标题： 因果抽象，范畴统一 显示英文标题

标题： Causal Abstractions, Categorically Unified

摘要： 我们提出一个范畴框架，用于关联在不同抽象层次上表示同一系统的因果模型。 我们将因果抽象定义为适当的马尔可夫函子之间的自然变换，这简洁地整合了因果抽象应表现出的期望属性。 我们的方法统一并推广了之前考虑过的因果抽象，并获得了现有因果抽象结果的范畴证明和推广。 使用字符串图工具，我们可以明确描述作为低层次图在干预下的一致抽象的图。 我们讨论了机制解释方法，如电路分析和稀疏自编码器，如何融入我们的范畴框架中。 我们还展示了在存在未观察混杂因素的情况下，在无环混合图（ADMG）的高层次图形抽象上应用do演算，可以在低层次图上得到有效结果，从而推广了Anand等人（2023年）的早期陈述。 我们认为与现有的范畴框架相比，我们的框架更适合建模因果抽象。 最后，我们讨论了诸如$\tau$-一致性以及构造性$\tau$-抽象等概念如何通过我们的框架得以恢复。 显示英文摘要

摘要： We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely consolidate desirable properties a causal abstraction should exhibit. Our approach unifies and generalizes previously considered causal abstractions, and we obtain categorical proofs and generalizations of existing results on causal abstractions. Using string diagrammatical tools, we can explicitly describe the graphs that serve as consistent abstractions of a low-level graph under interventions. We discuss how methods from mechanistic interpretability, such as circuit analysis and sparse autoencoders, fit within our categorical framework. We also show how applying do-calculus on a high-level graphical abstraction of an acyclic-directed mixed graph (ADMG), when unobserved confounders are present, gives valid results on the low-level graph, thus generalizing an earlier statement by Anand et al. (2023). We argue that our framework is more suitable for modeling causal abstractions compared to existing categorical frameworks. Finally, we discuss how notions such as $\tau$-consistency and constructive $\tau$-abstractions can be recovered with our framework.