qtBench：29 个代数组合学开放问题的 AI 求解基准

AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems

AI 导读

研究者提出 qtBench，一个包含 29 个代数组合学开放问题的基准，这些问题要求给出能解释给定多项式系数或恒等式的简单组合算法。为帮助 AI 智能体搜索这类算法，作者提供了用于操作组合对象、防范作弊尝试和测试候选解的脚手架。他们与 OpenAI 合作，其研究人员对其中若干问题给出了候选解，并由此讨论 AI 大规模发现是否合乎伦理、结果应如何发布以及证明消化如何组织等元问题。

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Abstract:We introduce $qt$Bench, a benchmark of 29 open problems in algebraic combinatorics. These problems ask for a simple combinatorial algorithm that explains given polynomial coefficients or identities. To help AI agents search for such algorithms, we provide a scaffold for playing with combinatorial objects, countering cheating attempts, and testing candidate solutions. To explore how far frontier AI systems can go on these problems, we collaborated with OpenAI, whose researchers obtained proposed solutions to several of them. This highlights bigger meta-problems: is AI discovery at scale ethical? How should these results be released? How should proof digestion be organized? We discuss these questions and give our views.

Comments:	15 pages
Subjects:	Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Combinatorics (math.CO)
Cite as:	arXiv:2610.16555 [cs.AI]
	(or arXiv:2610.16555v1 [cs.AI] for this version)
	https://doi.org/10.48550/arXiv.2610.16555 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Eugenio Cainelli [view email]
[v1] Mon, 12 Oct 2026 10:35:19 UTC (52 KB)

来源：arXiv cs.AI · arxiv.org