MSCR: Exploring the Vulnerability of LLMs' Mathematical Reasoning Abilities Using Multi-Source Candidate Replacement

TL;DR

This paper introduces MSCR, an automated adversarial attack method that uses multi-source candidate replacement to test and reveal vulnerabilities in LLMs' mathematical reasoning abilities, showing significant accuracy drops with minimal input perturbations.

Contribution

The paper presents MSCR, a novel scalable and semantically consistent adversarial attack technique combining multiple information sources to challenge LLMs in mathematical reasoning tasks.

Findings

Minor input perturbations can reduce model accuracy by up to 49.89%.

Perturbations increase response length and computational resource use.

Current LLMs show significant robustness weaknesses in mathematical reasoning.

Abstract

LLMs demonstrate performance comparable to human abilities in complex tasks such as mathematical reasoning, but their robustness in mathematical reasoning under minor input perturbations still lacks systematic investigation. Existing methods generally suffer from limited scalability, weak semantic preservation, and high costs. Therefore, we propose MSCR, an automated adversarial attack method based on multi-source candidate replacement. By combining three information sources including cosine similarity in the embedding space of LLMs, the WordNet dictionary, and contextual predictions from a masked language model, we generate for each word in the input question a set of semantically similar candidates, which are then filtered and substituted one by one to carry out the attack. We conduct large-scale experiments on LLMs using the GSM8K and MATH500 benchmarks. The results show that even a slight perturbation involving only a single word can significantly reduce the accuracy of all models, with the maximum drop reaching 49.89% on GSM8K and 35.40% on MATH500, while preserving the high semantic consistency of the perturbed questions. Further analysis reveals that perturbations not only lead to incorrect outputs but also substantially increase the average response length, which results in more redundant reasoning paths and higher computational resource consumption. These findings highlight the robustness deficiencies and efficiency bottlenecks of current LLMs in mathematical reasoning tasks.