# Source code for torch.autograd.function

```
import torch
import torch._C as _C
from torch._C import _functions
import torch.utils.hooks as hooks
from torch._six import with_metaclass
import functools
import warnings
from collections import OrderedDict
from typing import Any, List, Optional
# Formerly known as: _ContextMethodMixin
class FunctionCtx(object):
def save_for_backward(self, *tensors: torch.Tensor):
r"""Saves given tensors for a future call to :func:`~Function.backward`.
``save_for_backward`` should be called at most once, only from inside the
:func:`forward` method, and only with tensors.
All tensors intended to be used in the backward pass should be saved
with ``save_for_backward`` (as opposed to directly on ``ctx``) to prevent
incorrect gradients and memory leaks, and enable the application of saved
tensor hooks. See :class:`torch.autograd.graph.saved_tensors_hooks`.
In :func:`backward`, saved tensors can be accessed through the :attr:`saved_tensors`
attribute. Before returning them to the user, a check is made to ensure
they weren't used in any in-place operation that modified their content.
Arguments can also be ``None``. This is a no-op.
See :ref:`extending-autograd` for more details on how to use this method.
Example::
>>> class Func(Function):
>>> @staticmethod
>>> def forward(ctx, x: torch.Tensor, y: torch.Tensor, z: int):
>>> w = x * y * z
>>> out = x * y + y * z + w
>>> ctx.save_for_backward(x, y, w, out)
>>> ctx.z = z # z is not a tensor
>>> return out
>>>
>>> @staticmethod
>>> def backward(ctx, grad_out):
>>> x, y, w, out = ctx.saved_tensors
>>> z = ctx.z
>>> gx = grad_out * (y + y * z)
>>> gy = grad_out * (x + z + x * z)
>>> gz = None
>>> return gx, gy, gz
>>>
>>> a = torch.tensor(1., requires_grad=True, dtype=torch.double)
>>> b = torch.tensor(2., requires_grad=True, dtype=torch.double)
>>> c = 4
>>> d = Func.apply(a, b, c)
"""
self.to_save = tensors
def save_for_forward(self, *tensors: torch.Tensor):
r"""Saves given tensors for a future call to :func:`~Function.jvp`.
``save_for_forward`` should be only called once, from inside the :func:`forward`
method, and only be called with tensors.
In :func:`jvp`, saved objects can be accessed through the :attr:`saved_tensors`
attribute.
Arguments can also be ``None``. This is a no-op.
See :ref:`extending-autograd` for more details on how to use this method.
Example::
>>> class Func(torch.autograd.Function):
>>> @staticmethod
>>> def forward(ctx, x: torch.Tensor, y: torch.Tensor, z: int):
>>> ctx.save_for_backward(x, y)
>>> ctx.save_for_forward(x, y)
>>> ctx.z = z
>>> return x * y * z
>>>
>>> @staticmethod
>>> def jvp(ctx, x_t, y_t, _):
>>> x, y = ctx.saved_tensors
>>> z = ctx.z
>>> return z * (y * x_t + x * y_t)
>>>
>>> @staticmethod
>>> def vjp(ctx, grad_out):
>>> x, y = ctx.saved_tensors
>>> z = ctx.z
>>> return z * grad_out * y, z * grad_out * x, None
>>>
>>> a = torch.tensor(1., requires_grad=True, dtype=torch.double)
>>> t = torch.tensor(1., dtype=torch.double)
>>> b = torch.tensor(2., requires_grad=True, dtype=torch.double)
>>> c = 4
>>>
>>> with fwAD.dual_level():
>>> a_dual = fwAD.make_dual(a, t)
>>> d = Func.apply(a_dual, b, c)
"""
for tensor in tensors:
assert isinstance(tensor, torch.Tensor) or tensor is None, (
"save_for_forward expects all arguments to be tensors; you should "
"save non-tensors as attributes on ctx.")
self.saved_for_forward = tensors
def mark_dirty(self, *args: torch.Tensor):
r"""Marks given tensors as modified in an in-place operation.
