refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-focal-loss
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title: Focal Loss
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [focal loss, class imbalance, RetinaNet, hard example mining, dense detection]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.97
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verification_status: applied
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tags: [deep-learning, loss-function, focal-loss, class-imbalance, object-detection, retinanet]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python
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framework: PyTorch / TensorFlow
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---
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# Focal Loss
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## 매 한 줄
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> **"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.
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## 매 핵심
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### 매 formula
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```
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FL(p_t) = -α_t (1 - p_t)^γ log(p_t)
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```
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- p_t: 매 predicted prob 의 true class.
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- γ: 매 focusing parameter (typically 2).
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- α: 매 class weight (balance).
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### 매 motivation
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- 매 dense detection: 매 1000s neg vs 10s pos.
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- 매 CE 의 easy negs 의 dominate.
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- 매 (1-p_t)^γ 의 의 well-classified 의 의 의 weight ↓.
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### 매 응용
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1. **Object detection** (RetinaNet, FCOS, ATSS).
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2. **Instance segmentation**.
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3. **Imbalanced classification**.
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4. **Medical** (rare disease).
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5. **Fraud / anomaly**.
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### 매 alternative
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- **Class weights** (CE).
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- **Online Hard Example Mining (OHEM)**.
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- **Balanced sampling**.
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- **Asymmetric loss** (multi-label).
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- **Class-balanced loss** (Cui 2019).
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## 💻 패턴
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### Focal loss (binary)
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```python
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import torch
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import torch.nn.functional as F
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def focal_loss_binary(logits, targets, alpha=0.25, gamma=2.0):
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p = torch.sigmoid(logits)
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p_t = p * targets + (1 - p) * (1 - targets)
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alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
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ce = F.binary_cross_entropy_with_logits(logits, targets, reduction='none')
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focal = alpha_t * (1 - p_t).pow(gamma) * ce
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return focal.mean()
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```
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### Focal loss (multi-class)
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```python
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def focal_loss_multi(logits, targets, gamma=2.0, alpha=None):
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"""logits: [B, C], targets: [B]."""
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log_p = F.log_softmax(logits, dim=-1)
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log_pt = log_p.gather(1, targets.unsqueeze(1)).squeeze(1)
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pt = log_pt.exp()
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focal = -((1 - pt) ** gamma) * log_pt
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if alpha is not None:
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focal = alpha[targets] * focal
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return focal.mean()
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```
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### As nn.Module
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```python
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class FocalLoss(torch.nn.Module):
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def __init__(self, alpha=0.25, gamma=2.0):
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super().__init__()
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self.alpha = alpha
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self.gamma = gamma
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def forward(self, logits, targets):
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return focal_loss_binary(logits, targets, self.alpha, self.gamma)
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```
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### RetinaNet detection
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```python
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class RetinaNetLoss(torch.nn.Module):
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def __init__(self, n_classes, gamma=2.0, alpha=0.25):
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super().__init__()
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self.classification = FocalLoss(alpha=alpha, gamma=gamma)
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self.regression = torch.nn.SmoothL1Loss()
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def forward(self, cls_logits, box_preds, cls_targets, box_targets, fg_mask):
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cls_loss = self.classification(cls_logits, cls_targets)
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n_fg = fg_mask.sum().clamp(min=1)
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box_loss = self.regression(box_preds[fg_mask], box_targets[fg_mask])
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return cls_loss + box_loss / n_fg
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```
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### Class-balanced focal (Cui 2019)
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```python
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def class_balanced_focal(logits, targets, samples_per_class, beta=0.999, gamma=2.0):
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"""매 effective number per class."""
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eff_num = 1 - beta ** samples_per_class
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weights = (1 - beta) / eff_num
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weights = weights / weights.sum() * len(samples_per_class)
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log_p = F.log_softmax(logits, -1)
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log_pt = log_p.gather(1, targets.unsqueeze(1)).squeeze()
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pt = log_pt.exp()
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return (-weights[targets] * (1 - pt) ** gamma * log_pt).mean()
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```
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### Asymmetric focal (multi-label)
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```python
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def asymmetric_focal(logits, targets, gamma_pos=1, gamma_neg=4, clip=0.05):
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"""매 Ben-Baruch 2020. 매 asymmetric γ."""
