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Evaluating Mathematical Reasoning Beyond Accuracy

Paper · 2024 · Shijie Xia, Xuefeng Li, Yixin Liu et al.

Summary

Most benchmarks for LLM math reasoning check only whether the final answer is right. This can hide flawed logic or wasted steps inside a solution. The authors propose REASONEVAL, which scores every step of a solution on two dimensions:

  • Validity: the step contains no calculation or logical error.
  • Redundancy: the step is correct but does not move the solution forward.

Each step is classified as positive, neutral or negative. Step scores are then combined into solution-level scores using min (for validity) and max (for redundancy). The evaluators are LLMs such as Llama2 and Mistral variants, fine-tuned with a classification head on the human step labels in PRM800K.

The authors test the evaluators on a new meta-evaluation set, MR-MATH. The strongest setups, which pair math-capable base models with high-quality labels, clearly beat baseline methods and generalize well. Applying REASONEVAL to math-specialized LLMs shows that higher answer accuracy on hard problems does not always mean better reasoning. Used as a data filter, it can also shrink SFT data while keeping accuracy and improving step quality. The best evaluator and the evaluation scripts are open-sourced.

Key points

  • The training data is PRM800K, with about 800K step-level human labels on roughly 75K GPT-4 solutions to MATH problems.
  • MR-MATH contains Abel and WizardMath solutions labeled by undergraduates with strong math backgrounds: 83 have erroneous steps and 76 do not.
  • Model scale matters for the evaluated math LLMs' false positive rate. LLaMA13B-PRM800K scores 40.6% versus 21.8% for LLaMA70B-PRM800K, despite identical training data. RLHF helps only for stronger models.
  • For data selection, the authors filtered 10K MMIQC responses with REASONEVAL (WizardMath-7B-V1.1) and fine-tuned mistral-7b on the result:
    • The subset kept 56.7% of the data.
    • MATH accuracy was 22.0, versus 22.2 for the full set and 20.0 for a random subset of equal size.
    • Validity rose from 65.2 to 67.8.
    • Average solution length fell from about 723 to 701 tokens.
  • The code and models are available at github.com/GAIR-NLP/ReasonEval.

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

 Institutions

🎓Carnegie Mellon UniversityPittsburgh · United States365 works · 158,048 citations🎓Shanghai Jiao Tong UniversityShanghai · China63 works · 15,047 citations🎓Yale UniversityNew Haven · United States54 works · 11,964 citations🔬Shanghai Artificial Intelligence LaboratoryShanghai · China44 works · 10,162 citations

📚 Shelves 7The field of science this work belongs to (OpenAlex fields).Computer Science · 9,086 worksArtificial Intelligence · 8,889 worksArts and Humanities · 9,296 worksLanguage and Linguistics · 9,206 worksMathematics · 140 worksComputational Theory and Mathematics · 116 worksApplied Mathematics · 21 works

🧭 Topics 2Research subjects and languages the work is about.Reasoning · 510 worksEvaluation & benchmarks · 685 works

Cite

Cite as Shijie Xia, Xuefeng Li, Yixin Liu, Tongshuang Wu and Pengfei Liu. 2024. Evaluating Mathematical Reasoning Beyond Accuracy. arXiv:2404.05692.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2404.05692 · arXiv 2404.05692

@misc{xia2024evaluating,
  title = {{Evaluating Mathematical Reasoning Beyond Accuracy}},
  author = {Shijie Xia, Xuefeng Li, Yixin Liu, Tongshuang Wu and Pengfei Liu},
  year = {2024},
  doi = {10.48550/arxiv.2404.05692},
  eprint = {2404.05692},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2404.05692}
}

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