2nd/10_Wiki/Topics/AI_and_ML/Test-Time Compute Scaling (추론 시간 계산 스케일링).md

---
id: wiki-2026-0508-test-time-compute-scaling-추론-시간-
title: Test Time Compute Scaling (추론 시간 계산 스케일링)
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Test-Time Compute, Inference-Time Scaling, Reasoning Models]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [llm, reasoning, scaling, test-time-compute]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: vLLM / Anthropic SDK / OpenAI SDK
---

# Test Time Compute Scaling (추론 시간 계산 스케일링)

## 매 한 줄
> **"매 think longer, get smarter"**. Test-time compute scaling 매 inference 시 더 많은 compute (매 longer chain-of-thought, sampling, search) 로 quality 의 trade off. OpenAI o1 (2024-09) → o3 / DeepSeek-R1 (2025-01) → Claude 4.x extended thinking (2025+) 의 paradigm. 매 training-time scaling laws 의 보완.

## 매 핵심

### 매 두 axes
- **More thinking (long CoT)** — 매 single sample 안 더 긴 reasoning trace. o1, R1, Claude extended thinking.
- **Search / sampling** — 매 multiple samples + verifier (best-of-N, MCTS, beam). AlphaCode, ReST, MathShepherd.

### 매 modern (2025-2026)
- **RL on reasoning** — 매 RLHF + RL on verifiable rewards (math, code) → 매 long CoT 의 emerge. R1-zero, R1.
- **Extended thinking budgets** — 매 Claude 의 `thinking_budget` parameter, OpenAI 의 `reasoning_effort`.
- **Scaling law** — 매 log compute ↔ accuracy linear (Snell 2024, OpenAI o-series chart).
- **Cost shift** — 매 training 1x 의 inference Nx — 매 economics 의 reshape.

### 매 응용
1. Math (AIME, IMO).
2. Code (SWE-bench, competition).
3. Agentic planning (deep tool-use chains).
4. Scientific reasoning (GPQA).

## 💻 패턴

### Claude extended thinking
```python
from anthropic import Anthropic
client = Anthropic()

resp = client.messages.create(
    model="claude-opus-4-7",
    max_tokens=8000,
    thinking={"type": "enabled", "budget_tokens": 16000},
    messages=[{"role": "user", "content": "Solve: ..."}],
)
for block in resp.content:
    if block.type == "thinking":
        print("THINK:", block.thinking[:200])
    elif block.type == "text":
        print("ANS:", block.text)
```

### OpenAI reasoning effort
```python
from openai import OpenAI
client = OpenAI()
resp = client.responses.create(
    model="o3",
    input="Prove the AM-GM inequality.",
    reasoning={"effort": "high"},   # low / medium / high
)
print(resp.output_text)
```

### Best-of-N + verifier
```python
def best_of_n(prompt, n=8, verifier=None):
    samples = [client.messages.create(
        model="claude-opus-4-7",
        max_tokens=2000,
        temperature=0.8,
        messages=[{"role": "user", "content": prompt}],
    ).content[0].text for _ in range(n)]
    return max(samples, key=verifier)  # 매 verifier: unit test pass count, etc.
```

### Self-consistency (majority vote)
```python
from collections import Counter
answers = [extract_answer(s) for s in samples]
final = Counter(answers).most_common(1)[0][0]
```

### MCTS-style search (sketch)
```python
def expand(node):
    children = [llm.continue_from(node.partial, temp=0.9) for _ in range(k)]
    return [Node(c, score=verifier(c)) for c in children]

def search(root, depth=4):
    frontier = [root]
    for _ in range(depth):
        candidates = sum((expand(n) for n in frontier), [])
        frontier = sorted(candidates, key=lambda n: -n.score)[:beam]
    return max(frontier, key=lambda n: n.score)
```

### Budget controller
```python
def adaptive_thinking(prompt, easy_budget=2000, hard_budget=32000):
    # 매 difficulty classifier 의 first
    diff = client.messages.create(model="claude-haiku-4", ...).content[0].text
    budget = hard_budget if "hard" in diff else easy_budget
    return client.messages.create(
        model="claude-opus-4-7",
        thinking={"type": "enabled", "budget_tokens": budget},
        messages=[{"role": "user", "content": prompt}],
    )
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Math / code with verifier | RL-trained reasoning model (o3, R1) + search |
| Open-ended reasoning | Extended thinking (Claude 4.x) |
| Latency-critical | Skip — use small fast model |
| Cost-critical batch | Self-consistency 4-8 samples |
| Search exploitable | Best-of-N + verifier |
| Fuzzy quality | Reasoning model > base model |

**기본값**: 매 reasoning model (o3 / Claude extended thinking) 매 hard task, base model 매 easy task — 매 difficulty router 로 split.

## 🔗 Graph
- 부모: [[Scaling-Laws]]
- 변형: [[Chain-of-Thought]] · [[Self-Consistency]] · [[Best-of-N]] · [[MCTS]]
- 응용: [[Code-Generation]]
- Adjacent: [[RLHF]]

## 🤖 LLM 활용
**언제**: 매 hard reasoning task, verifiable output (math/code), agent planning, quality > latency.
**언제 X**: 매 simple lookup / chat — 매 thinking 매 cost waste.

## ❌ 안티패턴
- **Always max thinking budget**: 매 easy task 의 32k thinking 매 cost burn — 매 router 사용.
- **No verifier in best-of-N**: 매 random sample 매 noise — 매 verifier (unit test, math check) 의 essential.
- **Stream thinking to user**: 매 thinking content 매 internal — 매 user UI 에 final text 만.
- **Caching invalidation**: 매 thinking budget 변경 시 cache miss — 매 stable budget 권장.

## 🧪 검증 / 중복
- Verified (OpenAI o1/o3 system cards, DeepSeek-R1 paper 2025-01, Anthropic extended thinking docs, Snell et al. 2024).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — o-series / R1 / Claude extended thinking patterns |