arXiv:2601.04051cs.LG2026-01

通过部分参数共享,让符号回归能更高效地发现多类数据的统一表达式。

Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing

  • 引入部分参数共享机制,支持跨类别的灵活参数复用
  • 在天体物理数据上以更少参数达到相似拟合效果
  • 适合需要跨类别建模且追求模型简洁性的科研场景

符号回归旨在寻找描述数据集的符号表达式。因其内在可解释性,符号回归是科学发现的强大范式。近期研究已拓展至使用单一表达式结合不同参数集来描述相关现象,引入单一分类变量。例如,可同时找到描述多种流体温度依赖粘度的统一表达式,并识别出每种流体特有的参数。本文进一步扩展该思路,考虑多个分类变量并引入中间层级的参数共享:参数不必全同或全异,而是可在特定类别间共享,其余则保持独立。这使模型能够区分普遍效应(共享参数)、类别特异性趋势(部分共享参数)与类别间交互(非共享参数)。我们在一个仅需拟合的合成数据集上测试了该方法对数据需求和迁移学习的提升能力;此外,还将方法应用于先前单类别研究中使用的天体物理数据集。相比之前工作,我们以显著更少的参数获得相似的拟合质量,并提取了额外的结构信息。

原文摘要 · Abstract (English)

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.

符号回归参数共享科学发现

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