Multi-Agent Constraint Factorization Reveals Latent Invariant Solution Structure
This provides a formal explanation for performance gains in multi-agent systems, addressing a theoretical gap in AI research.
The paper tackles the problem of explaining why multi-agent systems with large language models improve problem-solving performance, showing that they converge to invariant solution sets defined by the intersection of agent constraints, which are not accessible to single agents.
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.