Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing

2026-01-07

arXiv.org

AI Summary

This work addresses the challenges of parameter sharing and expression compactness in symbolic regression when handling multicategorical variables. The authors propose a novel symbolic regression method that supports multicategorical variables by introducing, for the first time, a partial parameter sharing mechanism at an intermediate level: parameters are shared across certain categorical dimensions while remaining independent in others. This approach overcomes the limitations of traditional strategies that enforce either full sharing or no sharing at all, yielding more compact yet informative analytical expressions. Experiments on both synthetic and real astrophysical datasets demonstrate that the method significantly reduces the number of parameters while maintaining fitting accuracy, uncovers latent structural relationships in the data, and thereby enhances both data efficiency and model interpretability.

Technology Category

• Machine Learning: Classification and Regression
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Symbolic Regression aims to find symbolic expressions that describe datasets. Due to better interpretability, it is a machine learning paradigm particularly powerful for scientific discovery. In recent years, several works have expanded the concept to allow the description of similar phenomena using a single expression with varying sets of parameters, thereby introducing categorical variables. Some previous works allow only"non-shared"(category-value-specific) parameters, and others also incorporate"shared"(category-value-agnostic) parameters. We expand upon those efforts by considering multiple categorical variables, and introducing intermediate levels of parameter sharing. With two categorical variables, an intermediate level of parameter sharing emerges, i.e., parameters which are shared across either category but change across the other. The new approach potentially decreases the number of parameters, while revealing additional information about the problem. Using a synthetic, fitting-only example, we test the limits of this setup in terms of data requirement reduction and transfer learning. As a real-world symbolic regression example, we demonstrate the benefits of the proposed approach on an astrophysics dataset used in a previous study, which considered only one categorical variable. We achieve a similar fit quality but require significantly fewer individual parameters, and extract additional information about the problem.

Problem

• Symbolic Regression
• Parameter Sharing
• Categorical Variables
• Shared Expressions
• Interpretability

Innovation

• Symbolic Regression
• Partial Parameter Sharing
• Categorical Variables
• Interpretability
• Transfer Learning