Multi-agent systems (MAS) composed of large language models often exhibit improved problem-solving performance despite operating on identical information. In this work, we provide a formal explanation for this phenomenon grounded in operator theory and constrained optimization. We model each agent as enforcing a distinct family of validity constraints on a shared solution state, and show that a MAS implements a factorized composition of constraint-enforcement operators. Under mild conditions, these dynamics converge to invariant solution sets defined by the intersection of agent constraint sets. Such invariant structures are generally not dynamically accessible to a single agent applying all constraints simultaneously, even when expressive capacity and information are identical. We extend this result from exact constraint enforcement to soft constraints via proximal operators, and apply the formalism to contemporary text-based dialog systems.

翻译：由大型语言模型构成的多智能体系统（MAS）通常展现出改进的问题求解性能，尽管各智能体处理的是相同信息。本文基于算子理论和约束优化，为这一现象提供了形式化解释。我们将每个智能体建模为对共享解状态施加一个不同的有效性约束族，并证明多智能体系统实现了约束执行算子的分解复合。在温和条件下，这些动力学过程会收敛到由智能体约束集交集定义的不变解集。此类不变结构通常无法被同时施加所有约束的单个智能体动态访问，即使其表达能力与信息完全相同。我们将该结果从精确约束执行推广到通过邻近算子实现的软约束，并将该形式化框架应用于当代基于文本的对话系统。