属性（成员变量）
saved_tensors: 传给forward()的参数，在backward()中会用到。
needs_input_grad:长度为 :attr:num_inputs的bool元组，表示输出是否需要梯度。
可以用于优化反向过程的缓存。
num_inputs: 传给函数 :func:forward的参数的数量。
num_outputs: 函数 :func:forward返回的值的数目。
requires_grad: 布尔值，表示函数 :func:backward 是否永远不会被调用。
成员函数
forward()
forward()可以有任意多个输入、任意多个输出，但是输入和输出必须是tensor。
backward()
backward()的输入和输出的个数就是forward()函数的输出和输入的个数。其中，
backward()输入表示关于forward()输出的梯度(计算图中上一节点的梯度)，
backward()的输出表示关于forward()的输入的梯度。在输入不需要梯度时（通过查看needs_input_grad参数）
或者不可导时，可以返回None
forward的说明
1. 虽然说一个网络的输入是Variable形式，那么每个网络层的输出也是Variable形式。
但是，当自定义autograd时，在forward中，所有的Variable参数将会转成tensor！
因此在forward实际操作的对象是tensor。在传入forward前，
autograd engine会自动将Variable unpack成Tensor。
因此这里的input也是tensor.在forward中可以进行任意操作。
2. ctx是context，ctx.save_for_backward会将他们转换为tensor(Variable)形式。
也就是说, backward只对tensor(Variable)进行处理.
3. save_for_backward只能传入Variable或是Tensor的变量，如果是其他类型的，可以用
ctx.xyz = xyz，使其在backward中可以用。例如,ctx.constant = constant,
这里constant为常数,不能直接作为ctx.save_for_backward的参数.
backward说明
自动求导是根据每个op的backward创建的graph来进行的！
自动求导竟然是在backward的操作中创建计算图, 因此我们需要在backward中用全部用variable来操作，
而forward就没必要，forward只需要用tensor操作就可以。
y = x*w +b # 自己定义的LinearFunction
z = f(y)
下面的grad_output = dz/dy
根据复合函数求导法则:
1. dz/dx = dz/dy * dy/dx = grad_output*dy/dx = grad_output*w
2. dz/dw = dz/dy * dy/dw = grad_output*dy/dw = grad_output*x
3. dz/db = dz/dy * dy/db = grad_output*1
import torch.autograd.Function as Function
class LinearFunction(Function):
# 创建torch.autograd.Function类的一个子类
# 必须是staticmethod
@staticmethod
# 第一个是ctx，第二个是input，其他是可选参数。
# ctx在这里类似self，ctx的属性可以在backward中调用。
# 自己定义的Function中的forward()方法，所有的Variable参数将会转成tensor！
# 因此这里的input也是tensor．在传入forward前，
# autograd engine会自动将Variable unpack成Tensor。
def forward(ctx, input, weight, bias=None):
print(type(input))
ctx.save_for_backward(input, weight, bias) # 将Tensor转变为Variable保存到ctx中
output = input.mm(weight.t()) # torch.t()方法，对2D tensor进行转置
if bias is not None:
output += bias.unsqueeze(0).expand_as(output) ＃unsqueeze(0) 扩展处第0维
# expand_as(tensor)等价于expand(tensor.size()), 将原tensor按照新的size进行扩展
return output
@staticmethod
def backward(ctx, grad_output):
# grad_output为反向传播上一级计算得到的梯度值
input, weight, bias = ctx.saved_tensors
grad_input = grad_weight = grad_bias = None
# 分别代表输入,权值,偏置三者的梯度
# 判断三者对应的Variable是否需要进行反向求导计算梯度
if ctx.needs_input_grad[0]:
grad_input = grad_output.mm(weight) # 复合函数求导，链式法则
if ctx.needs_input_grad[1]:
grad_weight = grad_output.t().mm(input) # 复合函数求导，链式法则
if bias is not None and ctx.needs_input_grad[2]:
grad_bias = grad_output.sum(0).squeeze(0)
return grad_input, grad_weight, grad_bias
#建议把新操作封装在一个函数中
def linear(input, weight, bias=None):
