Transformer Semantic Genetic Programming for Symbolic Regression

TL;DR

This paper introduces Transformer Semantic Genetic Programming (TSGP), a novel approach using a generative transformer to improve semantic search in symbolic regression, producing high-quality solutions efficiently.

Contribution

TSGP is the first to apply a transformer model as a search operator in semantic genetic programming for symbolic regression.

Findings

TSGP achieves comparable or better prediction accuracy than existing methods.

TSGP generates semantically similar solutions without increasing solution size.

Solutions from TSGP explore the semantic space more effectively.

Abstract

In standard genetic programming (stdGP), solutions are varied by modifying their syntax, with uncertain effects on their semantics. Geometric-semantic genetic programming (GSGP), a popular variant of GP, effectively searches the semantic solution space using variation operations based on linear combinations, although it results in significantly larger solutions. This paper presents Transformer Semantic Genetic Programming (TSGP), a novel and flexible semantic approach that uses a generative transformer model as search operator. The transformer is trained on synthetic test problems and learns semantic similarities between solutions. Once the model is trained, it can be used to create offspring solutions with high semantic similarity also for unseen and unknown problems. Experiments on several symbolic regression problems show that TSGP generates solutions with comparable or even significantly better prediction quality than stdGP, SLIM_GSGP, DSR, and DAE-GP. Like SLIM_GSGP, TSGP is able to create new solutions that are semantically similar without creating solutions of large size. An analysis of the search dynamic reveals that the solutions generated by TSGP are semantically more similar than the solutions generated by the benchmark approaches allowing a better exploration of the semantic solution space.