Constraining Genetic Symbolic Regression via Semantic Backpropagation

TL;DR

This paper introduces a semantic backpropagation method for genetic symbolic regression that enforces domain-specific constraints, such as physical dimensions, improving the accuracy and robustness of discovered equations.

Contribution

It proposes a novel semantic backpropagation technique integrated into Gene Expression Programming to incorporate constraints during evolution.

Findings

Higher success rate in recovering original physical equations

Enhanced robustness against noisy data

Effective enforcement of domain-specific constraints

Abstract

Evolutionary symbolic regression approaches are powerful tools that can approximate an explicit mapping between input features and observation for various problems. However, ensuring that explored expressions maintain consistency with domain-specific constraints remains a crucial challenge. While neural networks are able to employ additional information like conservation laws to achieve more appropriate and robust approximations, the potential remains unrealized within genetic algorithms. This disparity is rooted in the inherent discrete randomness of recombining and mutating to generate new mapping expressions, making it challenging to maintain and preserve inferred constraints or restrictions in the course of the exploration. To address this limitation, we propose an approach centered on semantic backpropagation incorporated into the Gene Expression Programming (GEP), which integrates domain-specific properties in a vector representation as corrective feedback during the evolutionary process. By creating backward rules akin to algorithmic differentiation and leveraging pre-computed subsolutions, the mechanism allows the enforcement of any constraint within an expression tree by determining the misalignment and propagating desired changes back. To illustrate the effectiveness of constraining GEP through semantic backpropagation, we take the constraint of physical dimension as an example. This framework is applied to discovering physical equations from the Feynman lectures. Results have shown not only an increased likelihood of recovering the original equation but also notable robustness in the presence of noisy data.