Chaotic Dynamics in Multi-LLM Deliberation
arXiv:2603.09127v1 Announce Type: new 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 ($\hat{\lambda}$) 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 ($\hat{\lambda}=0.0541$ and $0.0947$, respectively), while homogeneous no-role committees also remain in a positive-divergence regime ($\hat{\lambda}=0.0221$). The combined mixed+roles condition is less unstable
arXiv:2603.09127v1 Announce Type: new 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 ($\hat{\lambda}$) 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 ($\hat{\lambda}=0.0541$ and $0.0947$, respectively), while homogeneous no-role committees also remain in a positive-divergence regime ($\hat{\lambda}=0.0221$). The combined mixed+roles condition is less unstable than mixed+no-role ($\hat{\lambda}=0.0519$ vs $0.0947$), showing non-additive interaction. Mechanistically, Chair-role ablation reduces $\hat{\lambda}$ 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.
Executive Summary
This study investigates the stability of multi-Language Model (LLM) deliberation systems, a crucial aspect of collective AI systems. The authors model five-agent LLM committees as random dynamical systems and quantify inter-run sensitivity using an empirical Lyapunov exponent. They identify two independent routes to instability: role differentiation in homogeneous committees and model heterogeneity in no-role committees. The findings have significant implications for the design and governance of multi-LLM systems, highlighting the importance of stability auditing. The study's results also suggest that non-additive interactions between different committee configurations can affect stability.
Key Points
- ▸ Multi-LLM deliberation systems exhibit chaotic dynamics, with two independent routes to instability identified.
- ▸ Role differentiation in homogeneous committees and model heterogeneity in no-role committees contribute to instability.
- ▸ Stability auditing is a core design requirement for multi-LLM governance systems.
- ▸ Non-additive interactions between committee configurations can affect stability.
Merits
Theoretical Contribution
The study provides a novel theoretical framework for understanding the dynamics of multi-LLM systems, addressing a critical gap in the field.
Methodological Rigor
The authors employ a robust empirical approach, using a factorial design and Lyapunov exponent analysis to quantify inter-run sensitivity.
Practical Implications
The study's findings have direct implications for the design and governance of multi-LLM systems, highlighting the importance of stability auditing and protocol optimization.
Demerits
Limited Generalizability
The study's findings may not generalize to larger or more complex multi-LLM systems, which could exhibit different dynamics.
Assumptions and Simplifications
The authors make several assumptions and simplifications in their model, which may not accurately capture real-world complexities.
Expert Commentary
This study makes a significant contribution to the field of AI governance, providing a novel theoretical framework for understanding the dynamics of multi-LLM systems. The authors' use of empirical Lyapunov exponent analysis is particularly noteworthy, offering a robust and quantifiable measure of inter-run sensitivity. While the study's findings are promising, further research is needed to fully generalize the results and explore the implications for larger and more complex multi-LLM systems. The study's emphasis on stability auditing and protocol optimization is well-timed, given the growing importance of multi-LLM systems in AI governance.
Recommendations
- ✓ Future research should focus on developing more sophisticated models and methods for understanding multi-LLM system dynamics, including the integration of multiple data sources and the evaluation of different protocol variants.
- ✓ Developers and deployers of multi-LLM systems should prioritize the implementation of stability auditing and protocol optimization techniques, leveraging the insights and methods developed in this study.