Focal Loss

Implement Focal Loss from “Focal Loss for Dense Object Detection” (Lin et al., 2017).

Focal loss addresses class imbalance by down-weighting easy examples:

$$\text{FL}(p_t) = -\alpha_t (1 - p_t)^\gamma \log(p_t)$$

Where $p_t$ is the model’s predicted probability for the true class.

For binary classification:

• If y=1: $p_t = p$, $\alpha_t = \alpha$
• If y=0: $p_t = 1-p$, $\alpha_t = 1-\alpha$

Given:

• probs: shape (batch,) — predicted probabilities (after sigmoid)
• targets: shape (batch,) — binary targets (0 or 1)
• alpha: float — class balancing factor
• gamma: float — focusing parameter

Output: Scalar (float) — mean focal loss over the batch.