How graph feedback controls consensus in open-weight LLM populations

A new arXiv paper by Samer Saab Jr. and Chaouki Abdallah examines how the runtime interaction graph influences consensus formation in multi-agent systems powered by open-weight language models (1.1B–32B parameters). Using a naming-game protocol, the authors measure prompt-conditioned score-state distributions and construct state-similarity graphs to separate sampled-label agreement from latent state-space consensus. They compare two routing strategies: threshold-similarity (connecting agents with similar states) and bridge-seeking (connecting agents with dissimilar states). The study also varies whether agents retain or discard past partner-label evidence.

The results are striking. In mixed-model populations (three seeds, four different open-weight models), threshold-similarity routing produced no final behavioral or state consensus in all 189 setting-seed runs. In contrast, bridge-seeking routing with retained memory recovered final behavioral consensus in 14 out of 18 runs. Homogeneous populations fared even better: Qwen2.5-32B reached stable behavioral and final state consensus in all 18 retained-history well-mixed settings, while threshold-similarity again failed everywhere. The qualitative ordering held across variations in state thresholds, population size, and vocabulary size. Early-window graph-energy features provided useful within-grid diagnostics for predicting fragmentation.

The work underscores that the design of agent interaction graphs is not an implementation detail—it critically determines whether a multi-agent system achieves shared conventions or splinters into isolated cliques. As open-weight models become more widely deployed in autonomous swarms, this research offers practical guidance: bridge-seeking routing with memory is far more likely to produce robust consensus than homophilous threshold-similarity.