Operator Feature Neural Network for Symbolic Regression

TL;DR

This paper introduces OF-Net, a neural network that uses operator representations and implicit feature encoding to improve symbolic regression by capturing the mathematical essence of operators, leading to better expression prediction.

Contribution

The paper presents a novel operator feature neural network that encodes the intrinsic mathematical logic of operators, enhancing symbolic regression performance.

Findings

Achieves superior recovery rates on public datasets.

Attains high R^2 scores in experiments.

Provides analysis and optimization strategies for OF-Net.

Abstract

Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however they treat variables and symbols merely as characters of natural language without considering their mathematical essence. This paper introduces the operator feature neural network (OF-Net) which employs operator representation for expressions and proposes an implicit feature encoding method for the intrinsic mathematical operational logic of operators. By substituting operator features for numeric loss, we can predict the combination of operators of target expressions. We evaluate the model on public datasets, and the results demonstrate that the model achieves superior recovery rates and high $R^2$ scores. With the discussion of the results, we analyze the merit and demerit of OF-Net and propose optimizing schemes.