that enables or disables inference mode

Default gradient layouts

When a non-sparse param receives a non-sparse gradient during torch.autograd.backward() or torch.Tensor.backward() param.grad is accumulated as follows.

If param.grad is initially None:

  1. If param’s memory is non-overlapping and dense, .grad is created with strides matching param (thus matching param’s layout).

  2. Otherwise, .grad is created with rowmajor-contiguous strides.

If param already has a non-sparse .grad attribute:

  1. If create_graph=False, backward() accumulates into .grad in-place, which preserves its strides.

  2. If create_graph=True, backward() replaces .grad with a new tensor .grad + new grad, which attempts (but does not guarantee) matching the preexisting .grad’s strides.

The default behavior (letting .grads be None before the first backward(), such that their layout is created according to 1 or 2, and retained over time according to 3 or 4) is recommended for best performance. Calls to model.zero_grad() or optimizer.zero_grad() will not affect .grad layouts.

In fact, resetting all .grads to None before each accumulation phase, e.g.:

for iterations...
    for param in model.parameters():
        param.grad = None

such that they’re recreated according to 1 or 2 every time, is a valid alternative to model.zero_grad() or optimizer.zero_grad() that may improve performance for some networks.

Manual gradient layouts

If you need manual control over .grad’s strides, assign param.grad = a zeroed tensor with desired strides before the first backward(), and never reset it to None. 3 guarantees your layout is preserved as long as create_graph=False. 4 indicates your layout is likely preserved even if create_graph=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)


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)

Tensor autograd functions


This attribute is None by default and becomes a Tensor the first time a call to backward() computes gradients for self.


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


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

torch.Tensor.backward([gradient, …])

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


Returns a new Tensor, detached from the current graph.


Detaches the Tensor from the graph that created it, making it a leaf.


Registers a backward hook.


Enables this Tensor to have their grad populated during backward().


class torch.autograd.Function(*args, **kwargs)[source]

Base class to create custom autograd.Function

To create a custom autograd.Function, subclass this class and implement the forward() and backward() static methods. Then, to use your custom op in the forward pass, call the class method apply. Do not call forward() directly.

To ensure correctness and best performance, make sure you are calling the correct methods on ctx and validating your backward function using torch.autograd.gradcheck().

See Extending torch.autograd for more details on how to use this class.


>>> class Exp(Function):
>>>     @staticmethod
>>>     def forward(ctx, i):
>>>         result = i.exp()
>>>         ctx.save_for_backward(result)
>>>         return result
>>>     @staticmethod
>>>     def backward(ctx, grad_output):
>>>         result, = ctx.saved_tensors
>>>         return grad_output * result
>>> # Use it by calling the apply method:
>>> output = Exp.apply(input)


Performs the operation.


Defines a formula for differentiating the operation with backward mode automatic differentiation (alias to the vjp function).


Defines a formula for differentiating the operation with forward mode automatic differentiation.

Context method mixins

When creating a new Function, the following methods are available to ctx.


Marks given tensors as modified in an in-place operation.


Marks outputs as non-differentiable.


Saves given tensors for a future call to backward().


Sets whether to materialize output grad tensors.

Numerical gradient checking


Check gradients computed via small finite differences against analytical gradients w.r.t.


Check gradients of gradients computed via small finite differences against analytical gradients w.r.t.


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, record_shapes=False, with_flops=False, profile_memory=False, with_stack=False, with_modules=False, use_kineto=False, use_cpu=True)[source]

Context manager that manages autograd profiler state and holds a summary of results. Under the hood it just records events of functions being executed in C++ and exposes those events to Python. You can wrap any code into it and it will only report runtime of PyTorch functions. Note: profiler is thread local and is automatically propagated into the async tasks

  • enabled (bool, optional) – Setting this to False makes this context manager a no-op.

  • use_cuda (bool, optional) – Enables timing of CUDA events as well using the cudaEvent API. Adds approximately 4us of overhead to each tensor operation.

  • record_shapes (bool, optional) – If shapes recording is set, information about input dimensions will be collected. This allows one to see which dimensions have been used under the hood and further group by them using prof.key_averages(group_by_input_shape=True). Please note that shape recording might skew your profiling data. It is recommended to use separate runs with and without shape recording to validate the timing. Most likely the skew will be negligible for bottom most events (in a case of nested function calls). But for higher level functions the total self cpu time might be artificially increased because of the shape collection.

  • with_flops (bool, optional) – If with_flops is set, the profiler will estimate the FLOPs (floating point operations) value using the operator’s input shape. This allows one to estimate the hardware performance. Currently, this option only works for the matrix multiplication and 2D convolution operators.

  • profile_memory (bool, optional) – track tensor memory allocation/deallocation.

  • with_stack (bool, optional) – record source information (file and line number) for the ops.

  • with_modules (bool) – record module hierarchy (including function names) corresponding to the callstack of the op. e.g. If module A’s forward call’s module B’s forward which contains an aten::add op, then aten::add’s module hierarchy is A.B Note that this support exist, at the moment, only for TorchScript models and not eager mode models.

  • use_kineto (bool, optional) – experimental, enable profiling with Kineto profiler.

  • use_cpu (bool, optional) – profile CPU events; setting to False requires use_kineto=True and can be used to lower the overhead for GPU-only profiling.


