A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programming

TL;DR

The paper tackles whether recent neural/deep-learning symbolic regression methods outperform traditional genetic-programming SR on real-world data. It benchmarks two neural approaches—an end-to-end transformer SR and SciMED—against GP SR implementations Operon and HeuristicLab on nine engineering datasets not present in SRBench, using the normalized mean squared error $NMSE$ (ranging from $0$ to $1$) as the primary metric. The results show that GP SR generally matches or outperforms the neural methods, with Operon achieving the best test NMSE and substantially faster runtimes, while E2E performs poorly and SciMED exhibits mixed performance. The findings highlight the robustness and efficiency of GP-based SR for practical deployment and stress the need for open, reproducible SR code to enable fair comparisons in symbolic regression research.

Abstract

Symbolic regression is a machine learning method with the goal to produce interpretable results. Unlike other machine learning methods such as, e.g. random forests or neural networks, which are opaque, symbolic regression aims to model and map data in a way that can be understood by scientists. Recent advancements, have attempted to bridge the gap between these two fields; new methodologies attempt to fuse the mapping power of neural networks and deep learning techniques with the explanatory power of symbolic regression. In this paper, we examine these new emerging systems and test the performance of an end-to-end transformer model for symbolic regression versus the reigning traditional methods based on genetic programming that have spearheaded symbolic regression throughout the years. We compare these systems on novel datasets to avoid bias to older methods who were improved on well-known benchmark datasets. Our results show that traditional GP methods as implemented e.g., by Operon still remain superior to two recently published symbolic regression methods.