用神经引导的λ演算自动发现复杂系统多尺度公式
Discovering Multiscale Deep Formulas in Complex Systems via Neural-Guided Lambda Calculus
- 结合λ演算符号回归与深度能量模型，分步解析多尺度关系
- 在6个复杂系统上效率比现有方法高7倍，可发现不同形式的规律
- 适合需要自动化科学发现的跨学科研究者
科学中的根本问题是如何从复杂系统中识别出简洁的数学公式。当前基于人工智能的方法在单尺度系统中表现良好，但在多尺度复杂系统中识别尺度特异性公式仍受限。我们提出Deflex，一种端到端的AI方法，可自动从复杂系统中提取可能具有不同形式（如守恒量和分布）的多尺度公式。Deflex由Deflexformer和Deflexpressor两个子系统构成：Deflexpressor是用于高阶公式的λ演算符号回归模型；Deflexformer是可分解的深度能量模型，用于学习跨尺度的统一表征。Deflexpressor生成合成数据预训练Deflexformer，后者通过解耦多尺度潜在关系指导公式发现。在六个具有多样行为的代表性复杂系统上，Deflex的效率最高可达最先进方法的7倍，并实现全自动多尺度发现。本工作可为跨学科科学发现提供有效工具。
原文摘要 · Abstract (English)
A fundamental problem in science is identifying underlying patterns of complex systems in the form of concise mathematical formulas. Current Artificial Intelligence (AI)-based methods have shown strong performance in single-scale systems, yet remain limited in identifying scale-specific formulas in multiscale complex systems. We present Deflex, an end-to-end AI method to automatically extract multiscale formulas with potentially different forms, including invariants and distributions, from complex systems. Deflex consists of two subsystems named Deflexformer and Deflexpressor. Deflexpressor is a lambda-calculus symbolic regression model for higher-order formulas. Deflexformer is a decomposable deep energy model for learning unified representations across scales. Deflexpressor generates synthetic data to pre-train Deflexformer, which then guides formula discovery by decoupling multiscale latent relationships. Across six representative complex systems with diverse behaviors, Deflex achieves up to 7-fold higher efficiency than the state-of-the-art methods while enabling automated multiscale discovery. Our work could be a useful tool for scientific discovery across disciplines.
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