---
id: wiki-2026-0508-focal-loss
title: Focal Loss
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [focal loss, class imbalance, RetinaNet, hard example mining, dense detection]
duplicate_of: none
source_trust_level: A
confidence_score: 0.97
verification_status: applied
tags: [deep-learning, loss-function, focal-loss, class-imbalance, object-detection, retinanet]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch / TensorFlow
---

# Focal Loss

## 매 한 줄
> **"매 cross-entropy 의 의 의 의 (1-p_t)^γ factor"**. Lin 2017 (RetinaNet). 매 easy example 의 down-weight + 매 hard example 의 focus. 매 dense object detection 의 enable. 매 modern: 매 detection, 매 imbalanced classification, 매 instance segmentation.

## 매 핵심

### 매 formula
```
FL(p_t) = -α_t (1 - p_t)^γ log(p_t)
```
- p_t: 매 predicted prob 의 true class.
- γ: 매 focusing parameter (typically 2).
- α: 매 class weight (balance).

### 매 motivation
- 매 dense detection: 매 1000s neg vs 10s pos.
- 매 CE 의 easy negs 의 dominate.
- 매 (1-p_t)^γ 의 의 well-classified 의 의 의 weight ↓.

### 매 응용
1. **Object detection** (RetinaNet, FCOS, ATSS).
2. **Instance segmentation**.
3. **Imbalanced classification**.
4. **Medical** (rare disease).
5. **Fraud / anomaly**.

### 매 alternative
- **Class weights** (CE).
- **Online Hard Example Mining (OHEM)**.
- **Balanced sampling**.
- **Asymmetric loss** (multi-label).
- **Class-balanced loss** (Cui 2019).

## 💻 패턴

### Focal loss (binary)
```python
import torch
import torch.nn.functional as F

def focal_loss_binary(logits, targets, alpha=0.25, gamma=2.0):
    p = torch.sigmoid(logits)
    p_t = p * targets + (1 - p) * (1 - targets)
    alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
    ce = F.binary_cross_entropy_with_logits(logits, targets, reduction='none')
    focal = alpha_t * (1 - p_t).pow(gamma) * ce
    return focal.mean()
```

### Focal loss (multi-class)
```python
def focal_loss_multi(logits, targets, gamma=2.0, alpha=None):
    """logits: [B, C], targets: [B]."""
    log_p = F.log_softmax(logits, dim=-1)
    log_pt = log_p.gather(1, targets.unsqueeze(1)).squeeze(1)
    pt = log_pt.exp()
    
    focal = -((1 - pt) ** gamma) * log_pt
    if alpha is not None:
        focal = alpha[targets] * focal
    return focal.mean()
```

### As nn.Module
```python
class FocalLoss(torch.nn.Module):
    def __init__(self, alpha=0.25, gamma=2.0):
        super().__init__()
        self.alpha = alpha
        self.gamma = gamma
    
    def forward(self, logits, targets):
        return focal_loss_binary(logits, targets, self.alpha, self.gamma)
```

### RetinaNet detection
```python
class RetinaNetLoss(torch.nn.Module):
    def __init__(self, n_classes, gamma=2.0, alpha=0.25):
        super().__init__()
        self.classification = FocalLoss(alpha=alpha, gamma=gamma)
        self.regression = torch.nn.SmoothL1Loss()
    
    def forward(self, cls_logits, box_preds, cls_targets, box_targets, fg_mask):
        cls_loss = self.classification(cls_logits, cls_targets)
        n_fg = fg_mask.sum().clamp(min=1)
        box_loss = self.regression(box_preds[fg_mask], box_targets[fg_mask])
        return cls_loss + box_loss / n_fg
```

### Class-balanced focal (Cui 2019)
```python
def class_balanced_focal(logits, targets, samples_per_class, beta=0.999, gamma=2.0):
    """매 effective number per class."""
    eff_num = 1 - beta ** samples_per_class
    weights = (1 - beta) / eff_num
    weights = weights / weights.sum() * len(samples_per_class)
    
    log_p = F.log_softmax(logits, -1)
    log_pt = log_p.gather(1, targets.unsqueeze(1)).squeeze()
    pt = log_pt.exp()
    return (-weights[targets] * (1 - pt) ** gamma * log_pt).mean()
```

