[RETRACTED]Evolving Form and Function: Dual-Objective Optimization in Neural Symbolic Regression Networks

TL;DR

This paper introduces a dual-objective neural symbolic regression method combining gradient descent and evolutionary algorithms to produce more accurate and interpretable equations from data, outperforming existing neural approaches.

Contribution

It presents a novel hybrid approach that optimizes both symbolic form and predictive behavior in neural symbolic regression, enhancing equation accuracy and interpretability.

Findings

Generated equations are more symbolically accurate.

Produced equations better match data behavior.

Outperformed state-of-the-art neural SR methods.

Abstract

[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation. However, symbolic regression (SR) faces the issue of requiring training from scratch for each new dataset. To generalize across all datasets, deep learning techniques have been applied to SR. These networks, however, are only able to be trained using a symbolic objective: NN-generated and target equations are symbolically compared. But this does not consider the predictive power of these equations, which could be measured by a behavioral objective that compares the generated equation's predictions to actual data. Here we introduce a method that combines gradient descent and evolutionary computation to yield neural networks that minimize the symbolic and behavioral errors of the equations they generate from data. As a result, these evolved networks are shown to generate more symbolically and behaviorally accurate equations than those generated by networks trained by state-of-the-art gradient based neural symbolic regression methods. We hope this method suggests that evolutionary algorithms, combined with gradient descent, can improve SR results by yielding equations with more accurate form and function.