🤖 AI Summary
Decomposing multi-factor causal responsibility in complex systems—such as legal reasoning, AI decision-making, biological pathways, and climate models—remains fundamentally challenging due to entangled causal interactions.
Method: This paper introduces the first intervention-based causal effect decomposition framework, integrating insights from partial information decomposition (PID) with Möbius inversion on a redundancy lattice. It constructs a closed-form Möbius function enabling exact quantification—under genuine causal interventions—of synergistic, redundant, and unique causal effects. Unlike correlation-based approaches, the framework supports context-sensitive causal power analysis.
Results: Empirically validated on logic gates, cellular automata, and chemical reaction networks, the method reveals systematic evolutionary patterns of causal components with respect to structural topology and parametric variation. It provides both theoretical foundations and computational tools for AI explainability, biological pathway dissection, and other domains requiring rigorous causal attribution.
📝 Abstract
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 M""obius 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 M""obius function of the redundancy lattice. The formalism is then illustrated by decomposing the causal power in logic gates, cellular automata, and chemical reaction networks. Our results reveal how the distribution of causal power can be context- and parameter-dependent. This 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.