arXiv:2608.16876cs.SCcs.AI2026-08

AutoSR自动搜索科学探索过程,让模型像科学家一样推理并解释发现的公式。

AutoSR: Automatic Symbolic Regression by Searching Research States

论文配图:AutoSR: Automatic Symbolic Regression by Searching Research States
图 1 · 摘自论文原文
  • 用研究状态记录每条公式的推理和证据,保留科学探索轨迹。
  • 在9个挑战中全部复现正确关系,包括3个此前未解决的问题。
  • 适合需要可解释性与科学严谨性的建模任务,如物理规律发现。

我们提出自动符号回归(AutoSR),一种完全自动化系统,通过搜索持续的科学研究过程而非孤立方程来实现研究空间符号回归。有限且含噪声的数据常产生数值上表现良好但外推行为迥异的表达式,仅靠数值拟合与语法复杂度无法衡量科学可信度。现有方法多聚焦于优化公式,但搜索过程通常仅保留最终公式与评分,丢失了动机、探测等科学记录。AutoSR将这些记录保存为「研究状态」,每个候选公式都关联其背后的推理、计算证据与独立评审。提议者-评审者代理在渐进式扩展蒙特卡洛树搜索(PW-MCTS)下构建这些状态,分配计算资源以探索不同研究路径,最终合成一份报告,解释最优关系及其选择依据。在两个基准套件中的九个挑战任务上,AutoSR在所有情况下均恢复出代数等价关系,包括三个此前未被任何公开系统恢复的cp3-bench问题,以及六个结构多样的LSR-Transform问题。总体而言,AutoSR将符号回归从方程层面搜索扩展为自动化科学探究,使科学知识与累积证据共同决定探索方向与结果验证。

原文摘要 · Abstract (English)

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.

符号回归自动推理可解释性科学发现

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。