Finetuning Large Language Model as an Effective Symbolic Regressor

Deriving governing equations from observational data, known as Symbolic Regression (SR), is a cornerstone of scientific discovery. Large Language Models, (LLMs) have shown promise in this task by leveraging their vast cross-disciplinary scientific knowledge. However, existing LLM-based methods primarily rely on direct inference or prompt engineering, often requiring excessive inference iterations to converge on correct formulas or failing to treat complex equation targets. These limitations in effectiveness and generalization stem from an inherent tension between pre-trained LLMs' proficiency in approximate reasoning and the high-precision demands of SR tasks. To bridge this gap, we propose to fine-tune LLMs for enhanced SR capability. Yet, the absence of dedicated datasets for SR-oriented fine-tuning remains a critical barrier. We thus introduce SymbArena, specifically engineered to optimize LLMs for SR. This benchmark comprises over 148,000 diverse equations formulated as corpora of 1.83 billion tokens for LLM utilization, enabling effective training and inference. Further, to ensure a more comprehensive and fair evaluation, SymbArena proposes a heuristics metric to precisely quantify form-level consistency, going beyond existing SR numerical-oriented evaluation strategies. With this benchmark, we explore mainstream LLM fine-tuning techniques for SR tasks and establish Symbolic-R1, a simple yet effective LLM-based SR strong baseline. Experimental results validate Symbolic-R1 as the first LLM to exceed traditional numerical methods in both numerical precision and symbolic form accuracy, outperforming the second-best LLM baseline with improvements of 2-fold gains in R2 score and 10.3% in form-level consistency score.