Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18325 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911547657289728 |
|---|---|
| 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 |
| id |
arxiv_https___arxiv_org_abs_2510_18325 |
| 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 |