Contrastive Symbolic Regression: Aligned Representations, Adaptive Prediction, and Diverse Ensembles

Existing symbolic regression approaches primarily focus on learning explicit input-output mappings, often neglecting relational structures among data instances. This paper introduces Contrastive Symbolic Regression (CSR), a feature-construction-based symbolic regression approach that integrates evolutionary feature construction with contrastive learning to shape a representation space where geometric proximity reflects similarity in the target space. CSR employs a contrastive objective that optimizes a linear transformation of constructed features, with a closed-form solution for aligning the feature space with the target space. The constructed features are applied to K-nearest neighbor regression, where we propose an efficient leave-one-out cross-validation (LOOCV) method to address standard LOOCV's computational expense, along with a linear-rank weighted K-nearest neighbor variant for adaptive selection of the neighborhood size and faithful assessment of representation quality during evolution. A determinantal point process-based ensemble selection mechanism further enhances robustness by jointly considering model quality and diversity. Extensive experiments on 58 real-world regression datasets demonstrate that CSR consistently surpasses both traditional symbolic regression and modern machine learning counterparts, highlighting CSR as a promising direction for interpretable and effective regression modeling.