构建数学猜想数据集，让AI学会像数学家一样提出新猜想。
Machine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematics
- 聚焦代数组合学中的开放问题，提供上百万条示例支持猜想生成。
- 每份数据集包含研究级问题与海量实例，用于训练模型发现规律。
- 适合研究AI数学推理、自动定理发现的学者与开发者。
随着人工智能能力的显著提升，利用机器学习解决高难度、量化型任务（尤其是数学）的兴趣日益增长。尽管已有大量资源覆盖中学、本科及研究生水平的数学内容，但针对专业数学家在解决开放问题时所面临的复杂性与开放性的资源仍十分稀缺。为此，我们推出了代数组合学数据集仓库（ACD Repo），涵盖代数组合学领域的基础成果或开放问题，该领域研究由抽象代数产生的离散结构。本数据集的独特之处在于其聚焦于猜想生成过程：每个数据集均包含一个开放式研究级问题和大规模示例集合（某些情况下高达1000万条），供模型从中归纳并提出新猜想。我们详细描述了九个数据集，探讨了机器学习模型的应用方式（如使用小型模型训练后进行可解释性分析，或利用大语言模型进行程序合成），并讨论了此类数据集设计中的若干挑战。
原文摘要 · Abstract (English)
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.
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