**This should be called at most once, only from inside the**
:func:`forward` **method, and all arguments should be inputs.**
Every tensor that's been modified in-place in a call to :func:`forward`
should be given to this function, to ensure correctness of our checks.
It doesn't matter whether the function is called before or after
modification.
Examples::
>>> class Inplace(Function):
>>> @staticmethod
>>> def forward(ctx, x):
>>> x_npy = x.numpy() # x_npy shares storage with x
>>> x_npy += 1
>>> ctx.mark_dirty(x)
>>> return x
>>>
>>> @staticmethod
>>> @once_differentiable
>>> def backward(ctx, grad_output):
>>> return grad_output
>>>
>>> a = torch.tensor(1., requires_grad=True, dtype=torch.double).clone()
>>> b = a * a
>>> Inplace.apply(a) # This would lead to wrong gradients!
>>> # but the engine would not know unless we mark_dirty
>>> b.backward() # RuntimeError: one of the variables needed for gradient
>>> # computation has been modified by an inplace operation
"""
self.dirty_tensors = args
def mark_shared_storage(self, *pairs):
warnings.warn(
'mark_shared_storage is deprecated. '
'Tensors with shared storages are automatically tracked. Note '
'that calls to `set_()` are not tracked')
def mark_non_differentiable(self, *args: torch.Tensor):
r"""Marks outputs as non-differentiable.
**This should be called at most once, only from inside the**
:func:`forward` **method, and all arguments should be tensor outputs.**
This will mark outputs as not requiring gradients, increasing the
efficiency of backward computation. You still need to accept a gradient
for each output in :meth:`~Function.backward`, but it's always going to
be a zero tensor with the same shape as the shape of a corresponding
output.
This is used e.g. for indices returned from a sort. See example::
>>> class Func(Function):
>>> @staticmethod
>>> def forward(ctx, x):
>>> sorted, idx = x.sort()
>>> ctx.mark_non_differentiable(idx)
>>> ctx.save_for_backward(x, idx)
>>> return sorted, idx
>>>
>>> @staticmethod
>>> @once_differentiable
>>> def backward(ctx, g1, g2): # still need to accept g2
>>> x, idx = ctx.saved_tensors
>>> grad_input = torch.zeros_like(x)
>>> grad_input.index_add_(0, idx, g1)
>>> return grad_input
"""
self.non_differentiable = args
def set_materialize_grads(self, value: bool):
r"""Sets whether to materialize output grad tensors. Default is ``True``.
**This should be called only from inside the** :func:`forward` **method**
If ``True``, undefined output grad tensors will be expanded to tensors full
of zeros prior to calling the :func:`backward` method.
Example::
>>> class SimpleFunc(Function):
>>> @staticmethod
>>> def forward(ctx, x):
>>> return x.clone(), x.clone()
>>>
>>> @staticmethod
>>> @once_differentiable
>>> def backward(ctx, g1, g2):
>>> return g1 + g2 # No check for None necessary
>>>
>>> # We modify SimpleFunc to handle non-materialized grad outputs
>>> class Func(Function):
>>> @staticmethod
>>> def forward(ctx, x):
>>> ctx.set_materialize_grads(False)
>>> ctx.save_for_backward(x)
>>> return x.clone(), x.clone()
>>>
>>> @staticmethod
>>> @once_differentiable
>>> def backward(ctx, g1, g2):
>>> x, = ctx.saved_tensors
>>> grad_input = torch.zeros_like(x)
>>> if g1 is not None: # We must check for None now
>>> grad_input += g1
>>> if g2 is not None:
>>> grad_input += g2
>>> return grad_input
>>>
>>> a = torch.tensor(1., requires_grad=True)
>>> b, _ = Func.apply(a) # induces g2 to be undefined
"""
self.materialize_grads = value
# DO NOT USE: This is only defined to be able to load old serialized models
_ContextMethodMixin = FunctionCtx
class _HookMixin(object):
@staticmethod
def _register_hook(backward_hooks, hook):
if backward_hooks is None:
backward_hooks = OrderedDict()
handle = hooks.RemovableHandle(backward_hooks)
backward_hooks[handle.id] = hook
return backward_hooks, handle
class BackwardCFunction(_C._FunctionBase, FunctionCtx, _HookMixin):
def apply(self, *args):
