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From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems

Paper · 2024 · A M Muntasir Rahman, Junyi Ye, Wei Yao et al.

Summary

Most work on LLM math reasoning assumes every problem has a valid answer. This paper asks whether models only compute mechanically (a "Blind Solver") or can notice that a problem is contradictory, underspecified or against common sense (a "Logical Thinker"). To test this, the authors built FaultyMath, a benchmark of 363 flawed problems covering several math areas, difficulty levels and types of flaws.

Problems written from scratch by AMC students came out unbalanced, so the authors switched to a three-step pipeline:

  • GPT-4 rewrote valid MATH problems into unsolvable ones and explained each flaw.
  • GPT-4 then checked its own outputs.
  • Human annotators confirmed the final set.

Ten open-source, closed-source and math-specialized LLMs were tested in three ways: spotting flaws without being told, behaving under correct or misleading hints, and explaining the flaws they found. Without hints, models mostly answered anyway and rarely flagged the fault. Correct hints helped but did not close the gap, and misleading hints pushed models toward accepting broken problems. The results suggest current LLMs act largely as blind solvers, which matters wherever their outputs are trusted without checking the problem itself.

Key points

  • Curation funnel: 2,000 MATH problems (400 each from Algebra, Geometry, Counting & Probability, Number Theory and Precalculus) were turned into candidate faulty problems. GPT-4 self-verification kept 635, and humans confirmed 363.
  • The best model without hints, Gemini 1.5 Pro, detected only 33.33% of the faulty problems.
  • Gemini and GPT-4 showed confirmation bias when told a flawed problem was solvable. In one appendix case, Gemini invented the false equality 16² − 14² = 58 (it is actually 60).
  • When Gemini and Qwen-1.5 did flag a fault, their explanations were reliably correct.
  • Data and code are published at github.com/JunyiYe/FaultyMathProblem.

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

🎓Pennsylvania State UniversityState College · United States56 works · 5,360 citations

 Fields, topics and concepts

📚 Shelves 6The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksMathematics · 177 worksApplied Mathematics · 46 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,426 works

Cite

Cite as A M Muntasir Rahman, Junyi Ye, Wei Yao, Sierra S. Liu, Jesse Yu, Jonathan Yu, Wenpeng Yin and Guiling Wang. 2024. From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems. arXiv:2410.18921.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2410.18921 · arXiv 2410.18921

@misc{rahman2024blind,
  title = {{From Blind Solvers to Logical Thinkers: Benchmarking LLMs' Logical Integrity on Faulty Mathematical Problems}},
  author = {A M Muntasir Rahman, Junyi Ye, Wei Yao, Sierra S. Liu, Jesse Yu, Jonathan Yu, Wenpeng Yin and Guiling Wang},
  year = {2024},
  doi = {10.48550/arxiv.2410.18921},
  eprint = {2410.18921},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2410.18921}
}

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