多智能体系统自主发现同调概念，验证数学发现的动态机制。
Discovering mathematical concepts through a multi-agent system
- 构建多智能体系统，自动生成猜想并尝试证明
- 成功从多面体数据中自主恢复同调概念
- 实验验证动态反馈对数学兴趣度的优化作用
数学概念源于实验、证明尝试与反例的相互作用。本文提出一种基于此认知的多智能体计算发现模型，旨在模拟科研过程。系统可自主提出猜想，并依据反馈与动态数据分布做出决策。以欧拉多面体猜想的历史及文献中的开放问题为灵感，我们在任务中要求系统从多面体数据和线性代数知识中自主重构同调概念。结果表明系统成功完成学习任务。更重要的是，实验设计包含消融分析，统计检验了完整动态系统的有效性，控制了实验设置变量。结果支持核心论点：合理组合局部过程的优化，能生成高度契合数学重要性的认知结构。
原文摘要 · Abstract (English)
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this observation. Our system, conceived with research in mind, poses its own conjectures and then attempts to prove them, making decisions informed by this feedback and an evolving data distribution. Inspired by the history of Euler's conjecture for polyhedra and an open challenge in the literature, we benchmark with the task of autonomously recovering the concept of homology from polyhedral data and knowledge of linear algebra. Our system completes this learning problem. Most importantly, the experiments are ablations, statistically testing the value of the complete dynamic and controlling for experimental setup. They support our main claim: that the optimisation of the right combination of local processes can lead to surprisingly well-aligned notions of mathematical interestingness.
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