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Sheaf-Theoretic Causal Emergence for Resilience Analysis in Distributed Systems

Anatoly A. Krasnovsky

TL;DR

This work tackles the problem of identifying and quantifying emergent resilience in distributed systems, where macro-scale groupings can exhibit stronger causal efficacy than individual components. It proposes a unified framework that combines directed attributed graphs, cellular sheaves, flow-on-graph dynamics, and effective-information-based causal emergence to measure resilience across micro and macro descriptions. Key contributions include formalizing $G=(V,E)$ with data spaces, the construction of a cellular sheaf $\mathcal{F}$ and global sections $\Gamma(\mathcal{F})$, a flow-based perturbation protocol, and an EI-based criterion for detecting causal emergence, along with a macro-node aggregation procedure that collapses subgraphs into higher-level units. The framework is domain-agnostic, enabling application to cloud microservices, neuroscience, and power grids, and offers a principled method for discovering resilient, emergent structures that can inform design and operation of robust 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).

Sheaf-Theoretic Causal Emergence for Resilience Analysis in Distributed Systems

TL;DR

This work tackles the problem of identifying and quantifying emergent resilience in distributed systems, where macro-scale groupings can exhibit stronger causal efficacy than individual components. It proposes a unified framework that combines directed attributed graphs, cellular sheaves, flow-on-graph dynamics, and effective-information-based causal emergence to measure resilience across micro and macro descriptions. Key contributions include formalizing with data spaces, the construction of a cellular sheaf and global sections , a flow-based perturbation protocol, and an EI-based criterion for detecting causal emergence, along with a macro-node aggregation procedure that collapses subgraphs into higher-level units. The framework is domain-agnostic, enabling application to cloud microservices, neuroscience, and power grids, and offers a principled method for discovering resilient, emergent structures that can inform design and operation of robust 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).

Paper Structure

This paper contains 20 sections, 4 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Work and Novel Contributions
  3. Problem Statement and Scope
  4. Theoretical Framework
  5. System Modeling with Attributed Graphs
  6. Sheaf Construction for Local-Global Consistency
  7. Flow-on-Graph Simulation of Dynamics and Failures
  8. Causal Emergence Analysis using Sheaves
  9. Macro-Node Aggregation Criteria
  10. EI Computation
  11. Potential Applications
  12. Cloud Microservices
  13. Computational Neuroscience
  14. Power Grid Networks
  15. Future Work
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Schematic Overview of the Proposed Framework. (1) Represent the system as an attributed graph. (2) Construct a cellular sheaf for local-to-global consistency. (3) Simulate flows and failures. (4) Aggregate subgraphs into macro-nodes. (5) Compare micro-level and macro-level EI to detect causal emergence.