# _forward_cls is defined by derived class
# The user should define either backward or vjp but never both.
backward_fn = self._forward_cls.backward # type: ignore[attr-defined]
vjp_fn = self._forward_cls.vjp # type: ignore[attr-defined]
if backward_fn is not Function.backward and vjp_fn is not Function.vjp:
raise RuntimeError("Implementing both 'backward' and 'vjp' for a custom "
"Function is not allowed. You should only implement one "
"of them.")
user_fn = vjp_fn if vjp_fn is not Function.vjp else backward_fn
return user_fn(self, *args)
def apply_jvp(self, *args):
# _forward_cls is defined by derived class
return self._forward_cls.jvp(self, *args) # type: ignore[attr-defined]
class FunctionMeta(type):
"""Function metaclass.
This metaclass sets up the following properties:
_backward_cls: The Function class corresponding to the differentiated
version of this function (which is generated on the fly by this
metaclass).
"""
def __init__(cls, name, bases, attrs):
backward_fn = type(name + 'Backward', (BackwardCFunction,), {'_forward_cls': cls})
cls._backward_cls = backward_fn
super(FunctionMeta, cls).__init__(name, bases, attrs)
# mypy doesn't understand `with_metaclass` from torch._six
[docs]class Function(with_metaclass(FunctionMeta, _C._FunctionBase, FunctionCtx, _HookMixin)): # type: ignore[misc]
r"""Base class to create custom `autograd.Function`
To create a custom `autograd.Function`, subclass this class and implement
the :meth:`forward` and :meth:`backward` static methods. Then, to use your custom
op in the forward pass, call the class method ``apply``. Do not call
:meth:`forward` directly.
To ensure correctness and best performance, make sure you are calling the
correct methods on ``ctx`` and validating your backward function using
:func:`torch.autograd.gradcheck`.
See :ref:`extending-autograd` for more details on how to use this class.
Examples::
>>> 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)
"""
def __init__(self, *args, **kwargs):
cls = self.__class__
warnings.warn(f"{cls} should not be instantiated. Methods on autograd functions"
"are all static, so you should invoke them on the class itself. "
"Instantiating an autograd function will raise an "
"error in a future version of PyTorch.", DeprecationWarning)
def __call__(self, *args, **kwargs):
raise RuntimeError(
"Legacy autograd function with non-static forward method is deprecated. "
"Please use new-style autograd function with static forward method. "
"(Example: https://pytorch.org/docs/stable/autograd.html#torch.autograd.Function)")
# for the tracer
is_traceable = False
@staticmethod
def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any:
r"""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 arbitrary data that can be then
retrieved during the backward pass. Tensors should not be stored
directly on `ctx` (though this is not currently enforced for
backward compatibility). Instead, tensors should be saved either with
:func:`ctx.save_for_backward` if they are intended to be used in
``backward`` (equivalently, ``vjp``) or :func:`ctx.save_for_forward`
if they are intended to be used for in ``jvp``.
"""
raise NotImplementedError("You must implement the forward function for custom"
" autograd.Function.")
@staticmethod
def backward(ctx: Any, *grad_outputs: Any) -> Any:
r"""Defines a formula for differentiating the operation with backward mode
automatic differentiation (alias to the vjp function).
This function is to be overridden by all subclasses.
It must accept a context :attr:`ctx` as the first argument, followed by
as many outputs as the :func:`forward` returned (None will be passed in
for non tensor outputs of the forward function),
and it should return as many tensors, as there were inputs to
:func:`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. If an input is not a Tensor or is a Tensor not
requiring grads, you can just pass None as a gradient for that input.
The context can be used to retrieve tensors saved during the forward
pass. It also has an attribute :attr:`ctx.needs_input_grad` as a tuple
of booleans representing whether each input needs gradient. E.g.,
:func:`backward` will have ``ctx.needs_input_grad[0] = True`` if the
first input to :func:`forward` needs gradient computated w.r.t. the
output.
