Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing

arXiv:2601.04051v2 Announce Type: replace 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.