用强化学习自动发现数学理论，评估其有趣程度。
Learning Interestingness in Automated Mathematical Theory Formation
- 构建符号化环境FERMAT，支持数学概念发现与定理证明的强化学习
- 通过进化算法生成有趣度评分，显著提升初等数论与有限域发现效果
- 结合大模型函数抽象能力，适合对数学自动发现感兴趣的读者
我们迈出自动化开放性数学理论发现的关键两步。首先，提出$ extit{FERMAT}$，一个基于符号动作的强化学习环境，模拟概念发现与定理证明，为理论发现相关强化学习问题提供新框架。其次，利用$ extit{FERMAT}$探索自动评估数学对象有趣度的问题。研究采用进化算法合成非平凡的有趣度度量，特别引入一种基于大语言模型的进化算法，具备函数抽象能力，在初等数论和有限域的发现任务中显著优于硬编码基线。代码已开源（https://github.com/trishullab/Fermat）。
原文摘要 · Abstract (English)
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through $\emph{FERMAT}$: automatically scoring the $\emph{interestingness}$ of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines. We open-source the $\emph{FERMAT}$ environment at this URL(https://github.com/trishullab/Fermat).
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