构建分层概率抽象框架，解决随机系统复杂性难题
An Algebraic Framework for Hierarchical Probabilistic Abstraction
- 基于测度论构建分层映射机制，支持模块化问题求解
- 实现从底层感知到高层概念的统一建模，提升可解释性
- 适用于需要系统1与系统2思维协同的AI场景
抽象是降低各类系统复杂性的关键，但针对概率模型的有效抽象方法设计极具挑战性，源于其随机行为与不确定性。现有方法常将详细概率数据简化为高层摘要以支持可处理且可解释的分析，但通常难以通过单层抽象完整表征关系与概率层级结构。本文提出一种分层概率抽象框架，通过扩展测度论基础以支持分层抽象。该框架通过分层映射实现模块化问题求解，既支持各层细节分析，又提供整体系统理解。方法连接高层概念与底层感知数据，增强可解释性并支持分层分析。框架为人工智能多个子领域中的抽象分析提供稳健基础，尤其有助于对齐系统1与系统2思维，推动多样化抽象方法的发展。
原文摘要 · Abstract (English)
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current approaches often distill detailed probabilistic data into higher-level summaries to support tractable and interpretable analyses, though they typically struggle to fully represent the relational and probabilistic hierarchies through single-layered abstractions. We introduce a hierarchical probabilistic abstraction framework aimed at addressing these challenges by extending a measure-theoretic foundation for hierarchical abstraction. The framework enables modular problem-solving via layered mappings, facilitating both detailed layer-specific analysis and a cohesive system-wide understanding. This approach bridges high-level conceptualization with low-level perceptual data, enhancing interpretability and allowing layered analysis. Our framework provides a robust foundation for abstraction analysis across AI subfields, particularly in aligning System 1 and System 2 thinking, thereby supporting the development of diverse abstraction methodologies.
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