Sheaf-Theoretic Causal Emergence for Resilience Analysis in Distributed Systems

Abstract: Distributed systems often exhibit emergent behaviors that impact their resilience (Franz-Kaiser et al., 2020; Adilson E. Motter, 2002; Jianxi Gao, 2016). This paper presents a theoretical framework combining attributed graph models, flow-on-graph simulation, and sheaf-theoretic causal emergence analysis to evaluate system resilience. We model a distributed system as a graph with attributes (capturing component state and connections) and use sheaf theory to formalize how local interactions compose into global states. A flow simulation on this graph propagates functional loads and failures. To assess resilience, we apply the concept of causal emergence, quantifying whether macro-level dynamics (coarse-grained groupings) exhibit stronger causal efficacy (via effective information) than micro-level dynamics. The novelty lies in uniting sheaf-based formalization with causal metrics to identify emergent resilient structures. We discuss limitless potential applications (illustrated by microservices, neural networks, and power grids) and outline future steps toward implementing this framework (Lake et al., 2015).