focal loss

Focal loss (Lin et al., 2017, the RetinaNet paper) is a modification of the standard cross-entropy classification loss designed to fix the extreme foreground-background imbalance that cripples dense one-stage detectors. The problem: a one-stage detector scores tens of thousands of anchors per image, but only a handful contain objects — the rest are 'easy' background. Even though each easy negative contributes a tiny loss, there are so many of them that their summed gradient drowns out the few hard, informative examples, and training stalls.

Focal loss attacks this by down-weighting easy examples so the model focuses on hard ones (hence 'focal'). Start from cross-entropy for the true class, CE = −log(p_t), where p_t is the predicted probability assigned to the correct class. Focal loss multiplies this by a modulating factor (1 − p_t)^γ: FL = −(1 − p_t)^γ · log(p_t). When an example is already classified confidently (p_t near 1), (1 − p_t)^γ is near 0, so its loss is suppressed; when it is misclassified (p_t small), the factor is near 1 and the full loss remains. The focusing parameter γ (commonly 2) controls how aggressively easy examples are discounted; an optional α balances the positive/negative classes.

The effect is that a flood of easy negatives, each now contributing almost nothing, can no longer overwhelm the gradient. With γ = 2, an example classified at p_t = 0.9 has its loss scaled by (0.1)² = 0.01 — a 100× reduction — while a hard example at p_t = 0.1 is scaled by (0.9)² ≈ 0.81, barely touched. This lets a one-stage detector train on the full dense set of anchors without the hard-negative-mining or 1:3 sampling tricks that SSD needed.

Focal loss was the missing piece that let one-stage detectors match two-stage accuracy: RetinaNet, a plain FPN-based dense detector trained with focal loss, beat the two-stage detectors of its day on COCO while remaining faster. The idea generalized far beyond detection to any task with heavy class imbalance, and remains a default tool for dense prediction.