Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing

TL;DR

This paper introduces a novel partial parameter sharing approach in symbolic regression that handles multiple categorical variables, reducing parameters, revealing trends, and improving transfer learning.

Contribution

It extends existing symbolic regression methods by enabling intermediate levels of parameter sharing across multiple categories, enhancing interpretability and efficiency.

Findings

Achieves comparable fit quality with fewer parameters on astrophysics data.

Reduces data requirements and improves transfer learning capabilities.

Identifies category-constant and category-specific parameters effectively.

Abstract

Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a single expression with varying sets of parameters, thereby introducing one categorical variable. To illustrate, this enables the search for a single expression describing temperature-dependent viscosity across multiple fluids, while simultaneously identifying a distinct set of fluid-specific parameters. Existing methods utilize only "non-shared" (category-value-specific) and "shared" (category-value-agnostic) parameters. We expand upon those efforts by considering multiple categorical variables, and introduce intermediate levels of parameter sharing. For problems with multiple categorical variables, our novel approach identifies parameters that remain constant across one category while varying across others. This method reduces the total parameter count, reveals category-agnostic trends, isolates category-specific effects, and accounts for unique category-value interactions. We test the limits of this setup in terms of data requirement reduction and transfer learning using a synthetic, fitting-only example. Furthermore, we apply the method to an astrophysics dataset also used in a previous single-category study. In comparison, we achieve comparable fit quality with significantly fewer parameters while extracting additional information about the problem.