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

arXiv: https://arxiv.org/abs/2605.29184 · HTML: https://mlsanity.com/paper/2605.29184/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 90 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 8 of 8)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Emergent autonomous scientific research capabilities of large language models](https://mlsanity.com/paper/2304.05332/) (2023)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Control](https://mlsanity.com/paper/2009.04278/) (2020)
- [Differentiable Genetic Programming for High-dimensional Symbolic Regression](https://mlsanity.com/paper/2304.08915/) (2023)
- [Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression](https://mlsanity.com/paper/2506.08267/) (2025)

## Built on by (most cited first, 11 of 11)

- [Dictionaries, Not Darwin: Set-Level Selection Beats LLM Evolution in Scientific Equation Discovery](https://mlsanity.com/paper/2607.04108/) (2026)
- [On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement](https://mlsanity.com/paper/2607.23753/) (2026)
- [Library Reachability in LSR-Synth: How Anti-Memorization Design Changes the Measurement of Symbolic Discovery](https://mlsanity.com/paper/2607.28684/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)
- [DASyR-LLM: Domain-Aware Symbolic Regression with LLMs for Kinetic Model Discovery](https://mlsanity.com/paper/2608.05120/) (2026)
- [AutoSR: Automatic Symbolic Regression by Searching Research States](https://mlsanity.com/paper/2608.16876/) (2026)
- [What Should a Large Language Model See? Physical Invariants as a Data Representation for PDE Discovery](https://mlsanity.com/paper/2608.25189/) (2026)
- [Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields](https://mlsanity.com/paper/2608.27475/) (2026)
- [Not Every Term Adds New Structure: Sobolev Novelty for Symbolic Regression](https://mlsanity.com/paper/2609.32597/) (2026)
- [Self-Evolving Multi-Agent Symbolic Discovery for Financial Fundamental Analysis](https://mlsanity.com/paper/2609.32746/) (2026)
- [SRHarness: A Harness for Agentic Symbolic Regression](https://mlsanity.com/paper/2609.35501/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) offer a promising avenue for scientific discovery, yet their application to symbolic regression is often constrained by inefficient search strategies and coarse feedback signals. Current methods typically guide LLMs using scalar metrics (e.g., global Mean Squared Error), which fail to identify which components of a proposed equation are driving performance or causing error. We introduce textitInfluence-Guided Symbolic Regression (IGSR), a method that frames equation discovery as an iterative two-step process combining diverse term generation with rigorous selection: an LLM generates candidate basis functions psij(x) for a linear model, which are then evaluated using granular influence scores Deltaj. These scores quantify each term's marginal contribution to generalization accuracy, enabling an influence-guided pruning process that systematically refines the model structure. Integrating this mechanism into a Monte Carlo Tree Search (MCTS) enables navigating the combinatorial search space while balancing exploration of novel functional forms with exploitation of high-influence components. We demonstrate IGSR's effectiveness on a diverse suite of benchmarks, including LLM-SRBench, pharmacological PKPD models, an epidemiological simulation, and real-world genomic data. Notably, we validate the framework's capacity for genuine discovery in a case study using a high-dimensional biological dataset, in which IGSR identified a novel relationship between DNA methylation and RNA Polymerase II pausing; a hypothesis that was subsequently supported via wet-lab experimentation.