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Spectral Properties of Complex Distributed Intelligence Systems Coupled with an Environment.

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Summary
This summary is machine-generated.

We developed a quantum-inspired framework to model collective behavior in distributed intelligent systems (DISs) with artificial intelligence agents. Our findings show how network structure and external influences impact opinion coherence and decision-making.

Keywords:
LLMdistributed intelligent systemsopen complex networksphase synchronizationrenormalization groupspectral entropy

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Area of Science:

  • Complex Systems
  • Artificial Intelligence
  • Quantum Computing

Background:

  • Distributed Intelligent Systems (DISs) leverage artificial intelligence agents (AIAs) like large language models (LLMs) for collective tasks.
  • Complex network topologies in DISs introduce uncertainty into consensus-building and decision-making processes.
  • Understanding how external influences interact with DIS structure is crucial for predictable collective behavior.

Purpose of the Study:

  • To propose a quantum-inspired graph signal processing framework for modeling collective behavior in DISs.
  • To analyze the impact of network topology and external influences on DIS dynamics.
  • To investigate methods for maintaining coherence in LLM-participated DISs.

Main Methods:

  • Utilized scale-free and Watts-Strogatz graphs to model DIS network topologies.
  • Employed a quantum-inspired graph signal processing approach with an influence matrix (IM) representing external environment.
  • Analyzed two interaction regimes: aligned (commuting) and non-aligned (non-commuting) adjacency matrix and IM.
  • Applied renormalization-group scaling and spectral entropy for analysis.

Main Results:

  • In aligned regimes, minimal external influence leads to full phase synchronization and coherent dynamics.
  • Non-commuting influences with negative couplings introduce spectral disorder, disrupting phase coherence.
  • The dominant collective mode (Perron mode) remains robust despite disorder, though opinions may fragment.
  • Spectral entropy effectively quantifies disorder and the extent of external influence.

Conclusions:

  • The proposed framework provides insights into the dynamics of LLM-participated DISs.
  • Network topology and external influences significantly modulate collective behavior and opinion coherence.
  • Strategies can be developed to design DISs that maintain coherence even under environmental perturbations.