将因果效应分解为协同、冗余和独有三部分，揭示变量间影响的复杂互动。
Decomposing Interventional Causality into Synergistic, Redundant, and Unique Components
- 基于莫比乌斯反演与部分信息分解，构建干预性因果分解框架。
- 在逻辑门、细胞自动机等系统中验证，因果分配依赖于上下文与参数。
- 适用于生物网络、AI责任归属等复杂系统分析，提供新视角。
我们提出一种新框架，将干预性因果效应分解为协同、冗余和独有三部分，基于部分信息分解（PID）的直觉与莫比乌斯反演原理。尽管已有研究对观测量进行类似分解，但我们指出真正的因果分解必须是干预性的。通过使用冗余格上的莫比乌斯函数闭式表达式，本方法系统量化了因果力量在系统变量间的分布。该形式化在逻辑门、细胞自动机、化学反应网络及Transformer语言模型中得到验证。结果表明，因果力量的分布具有上下文与参数依赖性。该分解为复杂系统提供了新洞察，揭示多个变量间因果影响如何共享与组合，潜在应用包括法律或人工智能系统中的责任归因、生物网络分析及气候模型研究。
原文摘要 · Abstract (English)
We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of Möbius inversion. While recent work has explored a similar decomposition of an observational measure, we argue that a proper causal decomposition must be interventional in nature. We develop a mathematical approach that systematically quantifies how causal power is distributed among variables in a system, using a recently derived closed-form expression for the Möbius function of the redundancy lattice. The formalism is then illustrated by decomposing the causal power in logic gates, cellular automata, chemical reaction networks, and a transformer language model. Our results reveal how the distribution of causal power can be context- and parameter-dependent. The decomposition provides new insights into complex systems by revealing how causal influences are shared and combined among multiple variables, with potential applications ranging from attribution of responsibility in legal or AI systems, to the analysis of biological networks or climate models.
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