AI 中文总结
该研究针对LLM-MAS共识性能与计算资源关联保证不足的问题，提出将集体信念动态表征为离散时间切换系统的控制论方法，构建共识-预算证书区域，实现资源感知的多智能体协调。
AI 中文摘要
大型语言模型多智能体系统（LLM-MAS）依赖智能体间通信解决复杂推理任务，但共识性能与计算资源间的严格关联保证仍有限。本文提出一种新方法，将集体信念动态表征为离散时间切换系统，其中通信拓扑具有不同的共识收缩率与token成本。通过在信念动态中加入剩余计算预算，定义了共识安全集，同时捕捉一致性与资源可行性。我们推导了共识时间与token消耗的显式边界，并构建了共识-预算证书区域，保证有限时间收敛且不耗尽资源。我们进一步建立了自适应拓扑切换实现收敛速度与通信成本间权衡的条件，对比固定拓扑策略。数值实验与实时LLM-MAS部署验证了预测的共识-成本权衡，证明控制论证书可实现AI系统中的资源感知协调。
英文摘要
Large language model multi-agent systems (LLM-MAS) rely on inter-agent communication to solve complex reasoning tasks, yet rigorous guarantees relating consensus performance to computational resources remain limited. Here, we present a novel way to characterize collective belief dynamics as a discrete-time switched system in which communication topologies have distinct consensus-contraction rates and token costs. By augmenting the belief dynamics with the remaining computational budget, we define a consensus safe set that jointly captures agreement and resource feasibility. We derive explicit bounds on consensus time and token expenditure and construct a consensus-budget certificate region guaranteeing finite-time convergence without resource exhaustion. We further establish conditions under which adaptive topology switching achieves a trade-off between convergence speed and communication cost relative to fixed-topology strategies. Numerical experiments and live LLM-MAS deployments show the predicted consensus-cost trade-offs, demonstrating how control-theoretic certificates can enable resource-aware coordination in AI systems.
