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-l1-and-l2-regularization
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title: L1 and L2 Regularization
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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: [L1, L2, Lasso, Ridge, ElasticNet, weight decay, regularization]
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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: [machine-learning, regularization, l1, l2, lasso, ridge, weight-decay]
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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: scikit-learn / PyTorch
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---
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# L1 and L2 Regularization
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## 매 한 줄
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> **"매 weight 의 magnitude 의 의 의 의 penalize"**. L1 (Lasso) → 매 sparsity. L2 (Ridge) → 매 small. ElasticNet (combine). 매 modern: 매 weight decay (DL), 매 AdamW의 decoupled. 매 dropout 도 regularizer.
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## 매 핵심
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### 매 L1 (Lasso)
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- 매 penalty: λ Σ |wᵢ|.
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- 매 effect: 매 sparse solutions (zeros).
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- 매 응용: 매 feature selection.
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### 매 L2 (Ridge)
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- 매 penalty: λ Σ wᵢ².
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- 매 effect: 매 small but non-zero.
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- 매 응용: 매 multicollinearity.
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### 매 ElasticNet
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- 매 α L1 + (1-α) L2.
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### 매 modern DL
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- **Weight decay** (= L2).
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- **AdamW**: 매 decoupled weight decay (Loshchilov 2019).
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- **Dropout**: 매 implicit reg.
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- **Batch norm**: 매 implicit reg.
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- **Early stopping**: 매 implicit reg.
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### 매 응용
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1. **Linear regression**: Ridge, Lasso.
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2. **Logistic regression**: 매 class_weight + L2.
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3. **DL training**: weight decay.
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4. **Feature selection**: Lasso.
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## 💻 패턴
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### Ridge (sklearn)
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```python
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from sklearn.linear_model import Ridge
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model = Ridge(alpha=1.0).fit(X, y)
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```
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### Lasso (sklearn)
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```python
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from sklearn.linear_model import Lasso
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model = Lasso(alpha=0.1).fit(X, y)
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print((model.coef_ == 0).sum(), 'zero coefficients')
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```
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### ElasticNet
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```python
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from sklearn.linear_model import ElasticNet
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model = ElasticNet(alpha=0.1, l1_ratio=0.5).fit(X, y)
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```
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### Logistic + L2
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```python
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from sklearn.linear_model import LogisticRegression
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model = LogisticRegression(penalty='l2', C=1.0).fit(X, y)
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# 매 C = 1/alpha (inverse strength)
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```
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### PyTorch weight decay
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```python
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import torch
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optim = torch.optim.SGD(model.parameters(), lr=0.01, weight_decay=1e-4)
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# 매 = L2 in SGD
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```
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### AdamW (decoupled, recommended)
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```python
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optim = torch.optim.AdamW(model.parameters(), lr=1e-3, weight_decay=0.01)
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# 매 better than Adam + weight_decay
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```
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### Manual L1 in PyTorch
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```python
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def l1_penalty(model, lam=1e-5):
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return lam * sum(p.abs().sum() for p in model.parameters())
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loss = task_loss + l1_penalty(model)
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```
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### CV-tune α (sklearn)
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```python
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from sklearn.linear_model import RidgeCV
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model = RidgeCV(alphas=[0.01, 0.1, 1, 10, 100]).fit(X, y)
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print(model.alpha_)
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```
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### LassoCV
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```python
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from sklearn.linear_model import LassoCV
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model = LassoCV(alphas=np.logspace(-4, 0, 50), cv=5).fit(X, y)
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```
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### Path plot (regularization strength sweep)
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```python
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import matplotlib.pyplot as plt
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alphas = np.logspace(-4, 1, 50)
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coefs = []
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for a in alphas:
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coefs.append(Lasso(alpha=a).fit(X, y).coef_)
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plt.plot(alphas, coefs)
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plt.xscale('log')
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plt.xlabel('alpha'); plt.ylabel('coefficient')
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```
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### Group L1 (group lasso)
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```python
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def group_lasso_penalty(weights, groups, lam):
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total = 0
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for group in groups:
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total += lam * np.sqrt(sum(weights[i]**2 for i in group))
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return total
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```
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### Different decay per layer (DL)
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```python
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optim = torch.optim.AdamW([
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{'params': model.encoder.parameters(), 'weight_decay': 0.01},
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{'params': model.head.parameters(), 'weight_decay': 0.001},
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])
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```
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### Bias / norm exclude (best practice)
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```python
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def get_param_groups(model, weight_decay):
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decay, no_decay = [], []
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for name, p in model.named_parameters():
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if p.requires_grad:
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if 'bias' in name or 'norm' in name: no_decay.append(p)
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else: decay.append(p)
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return [
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{'params': decay, 'weight_decay': weight_decay},
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{'params': no_decay, 'weight_decay': 0},
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]
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optim = torch.optim.AdamW(get_param_groups(model, 0.01), lr=1e-3)
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```
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### Effect on bias-variance
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```python
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def reg_effect(alphas, X_train, y_train, X_val, y_val):
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train_err, val_err = [], []
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for a in alphas:
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m = Ridge(alpha=a).fit(X_train, y_train)
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train_err.append(((m.predict(X_train) - y_train) ** 2).mean())
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val_err.append(((m.predict(X_val) - y_val) ** 2).mean())
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return train_err, val_err
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# 매 high alpha → train ↑, val ↓ (until point) → val ↑ (over-reg)
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```
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### Sparsity-induced (modern DL)
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```python
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def magnitude_pruning(model, sparsity=0.5):
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"""매 매 layer 의 의 의 의 magnitude bottom-x% 의 zero out."""
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for name, p in model.named_parameters():
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if 'weight' in name:
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threshold = p.abs().flatten().kthvalue(int(p.numel() * sparsity)).values
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p.data[p.abs() < threshold] = 0
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```
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## 매 결정 기준
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| 상황 | Method |
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| Linear | Ridge / Lasso / ElasticNet |
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| Feature selection | Lasso |
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| Multicollinearity | Ridge |
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| DL | AdamW weight decay |
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| Sparsity goal | Lasso / pruning |
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| Best DL practice | AdamW + exclude bias/norm |
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**기본값**: 매 DL = AdamW + 0.01-0.1 weight decay + bias/norm exclude. 매 linear = ElasticNet CV. 매 sparsity = Lasso.
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## 🔗 Graph
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- 부모: [[L1-and-L2-Regularization|Regularization]] · [[Optimization]]
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- 변형: [[Lasso]] · [[Ridge]] · [[ElasticNet]] · [[Weight-Decay]]
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- Adjacent: [[Generalization-in-AI]]
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## 🤖 LLM 활용
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**언제**: 매 모든 ML training.
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**언제 X**: 매 underfit (no need).
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## ❌ 안티패턴
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- **Adam + weight_decay**: 매 use AdamW.
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- **Same decay for bias / norm**: 매 hurt training.
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- **No CV α**: 매 wrong strength.
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- **L1 for DL** (without sparsity goal): 매 unstable.
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## 🧪 검증 / 중복
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- Verified (Hastie-Tibshirani-Friedman, Loshchilov AdamW 2019).
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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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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — L1/L2 + 매 sklearn / AdamW / param groups / pruning code |
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