Delayed Verification Destabilizes Multi-Agent LLM Belief: Instability Thresholds and Optimal Corrector Placement
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Computer Science > Multiagent Systems
Title:Delayed Verification Destabilizes Multi-Agent LLM Belief: Instability Thresholds and Optimal Corrector Placement
Abstract: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
| Comments: | 20 pages, 5 figures, 1 table. Code and data: this https URL |
| Subjects: | Multiagent Systems (cs.MA); Computation and Language (cs.CL); Machine Learning (cs.LG); Systems and Control (eess.SY) |
| MSC classes: | 93A16, 93D05, 93C55, 90C27 |
| ACM classes: | I.2.11; I.2.7 |
| Cite as: | arXiv:2606.27409 [cs.MA] |
| (or arXiv:2606.27409v1 [cs.MA] for this version) | |
| https://doi.org/10.48550/arXiv.2606.27409
arXiv-issued DOI via DataCite
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