因果与组合抽象

AI总结：

本文提出基于范畴论的因果抽象新方法，统一了多种因果抽象概念，并扩展到量子计算领域以提升可解释性AI。

摘要：

从低层次到更解释性的高层次描述进行抽象，并理想情况下同时保持因果结构，是科学实践、因果推断问题以及稳健、高效且可解释的AI的基础。我们提出了一种关于低层次和高层次模型之间抽象的一般论述，作为自然变换，重点在于因果模型的情况。这为因果抽象提供了新的形式化，统一了文献中的几个概念，包括构造性因果抽象、Q-τ一致性、基于交换干预的抽象以及‘分布式’因果抽象。我们的方法以范畴论的形式进行阐述，并利用具有给定查询集和语义的通用组合模型，在单调、cd-或马尔可夫范畴中；因果模型及其查询如干预是特殊情况。我们识别了两种基本的抽象概念：向下抽象将查询从高层次映射到低层次；向上抽象将具体的查询如Do干预从低层次映射到高层次。尽管通常被呈现为后者，我们展示了常见的因果抽象可能更根本上可以基于前者来理解。我们的方法还促使我们考虑一种新的更强的‘组件级’抽象概念，应用于模型的个别组件。特别是，这产生了新的、加强的构造性因果抽象形式，在机制层面，我们对其进行了特征化结果。最后，我们表明抽象可以进一步推广到其他组合模型，包括具有量子语义由量子电路实现的模型，并首次探索了量子组合电路模型与高层次经典因果模型之间的抽象，作为可解释性量子AI的手段。

英文摘要：

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.

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