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

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 \textit{Influence-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 $ψ_j(\mathbf{x})$ for a linear model, which are then evaluated using granular influence scores $Δ_j$. 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.

TemporAI: Facilitating Machine Learning Innovation in Time Domain Tasks for Medicine

TemporAI is an open source Python software library for machine learning (ML) tasks involving data with a time component, focused on medicine and healthcare use cases. It supports data in time series, static, and eventmodalities and provides an interface for prediction, causal inference, and time-to-event analysis, as well as common preprocessing utilities and model interpretability methods. The library aims to facilitate innovation in the medical ML space by offering a standardized temporal setting toolkit for model development, prototyping and benchmarking, bridging the gaps in the ML research, healthcare professional, medical/pharmacological industry, and data science communities. TemporAI is available on GitHub (https://github.com/vanderschaarlab/temporai) and we welcome community engagement through use, feedback, and code contributions.