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arXiv 2602.22583cs.AIcs.CL
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数学推理中的策略可执行性:利用人类-模型差异实现有效指导

Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance

National University of Singapore(新加坡国立大学);University of California, Berkeley(加州大学伯克利分校)

Weida Liang, Yiyou Sun, Shuyuan Nan, Chuang Li, Dawn Song, Kenji Kawaguchi

AI总结:

本文提出SSR框架,通过显式建模策略可执行性,利用人类-模型差异提升数学推理的指导效果。

摘要:

基于实例的指导被广泛用于在推理过程中提高数学推理能力,但其效果在不同问题和模型之间高度不稳定——即使指导是正确的且问题相关。我们展示这种不稳定性源于一个此前未被充分探讨的差距:策略使用(一种推理策略是否出现在成功的解决方案中)与策略可执行性(当该策略被作为目标模型的指导时是否仍然有效)之间的差距。通过控制分析配对的人类编写和模型生成的解决方案,我们识别出使用和可执行性之间系统性的脱节:人类和模型衍生的策略在结构上和领域相关的方式上有所不同,导致互补的优势和一致的来源依赖的反转。基于这一诊断,我们提出了Selective Strategy Retrieval(SSR),一个测试时框架,通过选择性检索和结合策略来显式建模可执行性,使用经验的、多路线的、来源感知的信号。在多个数学推理基准上,SSR在直接求解、上下文学习和单源指导上均取得可靠的改进,对紧凑推理模型在AIME25上提高准确率高达+13点,在Apex上提高5点。代码和基准已公开在:https://github.com/lwd17/strategy-execute-pipeline。

英文摘要:

Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models-even when the guidance is correct and problem-relevant. We show that this instability arises from a previously underexplored gap between strategy usage-whether a reasoning strategy appears in successful solutions-and strategy executability-whether the strategy remains effective when instantiated as guidance for a target model. Through a controlled analysis of paired human-written and model-generated solutions, we identify a systematic dissociation between usage and executability: human- and model-derived strategies differ in structured, domain-dependent ways, leading to complementary strengths and consistent source-dependent reversals under guidance. Building on this diagnosis, we propose Selective Strategy Retrieval (SSR), a test-time framework that explicitly models executability by selectively retrieving and combining strategies using empirical, multi-route, source-aware signals. Across multiple mathematical reasoning benchmarks, SSR yields reliable and consistent improvements over direct solving, in-context learning, and single-source guidance, improving accuracy by up to $+13$ points on AIME25 and $+5$ points on Apex for compact reasoning models. Code and benchmark are publicly available at: https://github.com/lwd17/strategy-execute-pipeline.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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