Spectral Properties of Complex Distributed Intelligence Systems Coupled with an Environment

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.