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home / papers / 2025 / MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations

MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations

Paper · 2025 · Kaixuan Huang, Jiacheng Guo, Zihao Li et al.

Summary

The paper asks whether strong LLM results on competition math come from real reasoning or from memorized solution patterns. Earlier robustness benchmarks mostly altered surface details such as numbers, so the original solution method still worked. The authors add hard perturbations: small textual edits that change the problem's mathematical nature, so the familiar solution path stops working. Twelve PhD-level annotators took level-5 problems from the MATH dataset and wrote two variants of each. MATH-P-Simple keeps the original solving method. MATH-P-Hard requires a different, usually harder, approach. Every variant has a new answer and was cross-checked by a second annotator. The authors tested 18 LLMs. All of them lost noticeable accuracy on MATH-P-Hard, including reasoning-focused models. Failure analysis points to a subtler kind of memorization: models apply learned techniques by reflex without checking whether those techniques still fit the edited problem. Showing models the original problem and its solution as an in-context example can make this worse. The work matters because it separates genuine understanding from pattern reuse.

Key points

  • MATH-P-Simple and MATH-P-Hard each contain 279 perturbed problems built from level-5 MATH (Hendrycks et al., 2021) seeds, 164 from the train split and 115 from the test split, covering all 7 subjects.
  • Annotators were told to keep edits minimal so that variants stay textually close to the originals, and every modified problem has a changed answer. Closeness was measured with normalized edit distance and embedding cosine similarity.
  • Across 18 models, accuracy on MATH-P-Hard fell by roughly 10–25%. Examples are o1-mini (−16.49%) and gemini-2.0-flash-thinking (−12.9%).
  • Using the unmodified problem and solution as an in-context example has two effects. It helps through a regular ICL effect, but it can also mislead models into reusing the original method on MATH-P-Hard.
  • The authors contrast their work with GSM-Symbolic, GSM-Plus, Functional-MATH and MATH². They argue that MATH-P-Hard serves both as a harder benchmark and as a testbed for studying memorization.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Fields, topics and concepts

📚 Shelves 7The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksArts and Humanities · 17,959 worksLanguage and Linguistics · 17,789 worksMathematics · 233 worksComputational Theory and Mathematics · 496 worksApplied Mathematics · 73 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,948 works

Cite

Cite as Kaixuan Huang, Jiacheng Guo, Zihao Li, Xiang Ji, Jiawei Ge, Wenzhe Li, Yingqing Guo, Tianle Cai, Hui Yuan, Runzhe Wang, Yue Wu, Ming Yin, Shange Tang, Yangsibo Huang, Chi Jin, Xinyun Chen, Chiyuan Zhang and Mengdi Wang. 2025. MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations. arXiv:2502.06453.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2502.06453 · arXiv 2502.06453

@misc{huang2025math,
  title = {{MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations}},
  author = {Kaixuan Huang, Jiacheng Guo, Zihao Li, Xiang Ji, Jiawei Ge, Wenzhe Li, Yingqing Guo, Tianle Cai, Hui Yuan, Runzhe Wang, Yue Wu, Ming Yin, Shange Tang, Yangsibo Huang, Chi Jin, Xinyun Chen, Chiyuan Zhang and Mengdi Wang},
  year = {2025},
  doi = {10.48550/arxiv.2502.06453},
  eprint = {2502.06453},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2502.06453}
}

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