前向自动微分 (Beta)

本教程演示了如何使用前向自动微分来计算方向导数（或等效地，雅可比矩阵向量积）。

以下教程使用了一些仅在版本 >= 1.11（或夜间构建版本）中才有的 API。

另请注意，前向自动微分当前处于 beta 阶段。API 会发生变化，运算符覆盖范围仍然不完整。

基本用法

与反向自动微分不同，前向自动微分在正向传递期间急切地计算梯度。我们可以使用前向自动微分通过执行与之前相同的正向传递来计算方向导数，不同的是，我们首先将输入与表示方向导数方向的另一个张量相关联（或等效地，v 在雅可比矩阵向量积中）。当输入（我们称为“原始值”）与“方向”张量（我们称为“切线”）相关联时，生成的新的张量对象被称为“对偶张量”，因为它与对偶数[0]相关联。

在执行正向传递时，如果任何输入张量是对偶张量，则会执行额外的计算来传播函数的“灵敏度”。

import torch
import torch.autograd.forward_ad as fwAD

primal = torch.randn(10, 10)
tangent = torch.randn(10, 10)

def fn(x, y):
    return x ** 2 + y ** 2

# All forward AD computation must be performed in the context of
# a ``dual_level`` context. All dual tensors created in such a context
# will have their tangents destroyed upon exit. This is to ensure that
# if the output or intermediate results of this computation are reused
# in a future forward AD computation, their tangents (which are associated
# with this computation) won't be confused with tangents from the later
# computation.
with fwAD.dual_level():
    # To create a dual tensor we associate a tensor, which we call the
    # primal with another tensor of the same size, which we call the tangent.
    # If the layout of the tangent is different from that of the primal,
    # The values of the tangent are copied into a new tensor with the same
    # metadata as the primal. Otherwise, the tangent itself is used as-is.
    #
    # It is also important to note that the dual tensor created by
    # ``make_dual`` is a view of the primal.
    dual_input = fwAD.make_dual(primal, tangent)
    assert fwAD.unpack_dual(dual_input).tangent is tangent

    # To demonstrate the case where the copy of the tangent happens,
    # we pass in a tangent with a layout different from that of the primal
    dual_input_alt = fwAD.make_dual(primal, tangent.T)
    assert fwAD.unpack_dual(dual_input_alt).tangent is not tangent

    # Tensors that do not have an associated tangent are automatically
    # considered to have a zero-filled tangent of the same shape.
    plain_tensor = torch.randn(10, 10)
    dual_output = fn(dual_input, plain_tensor)

    # Unpacking the dual returns a ``namedtuple`` with ``primal`` and ``tangent``
    # as attributes
    jvp = fwAD.unpack_dual(dual_output).tangent

assert fwAD.unpack_dual(dual_output).tangent is None

与模块一起使用

要在前向自动微分中使用 nn.Module，请在执行正向传递之前将模型的参数替换为对偶张量。在撰写本文时，无法创建对偶张量 `nn.Parameter`。作为一种变通方法，必须将对偶张量注册为模块的非参数属性。

import torch.nn as nn

model = nn.Linear(5, 5)
input = torch.randn(16, 5)

params = {name: p for name, p in model.named_parameters()}
tangents = {name: torch.rand_like(p) for name, p in params.items()}

with fwAD.dual_level():
    for name, p in params.items():
        delattr(model, name)
        setattr(model, name, fwAD.make_dual(p, tangents[name]))

    out = model(input)
    jvp = fwAD.unpack_dual(out).tangent

使用函数式模块 API (beta)

使用 nn.Module 和前向 AD 的另一种方法是利用函数式模块 API（也称为无状态模块 API）。

from torch.func import functional_call

# We need a fresh module because the functional call requires the
# the model to have parameters registered.
model = nn.Linear(5, 5)

dual_params = {}
with fwAD.dual_level():
    for name, p in params.items():
        # Using the same ``tangents`` from the above section
        dual_params[name] = fwAD.make_dual(p, tangents[name])
    out = functional_call(model, dual_params, input)
    jvp2 = fwAD.unpack_dual(out).tangent

# Check our results
assert torch.allclose(jvp, jvp2)

自定义自动微分函数

自定义函数也支持前向模式 AD。要创建支持前向模式 AD 的自定义函数，请注册 jvp() 静态方法。自定义函数可以支持前向和反向 AD，但并非必须。有关更多信息，请参阅 文档。

class Fn(torch.autograd.Function):
    @staticmethod
    def forward(ctx, foo):
        result = torch.exp(foo)
        # Tensors stored in ``ctx`` can be used in the subsequent forward grad
        # computation.
        ctx.result = result
        return result

    @staticmethod
    def jvp(ctx, gI):
        gO = gI * ctx.result
        # If the tensor stored in`` ctx`` will not also be used in the backward pass,
        # one can manually free it using ``del``
        del ctx.result
        return gO

fn = Fn.apply

primal = torch.randn(10, 10, dtype=torch.double, requires_grad=True)
tangent = torch.randn(10, 10)

with fwAD.dual_level():
    dual_input = fwAD.make_dual(primal, tangent)
    dual_output = fn(dual_input)
    jvp = fwAD.unpack_dual(dual_output).tangent

