SalaMAnder：基于Shapley值的链式思考推理数学表达式归因与度量方法
SalaMAnder: Shapley-based Mathematical Expression Attribution and Metric for Chain-of-Thought Reasoning
AI总结：
本文提出SalaMAnder框架，利用Shapley值对少样本CoT推理中的数学表达式进行归因，并开发CoSP指标，以数学上严格的方式解释并优化提示构建与模型性能之间的关系。
摘要：
链式思考（CoT）提示大幅提升了大语言模型（LLMs）的数学推理能力，然而这种改进背后的机制仍未得到探索。本文提出了SalaMAnder（基于Shapley值的数学表达式归因与度量），这是一种具有理论依据的方法论，同时也是一种数学上严格的评估指标，用于量化少样本CoT推理中的组件级贡献。具体而言，我们利用Shapley值进行数学表达式归因，并开发了一种高效的分层采样算法，显著降低了计算复杂度。此外，我们通过协方差分析开发了CoSP（Shapley正基数）指标。在流行的大语言模型和多种数学基准上的全面验证表明，SalaMAnder框架中的CoSP指标与模型性能表现出稳健的单调相关性，不仅为现有少样本CoT的经验性成功提供了理论解释，还为提示构建优化建立了数学上严格的原则。进一步地，我们验证了解释的可靠性，并在此基础上统一了先前工作的见解。
英文摘要：
Chain-of-Thought (CoT) prompting enhances the math reasoning capability of large language models (LLMs) to a large margin. However, the mechanism underlying such improvements remains unexplored. In this paper, we present \textbf{SalaMAnder} (\textbf{S}h\textbf{a}p\textbf{l}ey-b\textbf{a}sed \textbf{M}athematical Expression \textbf{A}ttribution a\textbf{nd} M\textbf{e}t\textbf{r}ic), a theoretically grounded methodology as well as a mathematically rigorous evaluation metric for quantifying component-level contributions in few-shot CoT reasoning. Concretely, we leverage the Shapley value for mathematical expression attribution and develop an efficient stratified sampling algorithm that significantly reduces the computational complexity. Besides, we develop the \textbf{CoSP} (\textbf{C}ardinality \textbf{o}f \textbf{S}hapley \textbf{P}ositives) metric through covariance analysis. Comprehensive validation across popular LLM models and diverse mathematical benchmarks demonstrates that the CoSP metric within our SalaMAnder framework exhibits a robust monotonic correlation with model performance, not only providing theoretical explanations for the empirical success of existing few-shot CoT but also establishing mathematically rigorous principles for prompt construction optimization. Furthermore, we verify the reliability of the explanation, based on which we unify the insights of previous work.
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。
