何時求解，何時驗證：面向LLM推理的計算最優問題解決與生成式驗證

When To Solve, When To Verify: Compute-Optimal Problem Solving and Generative Verification for LLM Reasoning

April 1, 2025

作者: Nishad Singhi, Hritik Bansal, Arian Hosseini, Aditya Grover, Kai-Wei Chang, Marcus Rohrbach, Anna Rohrbach

cs.AI

摘要

擴展測試時計算已成為提升大型語言模型（LLMs）推理能力的關鍵策略，尤其是在數學問題解決等任務中。傳統方法如自我一致性（Self-Consistency, SC）通過生成多個問題解決方案並通過多數投票選取最常見的答案。另一種常見方法是使用獎勵模型（驗證器）對每個解決方案進行評分，並選擇最佳方案。生成式獎勵模型（Generative Reward Models, GenRM）的最新進展將驗證重新定義為下一個令牌預測任務，從而實現了沿新軸的推理時擴展。具體而言，GenRM生成多個驗證思維鏈來評分每個解決方案。在有限的推理預算下，這引入了一個基本權衡：是應該將預算用於通過SC擴展解決方案，還是生成較少的解決方案並將計算資源分配給通過GenRM進行驗證？為解決這一問題，我們在固定推理預算下評估了GenRM與SC的表現。有趣的是，我們發現對於大多數實際推理預算，SC比GenRM更具計算效率。例如，GenRM在消耗高達8倍推理計算後才首次與SC持平，並且需要顯著更多的計算才能超越它。此外，我們推導了GenRM範式的推理擴展定律，揭示了計算最優推理更傾向於更積極地擴展解決方案生成，而非增加驗證次數。我們的工作為通過平衡解決方案生成與驗證來優化測試時擴展提供了實用指導。代碼可在https://github.com/nishadsinghi/sc-genrm-scaling獲取。

English

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.