qtBench：29 个代数组合学开放问题的 AI 基准，OpenAI 参与求解

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

AI 导读

研究者推出 qtBench，一个收录 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。团队提供了一套用于操作组合对象、识别作弊行为和测试候选解的脚手架，并与 OpenAI 合作，其研究者对其中若干问题给出了候选解。文章还讨论了大规模 AI 发现的伦理、结果发布方式与证明消化组织等元问题。

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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