# First braces create a Function object. Any arguments given here
# will be passed to __init__. Second braces will invoke the __call__
# operator, that will then use forward() to compute the result and
# return it.
return LinearFunction()(input, weight, bias)#调用forward()
# 或者使用apply方法并取个别名
linear = LinearFunction.apply
#检查实现的backward()是否正确
from torch.autograd import gradcheck
# gradchek takes a tuple of tensor as input, check if your gradient
# evaluated with these tensors are close enough to numerical
# approximations and returns True if they all verify this condition.
input = (Variable(torch.randn(20,20).double(), requires_grad=True),)
test = gradcheck(LinearFunction(), input, eps=1e-6, atol=1e-4)
print(test) # 没问题的话输出True
# 这里定义一个乘以常数的操作(输入参数是Tensor)
class MulConstant(Function):
@staticmethod
def forward(ctx, tensor, constant):
# ctx is a context object that can be used to stash information
# for backward computation
ctx.constant = constant
return tensor * constant
@staticmethod
def backward(ctx, grad_output):
# We return as many input gradients as there were arguments.
# Gradients of non-Tensor arguments to forward must be None.
# constant
return grad_output * ctx.constant, None # 这里并没有涉及到Variable
# 用自己定义的Function来创建Module
import torch.nn as nn
class Linear(nn.Module):
def __init__(self, input_features, output_features, bias=True):
super(Linear, self).__init__()
self.input_features = input_features
self.output_features = output_features
# nn.Parameter is a special kind of Variable, that will get
# automatically registered as Module's parameter once it's assigned
# 这个很重要！ Parameters是默认需要梯度的！
self.weight = nn.Parameter(torch.Tensor(output_features, input_features))
if bias:
self.bias = nn.Parameter(torch.Tensor(output_features))
else:
# You should always register all possible parameters, but the
# optional ones can be None if you want.
self.register_parameter('bias', None)
# Not a very smart way to initialize weights
self.weight.data.uniform_(-0.1, 0.1)
if bias is not None:
self.bias.data.uniform_(-0.1, 0.1)
def forward(self, input):
# See the autograd section for explanation of what happens here.
return LinearFunction.apply(input, self.weight, self.bias)
# 或者 return LinearFunction()(input, self.weight, self.bias)
import torch
from torch.autograd import Variable
class MyReLU(torch.autograd.Function):
"""
We can implement our own custom autograd Functions by subclassing
torch.autograd.Function and implementing the forward and backward passes
which operate on Tensors.
"""
@staticmethod
def forward(ctx, input):
"""
In the forward pass we receive a Tensor containing the input and return
a Tensor containing the output. ctx is a context object that can be used
to stash information for backward computation. You can cache arbitrary
objects for use in the backward pass using the ctx.save_for_backward method.
"""
ctx.save_for_backward(input)
return input.clamp(min=0)
@staticmethod
def backward(ctx, grad_output):
"""
In the backward pass we receive a Tensor containing the gradient of the loss
with respect to the output, and we need to compute the gradient of the loss
with respect to the input.
"""
input, = ctx.saved_tensors
grad_input = grad_output.clone()
grad_input[input < 0] = 0
return grad_input
dtype = torch.FloatTensor
# dtype = torch.cuda.FloatTensor # Uncomment this to run on GPU
# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10
# Create random Tensors to hold input and outputs, and wrap them in Variables.
x = Variable(torch.randn(N, D_in).type(dtype), requires_grad=False)
y = Variable(torch.randn(N, D_out).type(dtype), requires_grad=False)
# Create random Tensors for weights, and wrap them in Variables.
w1 = Variable(torch.randn(D_in, H).type(dtype), requires_grad=True)
w2 = Variable(torch.randn(H, D_out).type(dtype), requires_grad=True)
learning_rate = 1e-6
for t in range(500):
# To apply our Function, we use Function.apply method. We alias this as 'relu'.
relu = MyReLU.apply
# Forward pass: compute predicted y using operations on Variables; we compute
# ReLU using our custom autograd operation.
y_pred = relu(x.mm(w1)).mm(w2)
# Compute and print loss
loss = (y_pred - y).pow(2).sum()
print(t, loss.data[0])
# Use autograd to compute the backward pass.
loss.backward()
# Update weights using gradient descent
w1.data -= learning_rate * w1.grad.data
w2.data -= learning_rate * w2.grad.data
# Manually zero the gradients after updating weights
w1.grad.data.zero_()
w2.grad.data.zero_()
参考：
定义torch.autograd.Function的子类，自己定义某些操作，且定义反向求导函数
Pytorch入门学习（八）-----自定义层的实现
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