AutoSR: Automatic Symbolic Regression by Searching Research States

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. Recent LLM-based and agentic methods add tools, diagnostics, and memory, but they mainly use this history to propose the next equation; the search still compares candidate equations rather than the scientific record behind them, such as motivations, failed attempts, and criticism. 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 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 six structurally diverse LSR-Transform problems and three cp3-bench problems that none of the twelve systems in the original cp3-bench evaluation recovered. 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.