参考 http://pytorch123.com/
Tensor.requires_grad = True记录对Tensor的所有操作，后序.backward()自动计算所有梯度到.grad属性
import torch
x = torch.ones(2,2, requires_grad=True) # 默认是False
print(x)
tensor([[1., 1.],
[1., 1.]], requires_grad=True)- 停止记录调用
.detach()
x.detach_()
print(x.requires_grad) # False.grad_fn保存了创建张量的 Function 的引用
x = torch.ones(2,2, requires_grad=True)
y = x 2
print(y)
print(y.grad_fn)
tensor([[3., 3.],
[3., 3.]], grad_fn=<AddBackward0>)
<AddBackward0 object at 0x0000015716529D68>z = y*y*3
out = z.mean()
print(z, out)
tensor([[27., 27.],
[27., 27.]], grad_fn=<MulBackward0>)
tensor(27., grad_fn=<MeanBackward0>)# requires_grad 默认为 False
a = torch.randn(2, 2)
a = ((a*3)/(a-1))
print(a.requires_grad) # False
b = (a*a).sum()
print(b.grad_fn) # None
a.requires_grad_(True) # 设置为 True
print(a.requires_grad) # True
b = (a*a).sum()
print(b.grad_fn)
# <SumBackward0 object at 0x0000015717DC69E8>backward()后向传播
z = y*y*3
y = x 2
计算 d(out)/dxo u t = 1 4 ( ∑ 3 ( x i 2 ) 2 ) → d o u t d x i = 3 2 ( x i 2 ) out = frac{1}{4}(sum3(x_i 2)^2) rightarrow frac{d_{out}}{dx_i} = frac{3}{2}(x_i 2) out=41(∑3(xi 2)2)→dxidout=23(xi 2) x i = 1 , d o u t / d x i = 4.5 x_i = 1, d_{out}/dx_i = 4.5 xi=1,dout/dxi=4.5
代码语言：javascript复制out.backward()
print(y.grad) # None, 为什么？是 None
print(x.grad)
tensor([[4.5000, 4.5000],
[4.5000, 4.5000]])J = ( ∂ y 1 ∂ x 1 ⋯ ∂ y m ∂ x 1 ⋮ ⋱ ⋮ ∂ y 1 ∂ x n ⋯ ∂ y m ∂ x n ) J=left(begin{array}{ccc}frac{partial y_{1}}{partial x_{1}} & cdots & frac{partial y_{m}}{partial x_{1}} \ vdots & ddots & vdots \ frac{partial y_{1}}{partial x_{n}} & cdots & frac{partial y_{m}}{partial x_{n}}end{array}right) J=⎝⎜⎛∂x1∂y1⋮∂xn∂y1⋯⋱⋯∂x1∂ym⋮∂xn∂ym⎠⎟⎞
- 当又使用了一个函数 l = g ( y ) l = g(y) l=g(y)，v 是 l l l 对 y y y 的导数，链式求导相乘，得到 l l l 对 x x x 的导数 J ⋅ v = ( ∂ y 1 ∂ x 1 ⋯ ∂ y m ∂ x 1 ⋮ ⋱ ⋮ ∂ y 1 ∂ x n ⋯ ∂ y m ∂ x n ) ( ∂ l ∂ y 1 ⋮ ∂ l ∂ y m ) = ( ∂ l ∂ x 1 ⋮ ∂ l ∂ x n ) J cdot v=left(begin{array}{ccc}frac{partial y_{1}}{partial x_{1}} & cdots & frac{partial y_{m}}{partial x_{1}} \ vdots & ddots & vdots \ frac{partial y_{1}}{partial x_{n}} & cdots & frac{partial y_{m}}{partial x_{n}}end{array}right)left(begin{array}{c}frac{partial l}{partial y_{1}} \ vdots \ frac{partial l}{partial y_{m}}end{array}right)=left(begin{array}{c}frac{partial l}{partial x_{1}} \ vdots \ frac{partial l}{partial x_{n}}end{array}right) J⋅v=⎝⎜⎛∂x1∂y1⋮∂xn∂y1⋯⋱⋯∂x1∂ym⋮∂xn∂ym⎠⎟⎞⎝⎜⎛∂y1∂l⋮∂ym∂l⎠⎟⎞=⎝⎜⎛∂x1∂l⋮∂xn∂l⎠⎟⎞
上面代码改为：
代码语言：javascript复制v = torch.tensor(2, dtype=torch.float)
out.backward(v)
print(x.grad)
# 梯度乘以了 2
tensor([[9., 9.],
[9., 9.]])- 评估阶段可以使用
with torch.no_grad():不需要梯度计算和更新
print(x.requires_grad) # True
print((x ** 2).requires_grad) # True
# 取消梯度记录
with torch.no_grad():
print((x ** 2).requires_grad) # False