>>> x = torch.randn((1, 1), requires_grad=True)
>>> with torch.autograd.profiler.profile() as prof:
>>>     for _ in range(100):  # any normal python code, really!
>>>         y = x ** 2
>>          y.backward()
>>> # NOTE: some columns were removed for brevity
>>> print(prof.key_averages().table(sort_by="self_cpu_time_total"))
-----------------------------------  ---------------  ---------------  ---------------
Name                                 Self CPU total   CPU time avg     Number of Calls
-----------------------------------  ---------------  ---------------  ---------------
mul                                  32.048ms         32.048ms         200
pow                                  27.041ms         27.041ms         200
PowBackward0                         9.727ms          55.483ms         100
torch::autograd::AccumulateGrad      9.148ms          9.148ms          100
torch::autograd::GraphRoot           691.816us        691.816us        100
-----------------------------------  ---------------  ---------------  ---------------


Exports an EventList as a Chrome tracing tools file.


Averages all function events over their keys.


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


Averages all events.

class torch.autograd.profiler.emit_nvtx(enabled=True, record_shapes=False)[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.

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

  • record_shapes (bool, optional, default=False) – If record_shapes=True, the nvtx range wrapping each autograd op will append information about the sizes of Tensor arguments received by that op, in the following format: [[arg0.size(0), arg0.size(1), ...], [arg1.size(0), arg1.size(1), ...], ...] Non-tensor arguments will be represented by []. Arguments will be listed in the order they are received by the backend op. Please note that this order may not match the order in which those arguments were passed on the Python side. Also note that shape recording may increase the overhead of nvtx range creation.


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


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.


Opens an nvprof trace file and parses autograd annotations.

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.


This mode should be enabled only for debugging as the different tests will slow down your program execution.


>>> import torch
>>> from torch import autograd
>>> class MyFunc(autograd.Function):
...     @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
        torch.autograd.backward(self, gradient, retain_graph, create_graph)
      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
>>> with autograd.detect_anomaly():
...     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
        torch.autograd.backward(self, gradient, retain_graph, create_graph)
      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.


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

Saved tensors default hooks

Some operations need intermediary results to be saved during the forward pass in order to execute the backward pass. You can define how these saved tensors should be packed / unpacked using hooks. A common application is to trade compute for memory by saving those intermediary results to disk or to CPU instead of leaving them on the GPU. This is especially useful if you notice your model fits on GPU during evaluation, but not training. Also see Hooks for saved tensors.

class torch.autograd.graph.saved_tensors_hooks(pack_hook, unpack_hook)[source]

Context-manager that sets a pair of pack / unpack hooks for saved tensors.

Use this context-manager to define how intermediary results of an operation should be packed before saving, and unpacked on retrieval.

In that context, the pack_hook function will be called everytime an operation saves a tensor for backward (this includes intermediary results saved using save_for_backward() but also those recorded by a PyTorch-defined operation). The output of pack_hook is then stored in the computation graph instead of the original tensor.

The unpack_hook is called when the saved tensor needs to be accessed, namely when executing torch.Tensor.backward() or torch.autograd.grad(). It takes as argument the packed object returned by pack_hook and should return a tensor which has the same content as the original tensor (passed as input to the corresponding pack_hook).

The hooks should have the following signatures:

pack_hook(tensor: Tensor) -> Any

unpack_hook(Any) -> Tensor

where the return value of pack_hook is a valid input to unpack_hook.

In general, you want unpack_hook(pack_hook(t)) to be equal to t in terms of value, size, dtype and device.


>>> def pack_hook(x):
...     print("Packing", x)
...     return x
>>> def unpack_hook(x):
...     print("Unpacking", x)
...     return x
>>> a = torch.ones(5, requires_grad=True)
>>> b = torch.ones(5, requires_grad=True) * 2
>>> with torch.autograd.graph.saved_tensors_hooks(pack_hook, unpack_hook):
...     y = a * b
Packing tensor([1., 1., 1., 1., 1.])
Packing tensor([2., 2., 2., 2., 2.])
>>> y.sum().backward()
Unpacking tensor([1., 1., 1., 1., 1.])
Unpacking tensor([2., 2., 2., 2., 2.])


Performing an inplace operation on the input to either hooks may lead to undefined behavior.


Only one pair of hooks is allowed at a time. When recursively nesting this context-manager, only the inner-most pair of hooks will be applied.

class torch.autograd.graph.save_on_cpu(pin_memory=False)[source]

Context-manager under which tensors saved by the forward pass will be stored on cpu, then retrieved for backward.

When performing operations within this context manager, intermediary results saved in the graph during the forward pass will be moved to CPU, then copied back to the original device when needed for the backward pass. If the graph was already on CPU, no tensor copy is performed.

Use this context-manager to trade compute for GPU memory usage (e.g. when your model doesn’t fit in GPU memory during training).


pin_memory (bool) – If True tensors will be saved to CPU pinned memory during packing and copied to GPU asynchronously during unpacking. Defaults to False. Also see Use pinned memory buffers.


>>> a = torch.randn(5, requires_grad=True, device="cuda")
>>> b = torch.randn(5, requires_grad=True, device="cuda")
>>> c = torch.randn(5, requires_grad=True, device="cuda")
>>> def f(a, b, c):
...     prod_1 = a * b           # a and b are saved on GPU
...     with torch.autograd.graph.save_on_cpu():
...         prod_2 = prod_1 * c  # prod_1 and c are saved on CPU
...     y = prod_2 * a           # prod_2 and a are saved on GPU
...     return y
>>> y = f(a, b, c)
>>> del a, b, c  # for illustration only
>>> # the content of a, b, and prod_2 are still alive on GPU
>>> # the content of prod_1 and c only live on CPU
>>> y.sum().backward()  # all CPU tensors are moved back to GPU, for backward
>>> # all intermediary tensors are released (deleted) after the call to backward


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