---
title: "AutoSR: Automatic Symbolic Regression by Searching Research States"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2608.16876v1"
permalink: "https://feed.astralor.com/items/itm_f8870d2930c51e06483a1e41"
published: "2026-08-17T17:55:26.000Z"
score: 76
channel: "ai"
tags: ["arXiv","AutoSR","Symbolic Regression","Automated Scientific Discovery","MCTS"]
---

# AutoSR: Automatic Symbolic Regression by Searching Research States

## AI commentary

> The most notable aspect of this paper is that it elevates symbolic regression from simply finding formulas to simulating the scientific research process; the retention and reuse of "Research States" is an inspiring design. For those working on scientific discovery tools and explainable AI, this is a must-follow development, especially since it solved three previously unsolved cp3-bench problems, showing the approach is not just theoretical.

## At a glance

This paper introduces AutoSR, a fully automated symbolic regression system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations. Traditional methods merely optimize expressions and discard research records; AutoSR preserves candidate equations alongside reasoning, computational evidence, and independent review in a "Research State", and uses progressive-widening Monte Carlo tree search (PW-MCTS) to allocate computation. Across nine benchmark challenges, AutoSR recovers algebraically equivalent relations in every case, including three cp3-bench problems no published system has solved. AutoSR extends symbolic regression from equation-level search toward automated scientific investigation, allowing scientific knowledge and accumulated evidence to shape both exploration and final justification.

## Key points

- AutoSR stores candidate equations with motivations, computational evidence, and independent review in a Research State, preventing loss of research records.
- Uses progressive-widening Monte Carlo tree search (PW-MCTS) to allocate computation across competing investigations.
- Recovers algebraically equivalent relations in all 9 benchmark challenges, including 3 cp3-bench problems no previous system solved.
- Extends symbolic regression from equation-level search to automated scientific investigation, emphasizing scientific credibility over numerical fit.

## Full text

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.

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