# An Algebraic Framework for Hierarchical Probabilistic Abstraction

arXiv: https://arxiv.org/abs/2502.21216 · HTML: https://mlsanity.com/paper/2502.21216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 6 of 6)

- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Abstraction-Refinement for Hierarchical Probabilistic Models](https://mlsanity.com/paper/2206.02653/) (2022)
- [Explanatory machine learning for sequential human teaching](https://mlsanity.com/paper/2205.10250/) (2022)
- [State-Space Abstractions for Probabilistic Inference: A Systematic Review](https://mlsanity.com/paper/1804.06748/) (2018)
- [Abstracting Noisy Robot Programs](https://mlsanity.com/paper/2204.03536/) (2022)
- [Probabilistic Program Abstractions](https://mlsanity.com/paper/1705.09970/) (2017)

## Abstract (arXiv)

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.