chain rule will lead to Nan, sqrt() example

[zchky]

i find a interesting fact.

for example sqrt( ( x-1 )^2 ) =y and |x-1| = y , their grad of the two x should be same . but their grad of x different when x close to 1

>> x=Variable(torch.Tensor([1]),requires_grad=True)
>> y=torch.sqrt(torch.pow(x - 1,0))
>> y.backward()
>> x.grad
Variable containing:
nan
[torch.FloatTensor of size 1]

but in the fact, the grad of x for x-1 =y is just

>> x=Variable(torch.Tensor([1]),requires_grad=True)
>> y=x-1
>> y.backward()
>> x.grad
Variable containing:
 1
[torch.FloatTensor of size 1]

the formula is reasonable in mathematics, but it is different for autograd to compute.
i think the point is when one of sub chain's grad is Nan, the final grad will be Nan.

[vishwakftw]

sqrt((x-1)^2) = |x - 1| by definition. The derivative of |x - 1| at x = 1, is supposed to be nan, unless a subgradient is specified.

[ruotianluo]

Both (x-1).abs() and (x-1).norm(2) gives subgradient 0.

[fmassa]

The subgradient for norm at zero was added in #2775 and required some special casing.

I don't think we can do much when the user specifies a set of operations by hand, because the derivative of sqrt at zero is inf.

This is something we need to live with in numeric computing.
For example, log(x ** x) == x * log(x), but when x is zero, the limit (which is 0) gets undefined using the second expression:

print(np.log(0 ** 0))  # 0.0
print(0 * np.log(0))  # nan

Closing as a wontfix. Please let us know if you disagree.