Decomposing Interventional Causality into Synergistic, Redundant, and Unique Components
This work addresses the need for a proper causal decomposition in complex systems, with potential applications in AI, biology, and climate modeling, though it appears incremental as it builds on existing observational measures.
The authors tackled the problem of decomposing interventional causal effects into synergistic, redundant, and unique components by developing a mathematical framework based on Partial Information Decomposition and Möbius inversion, and applied it to systems like logic gates and transformer models to show context-dependent distributions of causal power.
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.