Influence-Guided Symbolic Regression: Scientific Discovery via LLM-Driven Equation Search with Granular Feedback

Researchers introduce Influence-Guided Symbolic Regression (IGSR), a novel framework combining LLMs with Monte Carlo Tree Search to discover scientific equations more efficiently. The method uses granular influence scores to evaluate which components of equations contribute to accuracy, enabling systematic refinement. The approach demonstrated genuine discovery potential by identifying a novel relationship between DNA methylation and RNA Polymerase II pausing that was subsequently validated experimentally.

IGSR represents a meaningful advancement in applying artificial intelligence to scientific discovery by addressing a fundamental limitation of current LLM-based approaches: reliance on coarse feedback signals that obscure which equation components drive performance or error. The research moves beyond scalar metrics like global Mean Squared Error toward granular influence scoring, where each proposed basis function receives a marginal contribution score. This architectural improvement enables more intelligent pruning and model refinement across a combinatorial search space.

The integration with Monte Carlo Tree Search provides structural sophistication, balancing exploration of novel functional forms against exploitation of high-influence components. Rather than naive equation generation, the system treats symbolic regression as an iterative selection problem where LLM creativity combines with rigorous statistical evaluation. This hybrid approach addresses genuine computational challenges in scientific discovery workflows.

The validation framework is particularly noteworthy. Beyond standard benchmarks like LLM-SRBench and pharmacological models, the researchers demonstrated practical utility through wet-lab experimentation validating a novel biological relationship. This translates abstract algorithmic improvements into measurable scientific value, suggesting IGSR could become a useful tool for researchers in genomics, pharmacology, and systems modeling. The ability to identify statistically meaningful relationships in high-dimensional biological datasets positions this method as potentially impactful for domains where traditional statistical methods struggle with feature interactions. Continued development and adoption depend on accessibility, computational efficiency at scale, and reproducibility across diverse scientific domains.

• →IGSR uses granular influence scores to identify which equation components drive performance, replacing inefficient scalar-based feedback in LLM-guided symbolic regression.
• →Integration with Monte Carlo Tree Search enables efficient navigation of combinatorial equation search spaces while balancing exploration and exploitation.
• →Wet-lab validation of a novel DNA methylation and RNA Polymerase II pausing relationship demonstrates practical scientific discovery capability beyond benchmark performance.
• →The method combines LLM-driven candidate generation with rigorous statistical selection, addressing a critical gap between creative hypothesis generation and empirical validation.
• →Results span diverse domains including pharmacological models, epidemiology, and genomics, suggesting broad applicability for scientific discovery workflows.