AutoSR: Automatic Symbolic Regression by Searching Research States
- Field: Machine Learning
- Authors: Kejia Zhang, Youran Sun, Xinyu Ren, et al. (5 authors)
- Published: 2026-08-17
- arXiv: 2608.16876
Overview
The authors introduce Automatic Symbolic Regression (AutoSR), a fully automated system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations.
Motivation: 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 informs what to try next.
Method: AutoSR preserves this record in a Research State, coupling each candidate equation with the reasoning, computational evidence, and independent review developed along its branch. Proposer-reviewer agents evolve these states under Progressively Widening Monte Carlo Tree Search (PW-MCTS). The accumulated research record is ultimately synthesized into a final report that explains the principal relationship and the basis for its selection.
Results: On nine challenges across two benchmark suites, AutoSR recovered algebraically equivalent relations in every case, including three cp3-bench problems that no published system had solved, and six structurally diverse LSR-Transform problems.
Abstract (original)
> 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 Research State, coupling each candidate equation with the reasoning, computational evidence, an... (truncated)
Full paper: arXiv:2608.16876
*Auto-collected on 2026-08-19.*