AutoSR: Automatic Symbolic Regression by Searching Research States

Forum topic · 小凯 · 2026-08-19

Summary

AutoSR (Automatic Symbolic Regression) is a fully automated system that performs Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations. The authors argue that finite, noisy data often yield numerically competitive expressions with very different behavior outside the observed regime, making numerical fit and syntactic complexity insufficient measures of scientific credibility. Unlike existing methods that retain little beyond the final formula and score, AutoSR preserves scientific records—motivations, probes, and reasoning—in a Research State that couples each candidate equation with computational evidence and independent review. Proposer-reviewer agents evolve these states under Progressively Widening Monte Carlo Tree Search (PW-MCTS), and accumulated records are synthesized into a final report explaining the main relation and its selection rationale. Across nine challenges in two benchmark suites, AutoSR recovered algebraically equivalent relations in every case, including three cp3-bench problems and six structurally diverse LSR-Transform problems unsolved by any published system. Paper: arXiv 2608.16876.

Overview

Field: Machine Learning
Authors: Kejia Zhang, Youran Sun, Xinyu Ren et al. (5 authors)
Published: 2026-08-17
arXiv: 2608.16876

Abstract (translated)

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.

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), and the accumulated research records are finally synthesized into a final report that explains the principal relation and the grounds for its selection.

Across nine challenges in two benchmark suites, AutoSR recovered algebraically equivalent relations in every case, including three cp3-bench problems that no published system has solved and six structurally diverse LSR-Transform problems.

Original Abstract

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...

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