### Asymmetric focal (multi-label)
```python
def asymmetric_focal(logits, targets, gamma_pos=1, gamma_neg=4, clip=0.05):
    """매 Ben-Baruch 2020. 매 asymmetric γ."""
    p = torch.sigmoid(logits)
    p_neg = (p - clip).clamp(min=0)
    
    pos_loss = targets * (1 - p) ** gamma_pos * torch.log(p.clamp(min=1e-8))
    neg_loss = (1 - targets) * p_neg ** gamma_neg * torch.log((1 - p).clamp(min=1e-8))
    return -(pos_loss + neg_loss).mean()
```

### γ tuning
```python
# 매 typical γ
GAMMA_VALUES = {
    'extreme_imbalance': 5.0,
    'object_detection': 2.0,  # RetinaNet
    'medical_rare_disease': 3.0,
    'mild_imbalance': 1.0,
    'no_imbalance': 0,  # 매 = CE
}
```

### Focal vs CE comparison
```python
def compare_losses(p_easy=0.95, p_hard=0.5):
    """매 easy 매 hard 의 contribution."""
    ce_easy = -torch.log(torch.tensor(p_easy))
    ce_hard = -torch.log(torch.tensor(p_hard))
    
    fl_easy = (1 - p_easy) ** 2 * ce_easy
    fl_hard = (1 - p_hard) ** 2 * ce_hard
    
    print(f'CE: easy {ce_easy:.3f}, hard {ce_hard:.3f}, ratio {ce_hard/ce_easy:.1f}x')
    print(f'Focal γ=2: easy {fl_easy:.4f}, hard {fl_hard:.3f}, ratio {fl_hard/fl_easy:.0f}x')
    # 매 focal 의 hard 의 의 의 의 dominate
```

### OHEM alternative
```python
def ohem_loss(logits, targets, ratio=0.25):
    """매 매 batch 의 매 hardest examples만 keep."""
    losses = F.cross_entropy(logits, targets, reduction='none')
    n_keep = int(len(losses) * ratio)
    topk = losses.topk(n_keep)[0]
    return topk.mean()
```

### Combine: focal + dice (segmentation)
```python
def focal_dice(logits, targets):
    fl = focal_loss_binary(logits, targets)
    p = torch.sigmoid(logits)
    intersection = (p * targets).sum()
    dice = 1 - 2 * intersection / (p.sum() + targets.sum() + 1)
    return fl + dice
```

### Eval metric (PR-AUC for imbalanced)
```python
from sklearn.metrics import average_precision_score
def eval_imbalanced(probs, targets):
    return {
        'pr_auc': average_precision_score(targets, probs),
        # 매 not accuracy — meaningless for imbalanced
    }
```

## 매 결정 기준
| 상황 | Loss |
|---|---|
| Dense object detection | Focal (γ=2) |
| Mild imbalance | Class-weighted CE |
| Extreme imbalance | Focal (γ=3-5) |
| Multi-label imbalanced | Asymmetric focal |
| Segmentation | Focal + Dice |
| Easy task | Plain CE |

**기본값**: 매 imbalance > 100:1 → focal γ=2 + α=0.25. 매 multi-label → asymmetric. 매 evaluation = PR-AUC, not accuracy.

## 🔗 Graph
- 부모: [[Loss-Function]] · [[Object-Detection]]
- 응용: [[RetinaNet]]
- Adjacent: [[Cross-Entropy-Loss]]

## 🤖 LLM 활용
**언제**: 매 detection. 매 imbalanced. 매 medical.
**언제 X**: 매 balanced. 매 regression.

## ❌ 안티패턴
- **Focal for balanced**: 매 underfit.
- **γ too high**: 매 most examples 의 ignore.
- **No α**: 매 class balance 의 still off.
- **Accuracy metric**: 매 imbalanced 의 misleading.

## 🧪 검증 / 중복
- Verified (Lin RetinaNet 2017, Cui 2019, Ben-Baruch ASL 2020).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-04-26 | LOSS-002 auto |
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — focal + 매 binary / multi / asymmetric / class-balanced code |