DeepPySR：具备动态剪枝、帕累托选择与层次化组合的符号回归框架

Jul 16, 2026

Symbolic regression (SR) derives analytical equations from data, producing interpretable, glass-box models essential for auditable decisions in clinical medicine and social science. Existing SR methods struggle with high-dimensional inputs, principled selection among Pareto-front formulas, and data irregularities such as multicollinearity and class imbalance. DeepPySR introduces dynamic variable pruning during search, exponential Pareto selection that balances accuracy and complexity, and multi-layer hierarchical symbolic composition. Experiments on physics benchmarks and real biomedical/social datasets show consistent gains over PySR and baselines.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages20

Reading Time50 min

Abstract

Introduction

Predictive accuracy vs. interpretability

Limits of post-hoc explainability

Challenges in real-world biomedical data

DeepPySR Contributions

Dynamic Variable Pruning Schedule (DVPS)

Exponential Pareto Selection (EPS)

Multi-layer symbolic regression

Evaluation

arXiv :2607 .08 150v 1 [ cs .LG] 9 Jul 2026 DeepPySR-A Symbolic Regression Framework with Dynamic Pruning, Pareto Selection, and Hierarchical Composition for Real-World Scientific Discovery Fuling Chen 1 ,∗ , Kevin Vinsen 1 , Phillip Melton2 ,3 , Rae-Chi Huang4 1 International Centre for Radio Astronomy Research (ICRAR), University of Western Australia, Perth, WA, Australia 2 The Raine Study, University of Western Australia, Perth, WA, Australia 3 Menzies Institute for Medical Research, University of Tasmania, Hobart, TAS, Australia 4 Nutrition & Health Innovation Research Institute, School of Medical and Health Sciences, Edith Cowan University, Perth, WA, Australia ∗ Correspondence: [fuling.chen@uwa.edu.au](fuling.chen@uwa.edu.au) Abstract Symbolic regression (SR) discovers analytical equations from data, yielding glass-box models with directly interpretable formulas, unlike black-box methods that rely on unstable post-hoc tools such as SHAP or LIME. This transparency is crucial in clinical medicine and social science, but SR faces three challenges: high-dimensional inputs, principled selection of Pareto-front formulae, and data irregularities such as multicollinearity and class imbalance. We introduce DeepPySR, which addresses these issues with a dynamic variable-pruning schedule to remove irrelevant features during search, an exponential Pareto selection criterion that eliminates tradeoffs between accuracy and complexity, and a multi-layer architecture for hierarchical symbolic composition. On four Feynman physics benchmarks and seven biomedical and social-science datasets, DeepPySR outperforms PySR and baselines on body fat (R2 : 0 .794 vs. 0.702), heart disease (F1: 0 .898 vs. 0.787), student performance (R2 : 0 .964 vs. 0.948), and Raine BMI (R2 : 0.525 vs. 0.370), producing interpretable formulas aligned with domain risk factors. 1 Main The tension between predictive accuracy and interpretability is a central problem in applied machine learning. In scientific disciplines, from biomedicine to astrophysics, understanding why a model makes a prediction is often as important as the prediction itself. This need is especially acute in high-stakes domains such as clinical medicine, public health, and social science, where model decisions directly affect individuals and must be auditable, legally defensible, and comprehensible to domain experts who are not machine-learning practitioners [1] . A cardiologist does not need just a risk score but the mechanistic factors driving it; an epidemiologist studying childhood BMI trajectories needs an equation that can be communicated and acted on; an astronomer needs more than a candidate ranking but the physical process that caused the ranking. The prevailing response has been to train high-accuracy black-box models and apply post-hoc explanation tools such as SHAP [2] or LIME [3] to approximate local feature attributions. This strategy has well-documented shortcomings: post-hoc explanations are approximations of a separate model, are unstable under small perturbations [4], and can be manipulated [5] . No amount of attribution substitutes for knowing the actual function the model computes [1] . Symbolic regression (SR) offers a different paradigm: it directly searches for an analytical, human-readable mathematical expression that fits the data [6, 7] . The field has seen renewed interest following the release of PySR [7] and the Feynman SR benchmark [8] . Kolmogorov-Arnold Networks (KAN) [9] have been proposed as a gradient-based interpretable alternative, but KAN requires a pre-specified architecture and pre-selected features [10], making it impractical when the relevant feature set is unknown. Real-world biomedical datasets impose additional difficulties. Intraclass correlation (ICC) is ubiquitous: weight, waist circumference, and BMI z-scores are near-collinear, and standard SR collapses onto correlated variables without improving generalisation. High

FAQs

DeepPySR为什么要解决符号回归中的高维、帕累托选择与数据不规则问题？

文中指出，现实数据常出现高维输入、需要对帕累托前沿公式进行更有原则的选择，以及共线性和类别不平衡等不规则性；这些会削弱现有SR框架的搜索与泛化表现。DeepPySR针对性地提出了DVPS、EPS与层次化组合来共同应对。

DVPS（动态变量剪枝计划）的作用是什么？

DVPS是一种在进化搜索过程中按时间表线性增强的变异算子，会自动移除无关特征，从而避免依赖单独的预处理步骤，并提升在变量数量很高时的可用性。

EPS（指数帕累托选择）如何从帕累托前沿选出单个最佳公式？

EPS使用可调的评分函数，在准确率与复杂度之间进行指数式的联合奖励与惩罚，从帕累托前沿直接挑选单个公式；文中强调其参数网格搜索成本很低，因为只对已有“冠军榜”方程打分而不需要重新训练。

多层符号回归如何帮助处理ICC与层次化结构？

多层架构通过逐层发现潜在中间符号函数来构建层次化表达，用于缓解由于ICC导致的共线性问题，并捕获更符合生物学结构的层次关系，而不是仅使用单层y=f(x)的形式。

Jul 16, 2026

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