Graph Feedback Controls Consensus and Clique Formation in Open-Weight Language-Model Populations

2026-07-13

AI Summary

This work addresses the fragmentation and lack of behavioral and state consensus in populations of open-weight language models caused by homogeneous routing strategies. The authors propose a multi-agent convention formation framework grounded in the naming game protocol, which constructs a state similarity graph using initial-token scores to distinguish between label agreement and latent state consensus. For the first time in this domain, graph-based feedback control is introduced. The approach incorporates homogeneity-threshold routing, a memory retention mechanism, and a novel bridging strategy that leverages discrepancies in state components and labels to effectively regulate population dynamics. Experiments demonstrate that, in mixed-model grids, bridging routing combined with memory retention achieves behavioral consensus in 14 out of 18 runs; notably, Qwen2.5-32B attains 100% stable consensus under full-history retention, substantially outperforming baseline methods.

Abstract

Multi-agent language-model systems increasingly route local interactions, yet the runtime interaction graph is often treated as an implementation detail. We study convention formation in open-weight LM populations spanning 1.1B-32B parameters with a naming-game protocol. Restricted first-token scores over tokenizer-safe labels let us measure prompt-conditioned score-state distributions, construct state-similarity graphs, and separate sampled-label agreement from latent state-space consensus. Across controlled interventions, in the main open-weight repair grids, retained partner-label evidence is necessary but not sufficient: homophilous threshold-similarity routing deletes cross-basin exposure and amplifies fragmentation, while bridge-seeking routing often repairs fragmentation when memory is available. In a three-seed mixed four-model grid, threshold-similarity produces no final behavioral or state consensus in 189 setting-seed runs, whereas state-component and label-disagreement bridges recover final behavioral consensus in 14/18 retained-memory runs. Across homogeneous model populations, retained history generally shifts fragmented dynamics toward consensus; the clearest case is Qwen2.5-32B, which reaches stable behavioral and final state consensus in all 18 retained-history well-mixed settings, while threshold-similarity reaches neither form of consensus in 189 settings. Robustness over state thresholds, population size, and vocabulary size preserves the qualitative ordering, and early-window graph-energy features provide useful within-grid diagnostics.

Problem

• consensus formation
• multi-agent language models
• interaction graph
• clique formation
• naming game

Innovation

• graph feedback control
• state-similarity graph
• naming game
• bridge-seeking routing
• latent consensus