延迟验证破坏多智能体大语言模型信念稳定性：不稳定性阈值与最优校正器部署

摘要

多智能体大语言模型（LLM）系统通常依赖验证与批评智能体来抑制幻觉，但验证过程存在延迟。在此延迟期间，错误主张可能通过智能体网络传播扩散。我们将该过程建模为带接地校正器节点的图上的延迟共识。通过接地拉普拉斯矩阵的谱分解，我们得出验证剂量的闭式稳定性阈值：过强或过度延迟的校正可能使共识转为振荡。当通信延迟与验证延迟重合时，系统处于最不稳定的状态；延迟为2时，阈值等于黄金分割比例的倒数。同一框架还给出了超模放置目标函数，以及针对有限校正器预算分配到影响力节点时的贪心(1-1/e)近似规则。在五个开源模型上的实验证实了预测的剂量-延迟振荡现象。相比之下，基于事实的接地回答将真相设为吸收边界并消除了该效应，表明这种不稳定性是符号信念任务的特性，而接地验证仍保持稳定作用。

English

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing