目录

一、函数解释

如果输入x，输出是y，则求y关于x的导数(梯度)：

def grad(outputs, inputs, grad_outputs=None, retain_graph=None, create_graph=False,

only_inputs=True, allow_unused=False):

r"""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.

Arguments:

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``.

"""

if not only_inputs:

warnings.warn("only_inputs argument is deprecated and is ignored now "

"(defaults to True). To accumulate gradient for other "

"parts of the graph, please use torch.autograd.backward.")

outputs = (outputs,) if isinstance(outputs, torch.Tensor) else tuple(outputs)

inputs = (inputs,) if isinstance(inputs, torch.Tensor) else tuple(inputs)

if grad_outputs is None:

grad_outputs = [None] * len(outputs)

elif isinstance(grad_outputs, torch.Tensor):

grad_outputs = [grad_outputs]

else:

grad_outputs = list(grad_outputs)

grad_outputs = _make_grads(outputs, grad_outputs)

if retain_graph is None:

retain_graph = create_graph

return Variable._execution_engine.run_backward(

outputs, grad_outputs, retain_graph, create_graph,

inputs, allow_unused)

二、代码范例(y=x^2)

import torch

x = torch.randn(3, 4).requires_grad_(True)

for i in range(3):

for j in range(4):

x[i][j] = i + j

y = x ** 2

print(x)

print(y)

weight = torch.ones(y.size())

print(weight)

dydx = torch.autograd.grad(outputs=y,

inputs=x,

grad_outputs=weight,

retain_graph=True,

create_graph=True,

only_inputs=True)

"""(x**2)' = 2*x """

print(dydx[0])

d2ydx2 = torch.autograd.grad(outputs=dydx[0],

inputs=x,

grad_outputs=weight,

retain_graph=True,

create_graph=True,

only_inputs=True)

print(d2ydx2[0])

x是：

tensor([[0., 1., 2., 3.],

[1., 2., 3., 4.],

[2., 3., 4., 5.]], grad_fn=)

y = x的平方：

tensor([[ 0., 1., 4., 9.],

[ 1., 4., 9., 16.],

[ 4., 9., 16., 25.]], grad_fn=)

weight：

tensor([[1., 1., 1., 1.],

[1., 1., 1., 1.],

[1., 1., 1., 1.]])

dydx就是

(一阶导数)，得到结果还需要乘以weight：

tensor([[ 0., 2., 4., 6.],

[ 2., 4., 6., 8.],

[ 4., 6., 8., 10.]], grad_fn=)

d2ydx2就是

(二阶导数)，得到结果还需要乘以weight：

tensor([[2., 2., 2., 2.],

[2., 2., 2., 2.],

[2., 2., 2., 2.]], grad_fn=)

是不是很简单呢～