GESR: A Geometric Evolution Model for Symbolic Regression

Zhitong Ma, Jinghui zhong

Keywords: symbolic regression; semantic approximation

Abstract:

Symbolic regression is a challenging task in machine learning that aims to automatically discover highly interpretable mathematical equations from limited data. Keen efforts have been devoted to addressing this issue, yielding promising results. However, there are still bottlenecks that current methods struggle with, especially when dealing with complex problems containing various noises or with intricate underlying mathematical formulas. In this work, we propose a novel Geometric Evolution Symbolic Regression(GESR) algorithm. Leveraging geometric semantics, the process of symbolic regression in GESR is transformed into an approximation to an unimodal target in n-dimensional topological space. Then, three key modules are proposed to enhance the approximation: (1) a new semantic gradient concept, proposed to assist the exploration, which aims to improve the accuracy of approximation; (2) a new geometric search operator, tailored for approximating the target formula directly in topological space; (3) the Levenberg-Marquardt algorithm with L2 regularization, used for the adjustment of expression structures and the balance of global subtree weights to assist the proposed geometric semantic search operator. With the proposal of these modules, GESR achieves state-of-the-art accuracy performance on multiple authoritative benchmark datasets and demonstrates a certain level of robustness against noise interference. The implementation is available at https://anonymous.4open.science/r/12331211321-014D.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 5491