Chaotic Dynamics in Multi-LLM Deliberation

2026-03-09

AI Summary

This study investigates the inter-run instability of multi-large language model (LLM) collaborative systems under theoretically deterministic zero-temperature (T=0) settings, where the underlying mechanisms remain unclear. Modeling a five-agent LLM committee as a stochastic dynamical system, the authors quantify preference trajectory divergence using empirical Lyapunov exponents and analyze stability through factorial experiments, role ablation, and memory window manipulation. They reveal for the first time that both role differentiation and model heterogeneity can independently induce chaotic dynamics, exhibiting non-additive interaction effects. On the HL-01 benchmark, the heterogeneous, role-free configuration shows the strongest divergence (λ̂ = 0.0947), while introducing a chairperson role or shortening the memory window significantly suppresses it. Critically, all scenarios yield positive Lyapunov exponents, indicating pervasive chaos and underscoring stability auditing as a core design principle in multi-LLM governance.

Technology Category

Machine Learning: Large Multimodal Models (LMMs)Multiagent Systems: Mechanism DesignNatural Language Processing: (Large) Language Models

Application Category

Economics, Online Markets and Human Computation: Cost models of using LLMs in production systemsSemantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactionsUser Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Collective AI systems increasingly rely on multi-LLM deliberation, but their stability under repeated execution remains poorly characterized. We model five-agent LLM committees as random dynamical systems and quantify inter-run sensitivity using an empirical Lyapunov exponent ($\hatλ$) derived from trajectory divergence in committee mean preferences. Across 12 policy scenarios, a factorial design at $T=0$ identifies two independent routes to instability: role differentiation in homogeneous committees and model heterogeneity in no-role committees. Critically, these effects appear even in the $T=0$ regime where practitioners often expect deterministic behavior. In the HL-01 benchmark, both routes produce elevated divergence ($\hatλ=0.0541$ and $0.0947$, respectively), while homogeneous no-role committees also remain in a positive-divergence regime ($\hatλ=0.0221$). The combined mixed+roles condition is less unstable than mixed+no-role ($\hatλ=0.0519$ vs $0.0947$), showing non-additive interaction. Mechanistically, Chair-role ablation reduces $\hatλ$ most strongly, and targeted protocol variants that shorten memory windows further attenuate divergence. These results support stability auditing as a core design requirement for multi-LLM governance systems.

Problem

• multi-LLM deliberation
• chaotic dynamics
• stability
• Lyapunov exponent
• collective AI systems

Innovation

• chaotic dynamics
• multi-LLM deliberation
• Lyapunov exponent
• stability auditing
• role differentiation