延遲驗證破壞多智能體大型語言模型的信念穩定性：不穩定閾值與最優修正器放置

摘要

多代理大型語言模型(LLM)系統常依賴驗證器與批評代理來抑制幻覺，但驗證過程存在延遲。在此延遲期間，虛假主張可能透過代理網路傳播。我們將此過程建模為帶有接地校正節點的圖上的延遲共識。透過接地拉普拉斯矩陣的譜分解，可推導出驗證劑量的閉合穩定性閾值：校正過強或過遲皆可能使共識轉為振盪。最不穩定的情況發生於通訊延遲與驗證延遲相等時；當延遲為二，其閾值即為黃金比例倒數。同一理論框架亦給出超模組化放置目標，以及針對有限校正預算分配至影響力節點的貪婪(1-1/e)近似規則。在五個開源模型上的實驗證實了預測的劑量-延遲振盪。相較之下，接地事實回答使真相成為吸收邊界並消除該效應，顯示此不穩定性為符號信念任務所特有，而接地驗證仍具穩定作用。

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