"""
raise NotImplementedError("You must implement either the backward or vjp method for "
"your custom autograd.Function to use it with backward "
"mode AD.")
# vjp and backward are alias of each other
vjp = backward
@staticmethod
def jvp(ctx: Any, *grad_inputs: Any) -> Any:
r"""Defines a formula for differentiating the operation with forward mode
automatic differentiation.
This function is to be overridden by all subclasses.
It must accept a context :attr:`ctx` as the first argument, followed by
as many inputs as the :func:`forward` got (None will be passed in
for non tensor inputs of the forward function),
and it should return as many tensors as there were outputs to
:func:`forward`. Each argument is the gradient w.r.t the given input,
and each returned value should be the gradient w.r.t. the
corresponding output. If an output is not a Tensor or the function is not
differentiable with respect to that output, you can just pass None as a
gradient for that input.
You can use the :attr:`ctx` object to pass any value from the forward to this
functions.
"""
raise NotImplementedError("You must implement the jvp function for custom "
"autograd.Function to use it with forward mode AD.")
def once_differentiable(fn):
@functools.wraps(fn)
def wrapper(ctx, *args):
with torch.no_grad():
outputs = fn(ctx, *args)
if not torch.is_grad_enabled():
return outputs
# If any of the inputs have requires_grad=True, we force the outputs
# to have requires_grad=True but point to a grad_fn which throws an
# error message during (double) back-propagation.
# XXX: this is only an approximation of requires_grad - there's no way
# to figure out if fn didn't use ctx.saved_tensors and as a result
# some Tensors might require grad, even if no args do.
# Unfortunately, this leads to unexpected error messages ("no nodes
# require computing gradients"), but I don't have a better idea.
# These functions would raise an error in backward anyway.
requires_grad = any(isinstance(arg, torch.Tensor) and arg.requires_grad
for arg in args)
if not requires_grad:
return outputs
if not isinstance(outputs, tuple):
outputs = (outputs,)
err_fn = _functions.DelayedError(
b"trying to differentiate twice a function that was marked "
b"with @once_differentiable", len(outputs))
# Create aliases of each output that has requires_grad=True. We need
# at least one of the inputs to err_fn to require grad so that the
# output will have a grad_fn.
def fake_requires_grad(var):
if var is not None:
var = var.detach()
var.requires_grad = True
return var
return err_fn(*[fake_requires_grad(v) for v in outputs])
return wrapper
def traceable(fn_cls):
r"""Marks Function as traceable for the JIT.
Traceable functions have additional restrictions - they can't pass any
data-dependent values to backward (e.g. Prod passes the output, which makes
it non-traceable), and their backward should be implemented entirely in terms
of operations on autograd Tensors in all cases.
DON'T USE THIS DECORATOR. IT IS FOR INTERNAL USE ONLY AND SHOULD BE HANDLED WITH
CARE (or can give incorrect results otherwise).
