Focal Loss

Overview

Focal loss addresses extreme class imbalance in segmentation (e.g., defects covering <1% of pixels). Standard BCE treats all pixels equally, so the loss is dominated by easy negatives. Focal loss adds a modulating factor (1-p_t)^gamma that suppresses the contribution of well-classified examples. With gamma=2, a pixel classified at 0.9 confidence contributes 100x less loss than one at 0.5. Combined with alpha-weighting for positive/negative balance, focal loss typically improves recall on rare classes by 5-15%.

Quick Start

import torch
import torch.nn as nn
import torch.nn.functional as F

class FocalLoss(nn.Module):
    def __init__(self, alpha=0.8, gamma=2.0):
        super().__init__()
        self.alpha = alpha
        self.gamma = gamma

    def forward(self, inputs, targets):
        inputs = torch.sigmoid(inputs).view(-1)
        targets = targets.view(-1)
        bce = F.binary_cross_entropy(inputs, targets, reduction='none')
        p_t = inputs * targets + (1 - inputs) * (1 - targets)
        focal_weight = self.alpha * (1 - p_t) ** self.gamma
        return (focal_weight * bce).mean()

# Usage
criterion = FocalLoss(alpha=0.8, gamma=2.0)
loss = criterion(logits, masks)

Workflow

1. Apply sigmoid to raw logits
2. Compute per-pixel binary cross-entropy
3. Compute modulating factor (1-p_t)^gamma to down-weight easy examples
4. Scale by alpha for positive/negative class balance
5. Average over all pixels

Key Decisions

• Gamma: 2.0 is standard; higher (3-5) for extreme imbalance, lower (0.5-1) for mild
• Alpha: 0.8 gives more weight to positives (minority class); tune on validation
• vs BCE: Use focal when positive pixels are <5% of total; BCE is fine for balanced masks
• Combining: Can add to Dice loss for a focal-dice hybrid

References

• Loss Function Library - Keras & PyTorch