I have a variable, say, a which has some gradient associated with it from some operations before. Then I have integers b and c which have no gradients. I want to compute the minimum of a, b, and c. MWE is as given below.
import torch
a = torch.tensor([4.], requires_grad=True) # As an example I have defined a leaf node here, in my program I have an actual variable with gradient
b = 5
c = 6
d = torch.min(torch.tensor([a, b, c])) # d does not have gradient associated
How can I write this differently so that the gradient from a flows through to d? Thanks.
The problem with your code is the line d = torch.min(torch.tensor([a, b, c]))
When you compute torch.tensor([a, b, c]), you create a new tensor that has no computational graph to the a, b or c tensors. For example:
a = torch.tensor([4.], requires_grad=True)
b = torch.tensor([5.])
c = torch.tensor([6.])
d = torch.tensor([a,b,c])
d.requires_grad
> False
The solution is to use the min function with the input tensors themselves.
a = torch.tensor([4.], requires_grad=True)
b = torch.tensor([5.])
c = torch.tensor([6.])
d = a.min(b).min(c)
d.requires_grad
> True
Note that the gradient of the min function is 1 for the min value and 0 for all other values. This means that you will lose gradient signal if the value you want to backprop through is not the min.
a = torch.tensor([4.], requires_grad=True)
b = torch.tensor([5.])
d = a.min(b)
d.backward()
a.grad
> tensor([1.])
a = torch.tensor([6.], requires_grad=True)
b = torch.tensor([5.])
d = a.min(b)
d.backward()
a.grad
> tensor([0.])