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p = torch.sigmoid(logits)
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p_neg = (p - clip).clamp(min=0)
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pos_loss = targets * (1 - p) ** gamma_pos * torch.log(p.clamp(min=1e-8))
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neg_loss = (1 - targets) * p_neg ** gamma_neg * torch.log((1 - p).clamp(min=1e-8))
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return -(pos_loss + neg_loss).mean()
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```
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### γ tuning
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```python
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# 매 typical γ
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GAMMA_VALUES = {
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'extreme_imbalance': 5.0,
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'object_detection': 2.0, # RetinaNet
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'medical_rare_disease': 3.0,
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'mild_imbalance': 1.0,
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'no_imbalance': 0, # 매 = CE
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}
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```
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### Focal vs CE comparison
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```python
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def compare_losses(p_easy=0.95, p_hard=0.5):
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"""매 easy 매 hard 의 contribution."""
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ce_easy = -torch.log(torch.tensor(p_easy))
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ce_hard = -torch.log(torch.tensor(p_hard))
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fl_easy = (1 - p_easy) ** 2 * ce_easy
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fl_hard = (1 - p_hard) ** 2 * ce_hard
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print(f'CE: easy {ce_easy:.3f}, hard {ce_hard:.3f}, ratio {ce_hard/ce_easy:.1f}x')
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print(f'Focal γ=2: easy {fl_easy:.4f}, hard {fl_hard:.3f}, ratio {fl_hard/fl_easy:.0f}x')
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# 매 focal 의 hard 의 의 의 의 dominate
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```
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### OHEM alternative
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```python
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def ohem_loss(logits, targets, ratio=0.25):
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"""매 매 batch 의 매 hardest examples만 keep."""
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losses = F.cross_entropy(logits, targets, reduction='none')
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n_keep = int(len(losses) * ratio)
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topk = losses.topk(n_keep)[0]
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return topk.mean()
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```
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### Combine: focal + dice (segmentation)
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```python
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def focal_dice(logits, targets):
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fl = focal_loss_binary(logits, targets)
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p = torch.sigmoid(logits)
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intersection = (p * targets).sum()
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dice = 1 - 2 * intersection / (p.sum() + targets.sum() + 1)
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return fl + dice
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```
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### Eval metric (PR-AUC for imbalanced)
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```python
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from sklearn.metrics import average_precision_score
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def eval_imbalanced(probs, targets):
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return {
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'pr_auc': average_precision_score(targets, probs),
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# 매 not accuracy — meaningless for imbalanced
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}
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```
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## 매 결정 기준
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| 상황 | Loss |
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| Dense object detection | Focal (γ=2) |
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| Mild imbalance | Class-weighted CE |
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| Extreme imbalance | Focal (γ=3-5) |
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| Multi-label imbalanced | Asymmetric focal |
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| Segmentation | Focal + Dice |
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| Easy task | Plain CE |
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**기본값**: 매 imbalance > 100:1 → focal γ=2 + α=0.25. 매 multi-label → asymmetric. 매 evaluation = PR-AUC, not accuracy.
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## 🔗 Graph
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- 부모: [[Loss-Function]] · [[Object-Detection]]
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- 응용: [[RetinaNet]]
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- Adjacent: [[Cross-Entropy Loss]]
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## 🤖 LLM 활용
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**언제**: 매 detection. 매 imbalanced. 매 medical.
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**언제 X**: 매 balanced. 매 regression.
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## ❌ 안티패턴
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- **Focal for balanced**: 매 underfit.
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- **γ too high**: 매 most examples 의 ignore.
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- **No α**: 매 class balance 의 still off.
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- **Accuracy metric**: 매 imbalanced 의 misleading.
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## 🧪 검증 / 중복
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- Verified (Lin RetinaNet 2017, Cui 2019, Ben-Baruch ASL 2020).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-04-26 | LOSS-002 auto |
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — focal + 매 binary / multi / asymmetric / class-balanced code |
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