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Antigravity Agent
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id: wiki-2026-0508-stochastic-gradient-descent
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title: Stochastic Gradient Descent
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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: [SGD, Mini-batch SGD, Stochastic Gradient Descent]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.95
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verification_status: applied
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tags: [machine-learning, optimization, deep-learning, gradient-descent]
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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
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---
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# Stochastic Gradient Descent (SGD)
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## 매 한 줄
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> **"매 한 sample (or mini-batch) 에 대한 gradient 로 매 step — 매 noisy 하지만 매 cheap, 매 escape from local minima"**. Robbins & Monro (1951) 의 stochastic approximation 의 후예. 2026 deep learning 의 foundation — 매 SGD+momentum, AdamW, Lion 가 매 default.
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## 매 핵심
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### 매 vs full-batch
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- **Batch GD**: 매 entire dataset gradient — 매 expensive, deterministic.
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- **SGD (online)**: 매 single sample — 매 noisy, fast.
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- **Mini-batch SGD**: 매 32–4096 samples — 매 modern default. 매 GPU 의 vectorize.
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### 매 update rule
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- Vanilla SGD: `θ ← θ − η ∇L(θ; x_i, y_i)`.
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- Momentum: `v ← μv + ∇L; θ ← θ − ηv`.
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- Nesterov: 매 lookahead momentum.
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### 매 modern variants
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- **AdamW** (Loshchilov 2019): adaptive lr + decoupled weight decay — 매 LLM/transformer default.
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- **Lion** (Chen 2023): sign-based momentum — 매 less memory, comparable.
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- **Sophia** (2023): second-order — 매 LLM pretrain.
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- **Muon** (Jordan 2024): orthogonalized momentum — 매 emerging.
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### 매 응용
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1. Neural network training (all of deep learning).
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2. Logistic regression, linear regression at scale.
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3. Online learning / streaming data.
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## 💻 패턴
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### PyTorch 2.5 — SGD with momentum
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```python
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import torch
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from torch import nn, optim
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model = nn.Linear(784, 10)
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optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9, nesterov=True)
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loss_fn = nn.CrossEntropyLoss()
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for epoch in range(10):
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for x, y in dataloader:
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optimizer.zero_grad()
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loss = loss_fn(model(x), y)
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loss.backward()
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optimizer.step()
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```
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### AdamW (transformer default 2026)
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```python
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optimizer = optim.AdamW(
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model.parameters(),
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lr=3e-4,
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betas=(0.9, 0.95),
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weight_decay=0.1,
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fused=True, # 매 GPU fused kernel
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)
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```
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### Cosine LR schedule
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```python
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from torch.optim.lr_scheduler import CosineAnnealingLR
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scheduler = CosineAnnealingLR(optimizer, T_max=num_steps, eta_min=1e-6)
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for step in range(num_steps):
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train_step()
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optimizer.step()
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scheduler.step()
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```
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### Linear warmup + cosine decay (LLM standard)
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```python
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def lr_lambda(step):
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if step < warmup:
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return step / warmup
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progress = (step - warmup) / (total - warmup)
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return 0.5 * (1 + math.cos(math.pi * progress))
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scheduler = optim.lr_scheduler.LambdaLR(optimizer, lr_lambda)
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```
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### Gradient clipping (stability)
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```python
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torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0)
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optimizer.step()
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```
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### Mixed precision SGD (bf16, H100)
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```python
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scaler = torch.amp.GradScaler("cuda")
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with torch.autocast("cuda", dtype=torch.bfloat16):
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loss = loss_fn(model(x), y)
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scaler.scale(loss).backward()
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scaler.unscale_(optimizer)
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torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)
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scaler.step(optimizer)
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scaler.update()
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```
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### Pure NumPy SGD (linear regression)
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```python
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import numpy as np
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def sgd(X, y, lr=0.01, epochs=100, batch=32):
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w = np.zeros(X.shape[1])
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for _ in range(epochs):
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idx = np.random.permutation(len(X))
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for i in range(0, len(X), batch):
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b = idx[i:i+batch]
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grad = X[b].T @ (X[b] @ w - y[b]) / len(b)
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w -= lr * grad
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return w
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```
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### Lion optimizer (2026 alt)
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```python
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# pip install lion-pytorch
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from lion_pytorch import Lion
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optimizer = Lion(model.parameters(), lr=1e-4, weight_decay=0.01)
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Image classification (ResNet, ViT) | SGD + momentum + cosine |
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| LLM / Transformer training | AdamW + linear warmup + cosine |
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| Memory-constrained large model | Lion or 8-bit Adam (bitsandbytes) |
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| Convex optimization, theoretical guarantee | Vanilla SGD with decreasing lr |
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| Online streaming data | Mini-batch SGD, lr ~ 1/sqrt(t) |
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**기본값**: 매 transformer/LLM → AdamW 3e-4 + warmup 1k steps + cosine. 매 CNN → SGD 0.1 + momentum 0.9 + cosine.
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## 🔗 Graph
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- 부모: [[Gradient Descent]] · [[Optimization]]
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- 변형: [[Adam]] · [[AdamW]]
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- 응용: [[Deep Learning]]
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- Adjacent: [[Gradient Clipping]] · [[데이터 사이언스 및 ML 엔지니어링|Backpropagation]]
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## 🤖 LLM 활용
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**언제**: 매 model training의 default optimizer choice; debug convergence (loss spike, plateau).
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**언제 X**: 매 closed-form solution exists (small linear regression — use normal equation); 매 second-order necessary (small classical ML).
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## ❌ 안티패턴
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- **lr too high**: 매 loss explosion / NaN. 매 warmup + clip.
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- **No weight decay**: 매 overfitting.
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- **Momentum with lr too high**: 매 oscillation.
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- **AdamW lr=1e-3 for LLM**: 매 too high — 1e-4 ~ 3e-4 가 매 standard.
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- **Batch size 1 on GPU**: 매 underutilization. 매 32+ 의 사용.
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## 🧪 검증 / 중복
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- Verified (PyTorch docs 2.5; Goodfellow *Deep Learning* ch.8; Loshchilov AdamW 2019).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — SGD + modern variants (AdamW, Lion, Muon) for 2026 |
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