MediumCalculusca-282

Focal Loss Gradient

Problem

For sigmoid focal loss with focusing parameter gamma, the gradient with respect to the logit z is:

y = 1: (1 - p)^gamma * (gamma * p * log(p) - (1 - p)) y = 0: p^gamma * (p - gamma * (1 - p) * log(1 - p))

where p = sigmoid(z). Given logits, targets, and gamma, return the gradient list.

Hint

Differentiate -(1-p)^gamma log p through the sigmoid using dp/dz = p(1-p).

case 1

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

expected: [-0.29828679513998635,0.29828679513998635]

case 2

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

expected: [-0.2689414213699951,0.2689414213699951]

case 3

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

expected: [0.9991172903489263,-0.9991172903489264]

Starter codePython

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

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