Network topology shapes consensus and vulnerability in LLM populations
As LLMs move from isolated tools to networked populations, the structure of who interacts with whom becomes a key safety variable. This paper studies how network topology shapes convention formation and adversarial tipping in populations of up to $10^5$ LLM-derived agents playing the naming game. By placing policies extracted from four models on fully connected, heterogeneous, and sparse regular networks, the authors show that topology modulates convergence speed, can rescue stuck populations, and creates hub-shaped vulnerabilities that well-mixed estimates miss.
The paper makes a timely and largely convincing case that interaction topology should be treated as a first-class variable in multi-agent AI safety. By moving beyond well-mixed populations, the authors demonstrate that sparser networks slow consensus, heterogeneous degree distributions create hub vulnerabilities, and local dynamical correlations can even rescue failing convergence. However, the findings are significantly model-dependent — Llama reverses several patterns observed in GPT-4o, QwQ, and Phi — and the naming game remains a highly stylized coordination task, so ecological validity is not yet established.
The experimental design is a clear strength. The authors systematically vary four topologies, four population scales, four LLM-derived policies, and eleven word pairs, while using annealed-network controls to isolate the role of persistent neighbourhood correlations. The finding that homogeneous low-degree networks restore consensus for Llama pairs that freeze in well-mixed populations is genuinely surprising and well supported: "Under annealing, both UCM5.0 and RRN fail to rescue either mixed-state pair at any population size: the consensus fraction is exactly 0.00 for {young/old} and {more/less} on both topologies at every $N \\in \\{1000,5000,10000,100000\\}$ (300 runs per condition)." The committed-minority experiments are equally rigorous, with the hub < random < low-degree ordering holding across every condition tested.
The strongest caveat is model dependence. As the authors note, "Llama departs from the majority pattern in speed ordering, in the topology dependence of $p^*$, and in having mixed-state pairs," which undermines universal claims and suggests these dynamics are driven by idiosyncratic policy features rather than general LLM behaviour. The study also relies entirely on a single minimalist coordination task with two words ($W=2$) and a fixed memory horizon of $H=5$; while this scalability trade-off is justified, it leaves open whether the same topological effects persist in richer interaction environments. Finally, the word pairs are drawn from the CrowS-Pairs stereotype benchmark, meaning the "conventions" are tightly coupled to identity-laden semantic associations; the dynamics might differ for arbitrary, affectively neutral labels.
The evidence generally supports the central claims. The statistical battery — Friedman and Page tests, Wilcoxon signed-rank tests, and Spearman correlations — is appropriate and reported transparently, including non-significant results for Llama (Table A1). The authors fairly position their work: they correctly note that prior networked LLM naming-game studies were limited to 16 agents, a claim confirmed by the cited source's use of "eight 16-node, fixed-degree ($k=3$) topologies." The annealed-network control is an elegant device that distinguishes exposure effects from correlation effects. One minor gap is that the paper does not quantify how sensitive the tipping thresholds are to the bisection resolution of $\Delta p \\leq 0.01$, which could matter when critical masses are small (e.g., $p^* < 0.01$ on hubs).
Reproducibility is strong. The authors provide a public GitHub repository (https://github.com/robertopassaro/llm-naming-game-networks), report exact parameters ($T_{\\max} = 100\\,000$ rounds, 1000 or 300 runs per condition, 200 network realisations), and build on a validated policy-extraction pipeline. The main barrier to full reproduction is that the stochastic policies themselves are not redistributed; a replicator must regenerate them via the cited protocol. Network generation is fully specified (UCM with $\gamma = 2.5$ and $5.0$, $k_{\\min} = 4$, RRN with $K = 4$), and the bisection search for $p^*$ is described with a clear stopping criterion.
As large language models (LLMs) are deployed in interacting populations, their collective behaviour depends not only on the models but also on who interacts with whom. Studies of convention formation in LLM populations have mainly tested well-mixed interactions. We place policies extracted from four LLMs on fully connected, random regular, and heterogeneous networks, with $10^3$ to $10^5$ agents playing the naming game. Topology affects how quickly consensus emerges, sometimes whether it emerges at all, and, in rare cases, which convention wins. Sparsest networks slow consensus up to twelvefold. Yet, by preserving correlations between persistent neighbours, they restore consensus in some cases that fail to converge under well-mixed interactions. Networks also govern vulnerability to adversarial attack. We measure the critical mass of committed agents needed to overturn an established convention. Tipping thresholds follow the same ordering across models and conditions: hubs $\leq$ random $\leq$ low-degree nodes. On the most heterogeneous topology, median critical masses are 3%, 16%, and 35%, respectively; targeting hubs requires one-sixth as many committed agents as random placement. For most models, networked populations are easier to tip than well-mixed ones, so well-mixed estimates can overstate robustness. Assessing the safety of multi-agent AI requires mapping who interacts with whom.
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