在推理预算有限时,生成多个解比精细验证更高效。
When To Solve, When To Verify: Compute-Optimal Problem Solving and Generative Verification for LLM Reasoning
- 对比自洽法与生成式验证的计算效率,发现前者更优。
- 生成式验证需8倍算力才追平自洽法,长期仍落后。
- 建议优先扩大解题数量,而非增加验证次数。
提升大语言模型推理能力的关键策略之一是扩展测试时计算资源,尤其在数学问题求解等任务中。传统方法如自洽性(Self-Consistency, SC)通过生成多个解并以多数投票选择答案;另一类方法使用奖励模型(验证器)评分每个解并选最优。近期生成式奖励模型(GenRM)将验证重构为下一个词预测任务,可在推理阶段沿新维度扩展计算。然而,在固定推理预算下,存在核心权衡:应将资源用于扩大解题数量(SC)还是增强验证(GenRM)?本文评估了两种方法在不同模型和数据集上的表现,发现对于大多数实际推理预算,SC比GenRM更高效。例如,GenRM需消耗高达8倍的推理算力才能达到与SC相当的效果,且要显著超越仍需更多算力。此外,我们推导出GenRM范式的推理缩放定律,表明计算最优推理应更激进地扩展解题生成,而非验证次数。本研究为测试时扩展的平衡提供了实用指导。代码已开源:https://github.com/nishadsinghi/sc-genrm-scaling。
原文摘要 · Abstract (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.
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