Benchmarking LLMs’ Mathematical Reasoning with Unseen Random Variables Questions

Abstract

Recent studies have raised significant concerns regarding the reliability of current mathematical benchmarks, highlighting key limitations such as simplistic design and potential data contamination that undermine evaluation accuracy. Consequently, developing a reliable benchmark that effectively evaluates large language models' (LLMs) genuine capabilities in mathematical reasoning remains a critical challenge. To address these concerns, we propose RV-Bench, a novel evaluation methodology for Benchmarking LLMs with Random Variables in mathematical reasoning. Specifically, we develop question-generating functions to produce random variable questions (RVQs), whose background content mirrors the original benchmark problems, but with randomized variable combinations, rendering them "unseen" to LLMs. Models must completely understand the inherent question pattern to correctly answer RVQs with diverse variable combinations. Thus, an LLMs' genuine reasoning capability is reflected through its accuracy and robustness on RV-Bench. We conducted extensive experiments on over 30 representative LLMs across more than 1,000 RVQs. Our findings reveal that LLMs exhibit a proficiency imbalance between encountered and "unseen" data distributions. Furthermore, RV-Bench reveals that proficiency generalization across similar mathematical reasoning tasks is limited, but we verified that it can still be effectively elicited through test-time scaling.