[2511.04124] Decomposable Neuro Symbolic Regression

Computer Science > Machine Learning arXiv:2511.04124 (cs) [Submitted on 6 Nov 2025 (v1), last revised 30 Mar 2026 (this version, v2)] Title:Decomposable Neuro Symbolic Regression Authors:Giorgio Morales, John W. Sheppard View a PDF of the paper titled Decomposable Neuro Symbolic Regression, by Giorgio Morales and John W. Sheppard View PDF Abstract:Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing equations, often producing overly complex or inaccurate expressions. To address this, we present a decomposable SR method that generates interpretable multivariate expressions leveraging transformer models, genetic algorithms (GAs), and genetic programming (GP). In particular, our explainable SR method distills a trained ``opaque'' regression model into mathematical expressions that serve as explanations of its computed function. Our method employs a Multi-Set Transformer to generate multiple univariate symbolic skeletons that characterize how each variable influences the opaque model's response. We then evaluate the generated skeletons' performance using a GA-based approach to select a subset of high-quality candidates before incrementally merging them via a GP-based cascade procedure that preserves their original skeleton structure. The final multivariate skeletons undergo coefficient optimiza...