发表机构
The Chinese University of Hong Kong; University of Maryland（香港中文大学; 马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
AutoSR是一个自动化符号回归系统，通过PW-MCTS搜索研究状态而非孤立方程，在9个基准挑战中成功恢复所有代数等价关系，扩展了符号回归至自动化科学探究。
AI 中文摘要
我们提出了AutoSR（Automatic Symbolic Regression），这是一个完全自动化的系统，它通过搜索持续的科学探究而非孤立的方程，实现了研究空间符号回归。有限且带噪声的数据通常会产生数值上具有竞争力的表达式，但这些表达式在观测范围之外可能表现出截然不同的行为，这使得数值拟合和句法复杂性不足以作为科学可信度的衡量标准。现有方法大多专注于改进表达式，但搜索过程通常仅保留最终公式和分数，丢失了用于指导后续尝试的科学记录，如动机和探索过程。AutoSR将此记录保存在“研究状态（Research State）”中，将每个候选方程与其分支过程中形成的推理、计算证据和独立评审关联起来。提出者-评审者（Proposer–reviewer）智能体在渐进加宽蒙特卡洛树搜索（PW-MCTS）下构建这些状态，该算法会在相互竞争的探究之间分配计算资源，而积累的研究记录最终会被综合成一份最终报告，解释最优关系及其选择依据。在来自两个基准套件的9个选定挑战中，AutoSR在所有案例中都恢复了代数等价的关系，包括3个cp3-bench问题（无已发表系统能恢复）和6个结构多样的LSR-Transform问题。总体而言，AutoSR将符号回归从方程级搜索扩展到自动化科学探究，使科学知识和积累的证据能够指导探索方向和所得方程的论证。
英文摘要
We introduce Automatic Symbolic Regression (AutoSR), a fully automated system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations. Finite, noisy data often yield numerically competitive expressions that imply very different behavior outside the observed regime, making numerical fit and syntactic complexity insufficient measures of scientific credibility. Existing approaches largely focus on improving expressions, yet the search typically retains little beyond the resulting formula and score, losing the scientific record, such as motivations and probes, that inform what to try next. AutoSR preserves this record in a \textbf{Research State}, coupling each candidate equation with the reasoning, computational evidence, and independent review developed along its branch. Proposer--reviewer agents develop these states under progressive-widening Monte Carlo tree search (PW-MCTS), which allocates computation across competing investigations, while the accumulated research record is ultimately synthesized into a final report that explains the leading relation and the basis for its selection. Across nine selected challenges from two benchmark suites, AutoSR recovers algebraically equivalent relations in every case, including three cp3-bench problems that no published system recovers and six structurally diverse LSR-Transform problems. Overall, AutoSR extends symbolic regression from equation-level search toward automated scientific investigation, allowing scientific knowledge and accumulated evidence to shape both what is explored and how the resulting equation is justified.
