@inproceedings{xin-etal-2025-salamander,
title = "{S}ala{MA}nder: Shapley-based Mathematical Expression Attribution and Metric for Chain-of-Thought Reasoning",
author = "Xin, Yue and
Shen, Chen and
Yan, Shaotian and
Yuan, Xiaosong and
Wang, Yaoming and
Zhang, Xiaofeng and
Huang, Chenxi and
Ye, Jieping",
editor = "Christodoulopoulos, Christos and
Chakraborty, Tanmoy and
Rose, Carolyn and
Peng, Violet",
booktitle = "Findings of the Association for Computational Linguistics: EMNLP 2025",
month = nov,
year = "2025",
address = "Suzhou, China",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.findings-emnlp.455/",
pages = "8558--8577",
ISBN = "979-8-89176-335-7",
abstract = "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."
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<abstract>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 SalaMAnder (Shapley-based Mathematical Expression Attribution and Metric), 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 CoSP (Cardinality of Shapley Positives) 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.</abstract>
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%0 Conference Proceedings
%T SalaMAnder: Shapley-based Mathematical Expression Attribution and Metric for Chain-of-Thought Reasoning
%A Xin, Yue
%A Shen, Chen
%A Yan, Shaotian
%A Yuan, Xiaosong
%A Wang, Yaoming
%A Zhang, Xiaofeng
%A Huang, Chenxi
%A Ye, Jieping
%Y Christodoulopoulos, Christos
%Y Chakraborty, Tanmoy
%Y Rose, Carolyn
%Y Peng, Violet
%S Findings of the Association for Computational Linguistics: EMNLP 2025
%D 2025
%8 November
%I Association for Computational Linguistics
%C Suzhou, China
%@ 979-8-89176-335-7
%F xin-etal-2025-salamander
%X 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 SalaMAnder (Shapley-based Mathematical Expression Attribution and Metric), 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 CoSP (Cardinality of Shapley Positives) 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.
%U https://aclanthology.org/2025.findings-emnlp.455/
%P 8558-8577
Markdown (Informal)
[SalaMAnder: Shapley-based Mathematical Expression Attribution and Metric for Chain-of-Thought Reasoning](https://aclanthology.org/2025.findings-emnlp.455/) (Xin et al., Findings 2025)
ACL
- Yue Xin, Chen Shen, Shaotian Yan, Xiaosong Yuan, Yaoming Wang, Xiaofeng Zhang, Chenxi Huang, and Jieping Ye. 2025. SalaMAnder: Shapley-based Mathematical Expression Attribution and Metric for Chain-of-Thought Reasoning. In Findings of the Association for Computational Linguistics: EMNLP 2025, pages 8558–8577, Suzhou, China. Association for Computational Linguistics.