arXiv:2510.05033stat.MLcs.LG2025-10

用范畴论统一不同抽象层级的因果模型,让跨层次推理更严谨。

Causal Abstractions, Categorically Unified

  • 以自然变换定义因果抽象,统一多种已有抽象方法。
  • 通过弦图工具可显式构造低层图在干预下的高层抽象图。
  • 适用于机械可解释性分析,支持带混杂因子的因果推断。

我们提出一种范畴论框架,用于关联在同一系统上不同抽象层级的因果模型。将因果抽象定义为适当马尔可夫函子之间的自然变换,简洁地整合了因果抽象应具备的理想性质。该方法统一并推广了先前的因果抽象形式,获得现有结果的范畴论证明与泛化。利用弦图工具,可显式描述低层图在干预下的一致高层抽象图。我们讨论了电路分析与稀疏自编码器等机械可解释性方法如何融入此框架。还证明:在存在未观测混杂因子时,对无环混合图(ADMG)的高层抽象应用do-演算,其结果在低层图上依然有效,从而推广了Anand等人(2023)的结论。我们认为本框架比现有范畴框架更适合建模因果抽象。最后,我们展示了τ-一致性与构造性τ-抽象等概念可通过本框架自然恢复。

原文摘要 · Abstract (English)

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 $τ$-consistency and constructive $τ$-abstractions can be recovered with our framework.

因果推断范畴论抽象建模可解释性

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