---
id: wiki-2026-0508-layer-normalization
title: Layer Normalization
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [LayerNorm, LN, RMSNorm]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [deep-learning, transformer, normalization, llm-internals]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: pytorch
---

# Layer Normalization

## 매 한 줄
> **"매 sample 마다 feature 축으로 정규화"**. BatchNorm 과 달리 batch 의존 없음 — RNN/Transformer 의 표준. 2026 LLM 은 대부분 **RMSNorm** + **pre-norm** 구조 (LLaMA, Mistral, Qwen).

## 매 핵심

### 매 수식
- **LayerNorm**: `y = γ * (x - μ) / sqrt(σ² + ε) + β`, μ/σ 는 **마지막 축** 기준.
- **RMSNorm**: μ 빼지 않음. `y = γ * x / sqrt(mean(x²) + ε)`. 7-15% faster, 거의 동등 성능.
- γ, β 는 learnable.

### 매 vs BatchNorm
| | LayerNorm | BatchNorm |
|---|---|---|
| 정규화 축 | feature | batch |
| Batch=1 동작 | 됨 | 통계 무의미 |
| Train/Eval 차이 | 없음 | running mean 사용 |
| 시퀀스 길이 가변 | 됨 | 안 됨 |
| GPU memory | 낮음 | 더 낮음 (가끔) |

### 매 Pre-norm vs Post-norm
- **Post-norm** (원조 Transformer): `LN(x + Sublayer(x))`. 깊으면 학습 불안정.
- **Pre-norm** (GPT-2+): `x + Sublayer(LN(x))`. gradient flow 안정, warmup 적게 필요.
- 2026: 거의 모든 대형 LLM = pre-norm + RMSNorm.

### 매 변형
- **GroupNorm**: feature 를 G group 으로 나눠 정규화. CNN/diffusion.
- **InstanceNorm**: per-sample, per-channel. style transfer.
- **DeepNorm** (Microsoft): post-norm 으로 1000 layer 가능.
- **ScaleNorm**: γ 하나만, β 제거.

## 💻 패턴

### PyTorch LayerNorm
```python
import torch.nn as nn
ln = nn.LayerNorm(normalized_shape=768)  # 마지막 차원
y = ln(x)  # x: (B, T, 768)
```

### RMSNorm 직접 구현
```python
class RMSNorm(nn.Module):
    def __init__(self, dim, eps=1e-6):
        super().__init__()
        self.weight = nn.Parameter(torch.ones(dim))
        self.eps = eps
    def forward(self, x):
        rms = x.pow(2).mean(-1, keepdim=True).add(self.eps).rsqrt()
        return self.weight * x * rms
```

### Pre-norm Transformer block
```python
class Block(nn.Module):
    def __init__(self, dim, n_heads):
        super().__init__()
        self.ln1 = nn.LayerNorm(dim)
        self.attn = nn.MultiheadAttention(dim, n_heads, batch_first=True)
        self.ln2 = nn.LayerNorm(dim)
        self.mlp = nn.Sequential(nn.Linear(dim, 4*dim), nn.GELU(), nn.Linear(4*dim, dim))
    def forward(self, x):
        x = x + self.attn(self.ln1(x), self.ln1(x), self.ln1(x))[0]
        x = x + self.mlp(self.ln2(x))
        return x
```

### Fused LN (Apex/Triton)
```python
# nvidia apex 또는 torch.compile 자동 fused
from apex.normalization import FusedLayerNorm
ln = FusedLayerNorm(768)  # ~20% faster on A100
```

### Manual LN (이해용)
```python
def layer_norm(x, gamma, beta, eps=1e-5):
    mu = x.mean(-1, keepdim=True)
    var = x.var(-1, unbiased=False, keepdim=True)
    return gamma * (x - mu) / (var + eps).sqrt() + beta
```

### LayerNorm vs RMSNorm 벤치마크 메모
```python
# A100, hidden=4096, seq=2048
# LayerNorm: 0.42ms
# RMSNorm:   0.35ms (-17%)
# 정확도 차이: < 0.1pp on perplexity
```

## 매 결정 기준
| 모델 | 정규화 |
|---|---|
| 표준 Transformer/BERT | LayerNorm post-norm or pre-norm |
| 대형 LLM (decoder-only) | RMSNorm + pre-norm |
| CNN | BatchNorm or GroupNorm |
| Diffusion U-Net | GroupNorm |
| Style transfer | InstanceNorm |
| 1000+ layer | DeepNorm |

**기본값**: LLM 만들면 RMSNorm + pre-norm.

## 🔗 Graph
- 부모: [[Normalization]], [[Transformer]]
- 변형: [[RMSNorm]], [[GroupNorm]], [[BatchNorm]], [[DeepNorm]]
- 응용: [[BERT]], [[GPT]], [[LLaMA]]
- Adjacent: [[Residual-Connection]], [[Weight-Initialization]], [[Gradient-Stability]]

## 🤖 LLM 활용
**언제**: Transformer 류, RNN, 가변 길이 시퀀스, batch=1 inference.
**언제 X**: 큰 batch CNN — BatchNorm 더 빠르고 정확.

## ❌ 안티패턴
- **Post-norm 으로 깊은 Transformer**: 발산. pre-norm 사용.
- **eps 너무 작음 (1e-12)**: fp16 underflow. 1e-5 ~ 1e-6 권장.
- **β 학습 (RMSNorm)**: RMSNorm 정의에 β 없음. γ 만.
- **마지막 축이 아닌 곳**: LayerNorm 은 last dim 정규화가 표준.

## 🧪 검증 / 중복
- Ba et al. 2016 (LayerNorm), Zhang & Sennrich 2019 (RMSNorm).
- LLaMA paper (Touvron 2023), Xiong et al. 2020 (pre-norm 분석).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — RMSNorm/pre-norm 표준화 반영, BatchNorm 비교표 |