LaSER: How Learning Can Guide the Evolution of Equations

Evolution and learning are two distinct yet complementary forms of adaptation. While evolutionary processes operate across generations via the selection of genotypes, learning occurs within the lifetime of an individual, shaping behavior through phenotypic adjustment. The Baldwin effect describes how lifetime learning can improve evolutionary search without altering inherited structures. While this has proven effective in areas like neuroevolution, where gradient-based learning is often used to fine-tune weights or behaviors produced by evolution, it remains underexplored in systems that evolve non-differentiable symbolic structures like Genetic Programming (GP). GP evolves explicit syntax trees that represent equations, offering strong interpretability but limited generalization due to the burden of discovering both useful representations and precise mappings. Here, we show for the first time that integrating a simple form of supervised learning, applied at the semantic or behavioral level during evaluation, can effectively guide the evolution of equations in GP. To achieve this, we propose a new GP pipeline, LaSER (Latent Semantic Evolutionary Regression), where each GP individual generates a semantic representation that is passed to a supervised learner. The quality of the learned mapping is used to assign fitness, without modifying the underlying syntax tree or evolutionary process. Across standard symbolic regression benchmarks, in terms of generalization ability, LaSER significantly outperforms traditional GP and, in several cases, matches or exceeds popular machine learning regressors, while preserving the symbolic interpretability. By separating evolution from learning, LaSER offers a practical route to integrating GP with modern ML workflows, and opens new avenues for research at the intersection of evolutionary computation and representation learning.