An Algebraic Framework for Hierarchical Probabilistic Abstraction
This foundational work addresses the problem of representing relational and probabilistic hierarchies in AI, particularly for aligning System 1 and System 2 thinking, though it appears incremental as it builds on existing abstraction approaches.
The paper tackles the challenge of designing effective abstraction methods for probabilistic models by introducing a hierarchical probabilistic abstraction framework that extends measure-theoretic foundations to enable modular problem-solving and layered analysis, enhancing interpretability and system-wide understanding.
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.