Deep Divide-and-Reduce in Symbolic Regression

Researchers propose Deep Divide and Reduce in Symbolic Regression (DDRSR), a method that broadens expression decomposition and reduction in symbolic regression while avoiding brute-force sub-structure searches, according to a new arXiv preprint (2608.02628v1). The method, backed by mathematical proofs, improves both expression decomposition and numerical regression tasks, addressing limitations of the AI Feynman approach.

arXiv:2608.02628v1 Announce Type: new 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 simplification 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. Through rigorous mathematical deduction and proofs, we propose our method, Deep Divide and Reduce in Symbolic Regression DDRSR . DDRSR fundamentally broadens the applicability of expression decomposition and reduction, circumvents the need for brute-force sub-structure searches, and ensures both wider versatility and strict theoretical correctness. Empirical evaluations demonstrate that these theoretical principles yield significant advantages in both expression decomposition and numerical regression tasks. Finally, we discuss the applicable scenarios and inherent limitations of this paradigm, alongside promising directions for future research.