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Main Author: Jang, Seong-Hoon
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.18325
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author Jang, Seong-Hoon
author_facet Jang, Seong-Hoon
contents Interpretable scientific machine learning often trades predictive performance for structural transparency. When physical targets arise from hierarchical and nonlinear descriptor entanglement, weakly interacting white-box models underfit, whereas highly expressive black-box models obscure physical insight. Here I introduce GoodRegressor, a hierarchical depth-controlled symbolic regression framework that systematically assembles nonlinear descriptor interactions through lexicographically-ordered expansion. Despite effective compositional search spaces approaching $\sim 10^{400}$ structures, disciplined depth control enables tractable and reproducible exploration under realistic computational constraints. Across oxygen-ion conductors, NASICONs, and superconducting oxides, as representative high-complexity testbeds, predictive performances match or exceed state-of-the-art black-box models, retaining explicit functional form. Moreover, interaction-depth evolution reveals system-dependent optimal windows, providing an empirical taxonomy of hierarchical complexity in scientific datasets. These results establish hierarchical inductive bias with explicit depth control as a design principle for interpretable artificial intelligence in high-dimensional compositional spaces, and position interaction depth as a structural axis for diagnosing hierarchical complexity in scientific systems.
format Preprint
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institution arXiv
publishDate 2025
record_format arxiv
spellingShingle GoodRegressor: A Hierarchical Inductive Bias for Navigating High-Dimensional Compositional Space
Jang, Seong-Hoon
Materials Science
Computational Physics
Interpretable scientific machine learning often trades predictive performance for structural transparency. When physical targets arise from hierarchical and nonlinear descriptor entanglement, weakly interacting white-box models underfit, whereas highly expressive black-box models obscure physical insight. Here I introduce GoodRegressor, a hierarchical depth-controlled symbolic regression framework that systematically assembles nonlinear descriptor interactions through lexicographically-ordered expansion. Despite effective compositional search spaces approaching $\sim 10^{400}$ structures, disciplined depth control enables tractable and reproducible exploration under realistic computational constraints. Across oxygen-ion conductors, NASICONs, and superconducting oxides, as representative high-complexity testbeds, predictive performances match or exceed state-of-the-art black-box models, retaining explicit functional form. Moreover, interaction-depth evolution reveals system-dependent optimal windows, providing an empirical taxonomy of hierarchical complexity in scientific datasets. These results establish hierarchical inductive bias with explicit depth control as a design principle for interpretable artificial intelligence in high-dimensional compositional spaces, and position interaction depth as a structural axis for diagnosing hierarchical complexity in scientific systems.
title GoodRegressor: A Hierarchical Inductive Bias for Navigating High-Dimensional Compositional Space
topic Materials Science
Computational Physics
url https://arxiv.org/abs/2510.18325