用范畴论统一因果抽象,让模型更可解释且保持因果结构。
Causal and Compositional Abstraction
- 用范畴论将因果抽象形式化为自然变换,统一多种现有理论。
- 提出组件级抽象新概念,强化机制层面的因果一致性。
- 拓展至量子电路与经典因果模型间抽象,助力可解释量子AI。
从低层描述抽象到更具解释性的高层描述,并尽可能保持因果结构,是科学实践、因果推断及鲁棒高效可解释AI的核心。本文提出一种通用因果抽象框架,将其形式化为自然变换,涵盖构造性因果抽象、Q-τ一致性、交换干预基础抽象及分布式因果抽象等。基于张量、cd或马尔可夫范畴,定义具有特定查询与语义的组合模型,其中因果模型及其干预查询为特例。识别出两类基本抽象:向下抽象(高到低层查询映射)与向上抽象(低层干预如Do-操作映射到高层)。尽管通常视为后者,我们表明常见因果抽象本质上可归于前者。进一步提出更强的‘组件级’抽象,导出机制层级的新构造性因果抽象形式,并给出刻画定理。最后,将抽象推广至量子语义的组合电路模型,初步探索量子电路模型与高层经典因果模型间的抽象关系,为可解释量子人工智能奠基。
原文摘要 · Abstract (English)
Abstracting from a low level to a more explanatory high level of description, and ideally while preserving causal structure, is fundamental to scientific practice, to causal inference problems, and to robust, efficient and interpretable AI. We present a general account of abstractions between low and high level models as natural transformations, focusing on the case of causal models. This provides a new formalisation of causal abstraction, unifying several notions in the literature, including constructive causal abstraction, Q-$τ$ consistency, abstractions based on interchange interventions, and `distributed' causal abstractions. Our approach is formalised in terms of category theory, and uses the general notion of a compositional model with a given set of queries and semantics in a monoidal, cd- or Markov category; causal models and their queries such as interventions being special cases. We identify two basic notions of abstraction: downward abstractions mapping queries from high to low level; and upward abstractions, mapping concrete queries such as Do-interventions from low to high. Although usually presented as the latter, we show how common causal abstractions may, more fundamentally, be understood in terms of the former. Our approach also leads us to consider a new stronger notion of `component-level' abstraction, applying to the individual components of a model. In particular, this yields a novel, strengthened form of constructive causal abstraction at the mechanism-level, for which we prove characterisation results. Finally, we show that abstraction can be generalised to further compositional models, including those with a quantum semantics implemented by quantum circuits, and we take first steps in exploring abstractions between quantum compositional circuit models and high-level classical causal models as a means to explainable quantum AI.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。