"A Simple and Provable Scaling Law for the Test-Time Compute of Large Language Models"

Scale up your LLM's test-time compute to achieve near-perfect reliability

This paper introduces a two-stage algorithm that improves LLM reliability through test-time computation. It proves that failure probability decreases exponentially with more compute, requiring only a black-box LLM without external verifiers.

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https://arxiv.org/abs/2411.19477

🤔 Original Problem:

LLMs still face reliability challenges in high-stakes scenarios where 99.9% success rate is needed instead of 90%. Current solutions like chain-of-thought or self-verification have limitations.

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🔧 Solution in this Paper:

→ The algorithm first generates N candidate solutions in parallel

→ It then runs a knockout tournament where pairs of solutions compete K times

→ Winners advance through tournament rounds until a final solution emerges

→ The process requires N×(K+1) LLM calls that can run in parallel

→ Success relies on two conditions: LLM can generate correct solutions (p_gen>0) and can compare solutions better than random (p_comp>0.5)

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💡 Key Insights:

→ Failure probability decreases exponentially with more compute

→ Method works best for reasoning-heavy tasks where side-by-side comparison helps

→ Performance varies across different problem types (math vs psychology)

→ Task decomposition can help tackle complex problems efficiently

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📊 Results:

→ Tested on MMLU-Pro benchmark across 14 categories

→ Accuracy improves significantly with increased N and K parameters

→ Math and engineering showed better gains than psychology

→ Method validated theoretical assumptions about p_gen and p_comp values