因果抽象：范畴论视角下的统一
Causal Abstractions, Categorically Unified
AI总结：
本研究提出基于范畴论的因果抽象统一框架，将其定义为马尔可夫函子间的自然变换，统一推广了现有因果抽象理论，结合弦图工具描述干预下的一致抽象图，验证了ADMG高层抽象上do-演算的低层有效性，可适配机制可解释性方法并重构相关抽象概念。
摘要：
我们提出了一个范畴论框架，用于关联在不同抽象层级上表征同一系统的因果模型。我们将因果抽象定义为恰当马尔可夫函子之间的自然变换，它简洁地整合了因果抽象应具备的理想性质。我们的方法统一并推广了此前研究的各类因果抽象，同时我们得到了因果抽象领域现有结果的范畴论证明与推广形式。借助弦图工具，我们能够明确描述在干预下可作为低层图一致抽象的图结构。我们探讨了机制可解释性中的方法（如电路分析和稀疏自编码器）如何适配我们的范畴论框架。我们还证明，当存在未观测混杂因子时，在有向无环混合图（ADMG）的高层图抽象上应用do-演算，可在低层图上得到有效结果，从而推广了Anand等人（2023）的早期结论。我们认为，与现有的范畴论框架相比，我们的框架更适合建模因果抽象。最后，我们讨论了如何通过我们的框架重构τ-一致性和构造性τ-抽象等概念。
英文摘要：
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 $τ$-consistency and constructive $τ$-abstractions can be recovered with our framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
