机器学习遇上代数组合学：一套捕捉纯数学研究级猜想能力的数据集
Machine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematics
AI总结：
本文提出代数组合学数据集仓库（ACD Repo），包含九个研究级开放问题及多达千万级示例，旨在支持机器学习模型从数据中生成数学猜想，并探讨了窄模型训练、可解释性分析和LLM程序合成等应用方式及数据集设计挑战。
摘要：
随着人工智能系统能力近期的显著提升，利用机器学习处理推理密集、定量化任务（尤其是数学）的兴趣日益增长。尽管已有许多资源涵盖高中、本科和研究生水平的数学内容，但与职业数学家处理开放问题时所面临的难度和开放性相匹配的资源却少得多。为此，我们引入了一个新的数据集集合——代数组合学数据集仓库（ACD Repo），它代表了代数组合学中的基础性结果或开放问题。代数组合学是数学的一个子领域，研究由抽象代数产生的离散结构。我们的数据集集合的另一个不同之处在于，它瞄准的是猜想过程。每个数据集都包含一个开放性的研究级问题以及大量示例（某些情况下多达1000万个），猜想应从这些示例中生成。我们描述了全部九个数据集，机器学习模型可以应用于它们的各种方式（例如，使用窄模型训练后进行可解释性分析，或使用大语言模型进行程序合成），并讨论了设计此类数据集所涉及的一些挑战。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
