pytorch之Variable對象之梯度推導

由簡入繁
看代碼：
import torch
from torch.autograd import Variable

a = Variable(torch.ones(4),requires_grad=True)
b=a+2
c=b.mean()
print©
c.backward()
print(a.grad)
輸出：
tensor(3., grad_fn=)
tensor([0.2500, 0.2500, 0.2500, 0.2500])
解析：a是一個4維數組，所以b=(1/4)a，求導爲1/4，所以a的梯度爲 [0.2500, 0.2500, 0.2500, 0.2500]

加點難度：
import torch
from torch.autograd import Variable

a = Variable(torch.ones(4),requires_grad=True)
b=a*a
c=b.mean()
print©
c.backward()
print(a.grad)
輸出爲：
tensor(1., grad_fn=)
tensor([0.5000, 0.5000, 0.5000, 0.5000])
解析：這裏a=(1/4)a2，求導爲1/2

再看代碼：
import torch
from torch.autograd import Variable
import torch.nn as nn

sig=nn.CosineSimilarity()
t1=torch.ones(4)
for i in range(4):
t1[i]=i
print(t1)
a = Variable(t1,requires_grad=True)
c=torch.sin(a)
print(c.grad_fn)
d=c.mean()
d.backward()
print(a.grad)
結果：
tensor([0., 1., 2., 3.])
<SinBackward object at 0x000001937C9BAD30>
tensor([ 0.2500, 0.1351, -0.1040, -0.2475])
解析：複合函數求導，d=f(g(x)),f(x)=1/4x,g(x)=sin(x),所以複合導數爲(1/4)*cos(x)，而x=[0,1,2,3]，帶入即可得到結果