An Investigation of Robustness of LLMs in Mathematical Reasoning: Benchmarking with Mathematically-Equivalent Transformation of Advanced Mathematical Problems

Yuren Hao, Xiang Wan, ChengXiang Zhai

Track: long paper (up to 10 pages)

Keywords: mathematical reasoning, benchmark, dataset, language model, robustness, generalization

TL;DR: We introduce the GAP framework and 6,306‑item PutnamGAP benchmark, showing that even top LLMs suffer large accuracy drops when math-equivalent problems are reworded or reparametrized.

Abstract: In this paper, we introduce a systematic framework beyond conventional methods to assess LLMs’ mathematical‑reasoning robustness by stress‑testing them on advanced math problems that are mathematically equivalent but with linguistic and parametric variation. These transformations allow us to measure the sensitivity of LLMs to non-mathematical perturbations, thereby enabling a more accurate evaluation of their mathematical reasoning capabilities. Using this new evaluation methodology, we created PutnamGAP, a new benchmark dataset with multiple mathematically-equivalent variations of competition-level math problems. With the new dataset, we evaluate multiple families of representative LLMs and examine their robustness. Across 18 commercial and open-source models we observe sharp performance degradation on the variants. OpenAI's flagship reasoning model, O3, scores 51.5 % on the originals but drops by 4.7 percentage points on surface-renaming variants, and by 12.9 percentage points on parametric variants, while smaller models fare far worse. Overall, the results show that the proposed new evaluation methodology is effective for deepening our understanding of the robustness of LLMs and generating new insights for further improving their mathematical reasoning capabilities.

Presenter: ~Yuren_Hao1

Format: Yes, the presenting author will attend in person if this work is accepted to the workshop.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Funding: Yes, the presenting author of this submission falls under ICLR’s funding aims, and funding would significantly impact their ability to attend the workshop in person.

Submission Number: 20