# It is important to use ``autograd.gradcheck`` to verify that your
# custom autograd Function computes the gradients correctly. By default,
# ``gradcheck`` only checks the backward-mode (reverse-mode) AD gradients. Specify
# ``check_forward_ad=True`` to also check forward grads. If you did not
# implement the backward formula for your function, you can also tell ``gradcheck``
# to skip the tests that require backward-mode AD by specifying
# ``check_backward_ad=False``, ``check_undefined_grad=False``, and
# ``check_batched_grad=False``.
torch.autograd.gradcheck(Fn.apply, (primal,), check_forward_ad=True,
                         check_backward_ad=False, check_undefined_grad=False,
                         check_batched_grad=False)

True

函数式 API（测试版）

我们还在 functorch 中提供了一个更高级的函数式 API 用于计算雅可比向量积，根据您的用例，您可能会发现它更易于使用。

函数式 API 的优点是无需了解或使用底层的双重张量 API，并且可以将其与其他 functorch 变换（如 vmap） 组合；缺点是它提供的控制较少。

请注意，本教程的其余部分需要运行 functorch (https://github.com/pytorch/functorch)。请在指定链接处查找安装说明。

import functorch as ft

primal0 = torch.randn(10, 10)
tangent0 = torch.randn(10, 10)
primal1 = torch.randn(10, 10)
tangent1 = torch.randn(10, 10)

def fn(x, y):
    return x ** 2 + y ** 2

# Here is a basic example to compute the JVP of the above function.
# The ``jvp(func, primals, tangents)`` returns ``func(*primals)`` as well as the
# computed Jacobian-vector product (JVP). Each primal must be associated with a tangent of the same shape.
primal_out, tangent_out = ft.jvp(fn, (primal0, primal1), (tangent0, tangent1))

# ``functorch.jvp`` requires every primal to be associated with a tangent.
# If we only want to associate certain inputs to `fn` with tangents,
# then we'll need to create a new function that captures inputs without tangents:
primal = torch.randn(10, 10)
tangent = torch.randn(10, 10)
y = torch.randn(10, 10)

import functools
new_fn = functools.partial(fn, y=y)
primal_out, tangent_out = ft.jvp(new_fn, (primal,), (tangent,))

/var/lib/workspace/intermediate_source/forward_ad_usage.py:203: FutureWarning:

We've integrated functorch into PyTorch. As the final step of the integration, `functorch.jvp` is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use `torch.func.jvp` instead; see the PyTorch 2.0 release notes and/or the `torch.func` migration guide for more details https://pytorch.ac.cn/docs/main/func.migrating.html

/var/lib/workspace/intermediate_source/forward_ad_usage.py:214: FutureWarning:

We've integrated functorch into PyTorch. As the final step of the integration, `functorch.jvp` is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use `torch.func.jvp` instead; see the PyTorch 2.0 release notes and/or the `torch.func` migration guide for more details https://pytorch.ac.cn/docs/main/func.migrating.html

将函数式 API 与模块一起使用

要将 nn.Module 与 functorch.jvp 一起使用以计算相对于模型参数的雅可比向量积，我们需要将 nn.Module 重构为一个接受模型参数和模块输入的函数。

model = nn.Linear(5, 5)
input = torch.randn(16, 5)
tangents = tuple([torch.rand_like(p) for p in model.parameters()])

# Given a ``torch.nn.Module``, ``ft.make_functional_with_buffers`` extracts the state
# (``params`` and buffers) and returns a functional version of the model that
# can be invoked like a function.
# That is, the returned ``func`` can be invoked like
# ``func(params, buffers, input)``.
# ``ft.make_functional_with_buffers`` is analogous to the ``nn.Modules`` stateless API
# that you saw previously and we're working on consolidating the two.
func, params, buffers = ft.make_functional_with_buffers(model)

# Because ``jvp`` requires every input to be associated with a tangent, we need to
# create a new function that, when given the parameters, produces the output
def func_params_only(params):
    return func(params, buffers, input)

model_output, jvp_out = ft.jvp(func_params_only, (params,), (tangents,))

/var/lib/workspace/intermediate_source/forward_ad_usage.py:235: FutureWarning:

We've integrated functorch into PyTorch. As the final step of the integration, `functorch.make_functional_with_buffers` is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use `torch.func.functional_call` instead; see the PyTorch 2.0 release notes and/or the `torch.func` migration guide for more details https://pytorch.ac.cn/docs/main/func.migrating.html

/var/lib/workspace/intermediate_source/forward_ad_usage.py:242: FutureWarning:

We've integrated functorch into PyTorch. As the final step of the integration, `functorch.jvp` is deprecated as of PyTorch 2.0 and will be deleted in a future version of PyTorch >= 2.3. Please use `torch.func.jvp` instead; see the PyTorch 2.0 release notes and/or the `torch.func` migration guide for more details https://pytorch.ac.cn/docs/main/func.migrating.html

[0] https://en.wikipedia.org/wiki/Dual_number