"""
fn_cls.is_traceable = True
return fn_cls
class InplaceFunction(Function):
def __init__(self, inplace=False):
super(InplaceFunction, self).__init__()
self.inplace = inplace
def _nested_map(condition, fn, condition_msg=None):
def _map(obj):
if condition(obj):
return fn(obj)
elif obj is None:
return None
elif isinstance(obj, (list, tuple)):
mapped = (_map(x) for x in obj)
if hasattr(obj, '_fields'):
# obj is namedtuple
return type(obj)(*mapped)
return type(obj)(mapped)
elif isinstance(obj, dict):
return {x : _map(obj[x]) for x in obj}
else:
raise ValueError("Auto nesting doesn't know how to process "
"an input object of type " + torch.typename(obj) +
(". Accepted types: " + condition_msg +
", or lists/tuples of them"
if condition_msg else ""))
return _map
def _jit_unwrap_structured(obj):
if hasattr(obj, "_jit_unwrap"):
return obj._jit_unwrap()
return obj
def _iter_filter(condition, allow_unknown=False, condition_msg=None,
conversion=None):
def _iter(obj):
if conversion is not None:
obj = conversion(obj)
if condition(obj):
yield obj
elif obj is None:
return
elif isinstance(obj, (list, tuple)):
for o in obj:
for var in _iter(o):
yield var
elif isinstance(obj, dict):
# We only accept primitive key types, so we needn't inspect them
for o in obj.values():
for var in _iter(o):
yield var
elif allow_unknown:
yield obj
else:
raise ValueError("Auto nesting doesn't know how to process "
"an input object of type " + torch.typename(obj) +
(". Accepted types: " + condition_msg +
", or lists/tuples of them"
if condition_msg else ""))
return _iter
def _unflatten(input, proto):
# unflatten a list or tuple input into a nested list/tuple structure
# specified by proto
def unflatten_helper(input, proto):
res: List[Optional[torch.Tensor]] = []
if hasattr(proto, "_jit_wrap"):
return proto._jit_wrap(input)
if not isinstance(proto, (list, tuple)):
return input[0], input[1:]
for e in proto:
if e is None:
res.append(e)
else:
res_e, input = unflatten_helper(input, e)
res.append(res_e)
return type(proto)(res), input
return unflatten_helper(input, proto)[0]
_iter_jit_values = _iter_filter(lambda o: o is None or isinstance(o, torch._C.Value),
condition_msg="jit's Values or None")
_iter_tensors = _iter_filter(lambda x: isinstance(x, torch.Tensor), condition_msg="Tensors",
conversion=_jit_unwrap_structured)
_iter_tensors_permissive = _iter_filter(lambda x: isinstance(x, torch.Tensor),
allow_unknown=True,
condition_msg="Tensors (permissive)")
_iter_None_tensors = _iter_filter(lambda o: o is None or isinstance(o, torch.Tensor),
condition_msg="Tensors or None")
_map_tensor_data = _nested_map(lambda x: isinstance(x, torch.Tensor), lambda o: o.data,
condition_msg="Tensors")
class NestedIOFunction(Function):
# The 'type: ignore' statements are needed here because these functions are declared as '@staticmethod' in the
# superclass (Function) but are instance methods here, which mypy reports as incompatible.
def _do_forward(self, *input):
self._nested_input = input
flat_input = tuple(_iter_tensors(input))
flat_output = super(NestedIOFunction, self)._do_forward(*flat_input)
nested_output = self._nested_output
nested_tensors = _unflatten(flat_output, self._nested_output)
return nested_tensors
def _do_backward(self, gradients, retain_variables):
self.retain_variables = retain_variables
result = super(NestedIOFunction, self)._do_backward(gradients, retain_variables)
if not retain_variables:
del self._nested_output
del self._to_save_nested
return result
def backward(self, *gradients: Any) -> Any: # type: ignore[override]
nested_gradients = _unflatten(gradients, self._nested_output)
result = self.backward_extended(*nested_gradients) # type: ignore[func-returns-value]
return tuple(_iter_None_tensors(result))
__call__ = _do_forward
def forward(self, *args: Any) -> Any: # type: ignore[override]
nested_tensors = _map_tensor_data(self._nested_input)
result = self.forward_extended(*nested_tensors) # type: ignore[func-returns-value]
del self._nested_input
self._nested_output = result
return tuple(_iter_tensors(result))
def save_for_backward(self, *args: Any) -> None:
self.to_save = tuple(_iter_tensors(args))
self._to_save_nested = args
@property
def saved_tensors(self):
flat_tensors = super(NestedIOFunction, self).saved_tensors
return _unflatten(flat_tensors, self._to_save_nested)
def mark_dirty(self, *args: Any, **kwargs: Any) -> None:
self.dirty_tensors = tuple(_iter_tensors((args, kwargs)))
def mark_non_differentiable(self, *args: Any, **kwargs: Any) -> None:
self.non_differentiable = tuple(_iter_tensors((args, kwargs)))
def forward_extended(self, *input: Any) -> None:
raise NotImplementedError
def backward_extended(self, *grad_output: Any) -> None:
raise NotImplementedError
```