基于Koopman谱分析的多智能体系统集体推理验证
Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis
浏览论文内容
中文总结 AI 辅助
本文提出基于Koopman算子理论的框架，通过分析多智能体集体的Koopman转移算子谱，实现对其推理收敛时间、派系及决策的可验证，在注意力共识模型上验证了方法的有效性，且运行高效。
中文摘要 AI 辅助
由大型语言模型（LLM）智能体组成的、可进行辩论和投票的协调集体是一种新兴的计算智能形式：智能行为存在于交互中，而非单个智能体。它们能提升任务准确率，但在系统层面仍是黑箱：缺乏收敛性的原则性测试、所需轮次的边界，以及对决策驱动因素的可靠说明。本文开发了一种基于Koopman算子理论的新框架，并在多智能体共识动力学上验证了其理论保证。将集体视为通信图上的一个非线性动力系统，我们从其Koopman转移算子的谱中读取其基本行为，该算子是从交互轨迹估计得到的非线性动力学的精确线性表示。该谱产生三种可由机器检查的验证：次主导特征值λ₂确定推理的内在时间尺度，并产生可在辩论运行前计算的收敛截止时间；其特征向量命名了集体推理的一致派系，且|λ₂|可验证该解释何时有效；主导谱坐标构成压缩、可审计的消息基。在注意力共识模型上，该截止时间以对数-对数相关系数0.93跟踪观测到的收敛，并在24种配置中的96%里对其进行了界定；当谱验证到亚稳定性时，归因是精确的；32个坐标中有8个以99.7%的保真度保留了决策；从60场辩论中留出的15场辩论学到的验证，在60/60留出的辩论上有效。该研究在CPU上运行仅需数分钟，使谱验证成为可信集体推理的实用层。
英文摘要
Orchestrated collectives of large language model (LLM) agents that debate and vote are an emerging form of computational intelligence: the intelligent behaviour resides in the \emph{interaction}, not in any single agent. They improve task accuracy, yet remain black boxes at the system level: there is no principled test of convergence, no bound on the rounds needed, and no faithful account of what drove a decision. This paper develops a novel framework based on Koopman operator theory and validates its theoretical guarantees on multi-agent consensus dynamics. Treating the collective as one nonlinear dynamical system on a communication graph, we read its essential behaviour off the spectrum of its Koopman transfer operator, an exact linear representation of the nonlinear dynamics estimated from interaction traces. The spectrum yields three machine-checkable certificates: the sub-dominant eigenvalue $λ_2$ fixes the intrinsic timescale of reasoning and yields a convergence deadline computable \emph{before} the debate runs; its eigenvector names the coherent factions the collective reasons in, and $|λ_2|$ certifies when that explanation is valid; and the leading spectral coordinates form a compressed, auditable message basis. On an attention-consensus model, the deadline tracks observed convergence with log--log correlation $0.93$ and bounds it in 96\% of 24 configurations; attribution is exact whenever the spectrum certifies metastability; eight of 32 coordinates preserve the decision at 99.7\% fidelity; and a certificate learned from 15 debates held on 60/60 held-out debates. The study runs in minutes on a CPU, making spectral certification a practical layer for trustworthy collective reasoning.
