Deep Divide-and-Reduce in Symbolic Regression

Abstract

Symbolic regression (SR) is the task of discovering underlying patterns from data and representing them using mathematical expressions. Current machine learning approaches to SR often lack a profound understanding of the intrinsic mathematical and physical principles governing these expressions. While the pioneering AI Feynman method leverages the mathematical properties underlying the data, its expression decomposition mechanism suffers from a narrow scope of applicability and is prone to failure on complex equations. Furthermore, its underlying mechanisms rely heavily on brute-force searches for sub-expressions, severely limiting its practical utility. Building on AI Feynman, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a principled extension derived from a formal analysis of a broader class of decomposition structures. DDRSR fundamentally broadens the applicability of expression decomposition and reduction and ensures both wider versatility and sound analytical grounding. Empirical evaluations demonstrate that these theoretical principles yield substantial advantages in both expression decomposition and downstream symbolic regression performance. Finally, we discuss the applicable scenarios and inherent limitations of this paradigm, alongside promising directions for future research.