How torch.Tensor.backward() works?

Question

I recently study Pytorch and backward function of the package. I understood how to use it, but when I try

x = Variable(2*torch.ones(2, 2), requires_grad=True)
x.backward(x)
print(x.grad)

I expect

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

because it is an identity function. However, it returns

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

Why this happens?

Answer 1

Actually, this is what you are looking for:

Case 1: when z = 2*x**3 + x

import torch
from torch.autograd import Variable
x = Variable(2*torch.ones(2, 2), requires_grad=True)
z = x*x*x*2+x
z.backward(torch.ones_like(z))
print(x.grad)

output:

tensor([[25., 25.],
        [25., 25.]])

Case 2: when z = x*x

x = Variable(2*torch.ones(2, 2), requires_grad=True)
z = x*x
z.backward(torch.ones_like(z))
print(x.grad)

output:

tensor([[4., 4.],
        [4., 4.]])

Case 3: when z = x (your case)

x = Variable(2*torch.ones(2, 2), requires_grad=True)
z = x
z.backward(torch.ones_like(z))
print(x.grad)

output:

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

To learn more how to calculate gradient in pytorch, check this.