Sigmoid BCE Gradient with Logits

Problem

For binary cross-entropy with a sigmoid output, the gradient with respect to the logit z is sigmoid(z) - y, where y is the target in {0, 1}.

Given the logits and targets, return the per-example gradient list.

Hint

The BCE and sigmoid derivatives cancel into p - y.

case 1

in: [[0,0],[0,1]]

expected: [0.5,-0.5]

case 2

in: [[1,-1],[1,0]]

expected: [-0.2689414213699951,0.2689414213699951]

case 3

in: [[2,2,2],[1,1,0]]

expected: [-0.11920292202211769,-0.11920292202211769,0.8807970779778823]

Starter codePython

def sigmoid_bce_gradient(logits, targets):
    # Your code here
    pass

3 test cases · run your code against them in the editor