Title: Partial Parameter Sharing for Symbolic Regression of Shared Expressions: A New Approach

Original: arXiv:2601.04051v3 Announce Type: replace Abstract: Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) 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 a single categorical variable. To illustrate, this enables the search for a single expression describing temperaturedependent viscosity across multiple fluids, while simultaneously identifying a distinct set of fluid-specific parameters. We expand upon prior efforts by considering multiple categorical variables and introducing intermediate levels of parameter sharing. Rather than parameters being either entirely universal or entirely unique, some parameters can also be shared across specific categories while remaining distinct for others. This allows for separating universal effects (shared parameters), category-specific trends (partially-shared parameters), and category interactions (non-shared parameters). We test the limits of this setup in terms of reducing data requirements 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 similar fit quality with significantly fewer parameters while extracting additional information about the problem.

Rewrite:

Title: Introducing Partial Parameter Sharing in Symbolic Regression for Shared Expressions

Original: arXiv:2601.04051v3 Announce Type: replace Abstract: Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) 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 a single 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. We expand upon prior efforts by considering multiple categorical variables and introducing intermediate levels of parameter sharing. Rather than parameters being either entirely universal or entirely unique, some parameters can also be shared across specific categories while remaining distinct for others. This allows for separating universal effects (shared parameters), category-specific trends (partially-shared parameters), and category interactions (non-shared parameters). We test the limits of this setup in terms of reducing data requirements 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 similar fit quality with significantly fewer parameters while extracting additional information about the problem.

Rewrite:

Title: Partial Parameter Sharing in Symbolic Regression for Shared Expressions: A Novel Framework

Original: arXiv:2601.04051v3 Announce Type: replace Abstract: Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) 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 a single 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. We expand upon prior efforts by considering multiple categorical variables and introducing intermediate levels of parameter sharing. Rather than parameters being either entirely universal or entirely unique, some parameters can also be shared across specific categories while remaining distinct for others. This allows for separating universal effects (shared parameters), category-specific trends (partially-shared parameters), and category interactions (non-shared parameters). We test the limits of this setup in terms of reducing data requirements 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 similar fit quality with significantly fewer parameters while extracting additional information about the problem.

Rewrite:

Title: Partial Parameter Sharing for Symbolic Regression of Shared Expressions: A Novel Approach

Original: arXiv:2601.04051v3 Announce Type: replace Abstract: Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) 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 a single 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. We expand upon prior efforts by considering multiple categorical variables and introducing intermediate levels of parameter sharing. Rather than parameters being either entirely universal or entirely unique, some parameters can also be shared across specific categories while remaining distinct for others. This allows for separating universal effects (shared parameters), category-specific trends (partially-shared parameters), and category interactions (non-shared parameters). We test the limits of this setup in terms of reducing data requirements 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 similar fit quality with significantly fewer parameters while extracting additional information about the problem.

Rewrite:

Title: Partial Parameter Sharing in Symbolic Regression for Shared Expressions: A New Perspective

Original: arXiv:2601.04051v3 Announce Type: replace Abstract: Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) 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 a single 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. We expand upon prior efforts by considering multiple categorical variables and introducing intermediate levels of parameter sharing. Rather than parameters being either entirely universal or entirely unique, some parameters can also be shared across specific categories while remaining distinct for others. This allows for separating universal effects (shared parameters), category-specific trends (partially-shared parameters), and category interactions (non-shared parameters). We test the limits of this setup in terms of reducing data requirements 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 similar fit quality with significantly fewer parameters while extracting additional information about the problem.

Rewrite:

Title: Partial Parameter Sharing for Symbolic Regression of Shared Expressions: A New Framework

Original: arXiv:2601.04051v3 Announce Type: replace Abstract: Symbolic regression aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, symbolic regression (SR) 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 a single 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. We expand upon prior efforts

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC