Implement Binary Focal Loss Gradients

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Your question is Implement Binary Focal Loss Gradients. Start with the requirements on the right.

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Problem

Implement binary focal loss for logits and its gradient with respect to each logit. Given a list of real-valued logits logits, binary labels labels in {0,1}, focusing parameter gamma, balancing factor alpha, and reduction mode ("none", "sum", or "mean"), return both the forward loss and the backward gradient vector. Use a numerically stable sigmoid/log-sigmoid formulation.

Constraints

1 <= len(logits) == len(labels) <= 10^5
labels[i] is either 0 or 1
0 <= alpha <= 1
0 <= gamma <= 5
reduction is one of "none", "sum", or "mean"

Function Signature

def focal_loss_with_grad(logits, labels, alpha, gamma, reduction):

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