Decomposable Neuro Symbolic Regression

TL;DR

This paper introduces a decomposable neuro-symbolic regression method that combines transformers, genetic algorithms, and genetic programming to produce interpretable, accurate multivariate symbolic models from opaque regressors.

Contribution

It presents a novel explainable SR approach that distills complex models into structured mathematical expressions, improving interpretability and structure recovery.

Findings

Lower or comparable errors to existing methods on noisy data.

Consistently recovers original mathematical structures.

Achieves high symbolic solution recovery rate on Feynman dataset.

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 optimization via a GA. We evaluated our method on problems with controlled and varying degrees of noise, demonstrating lower or comparable interpolation and extrapolation errors compared to two GP-based methods, three neural SR methods, and a hybrid approach. Unlike them, our approach consistently learned expressions that matched the original mathematical structure. Similarly, our method achieved both a high symbolic solution recovery rate and competitive predictive performance relative to benchmark methods on the Feynman dataset.