How much should an LLM agent remember, and how should multi-agent systems be connected when trying to reach consensus? We show these two design choices interact in a way that flips the sign of memory's effect on coordination. Across 432 simulation runs of a networked Naming Game on eight fixed 16-agent topologies, we vary memory depth and network structure. Longer memory slows the time to reach steady state in decentralized networks but accelerates it in centralized ones; the same parameter pushes the system in opposite directions depending on topology. Critically, "faster settling" in centralized networks means locking in to a fragmented plateau more quickly, not reaching system-wide consensus, which can be used to generate diverging opinions. We further document a memory-mediated speed-unity trade-off: centralized networks consistently preserve more competing conventions than decentralized networks, but their settling speed depends sharply on memory. At the agent level, within-network analyses show that high-betweenness bridges suffer a brokerage penalty while agents in locally clustered neighborhoods achieve higher coordination success. Finally, in search of analytically tractable generative mechanisms, we find that agents' choices are well captured by Fictitious Play, indicating belief-based rather than reward-based adaptation. The practical implication: memory depth and communication topology should be co-designed, not optimized in isolation.

翻译：大语言模型（LLM）智能体应当记忆多少信息？在试图达成共识时，多智能体系统应如何连接？我们证明，这两种设计选择会相互影响，从而反转记忆对协调效果的正负作用。通过对八个固定16节点拓扑结构上的网络化命名游戏进行432次仿真实验，我们系统变化了记忆深度与网络结构。在去中心化网络中，较长的记忆会延长系统达到稳态的时间，但在中心化网络中则加速这一过程；同一参数根据拓扑结构的不同，推动系统向相反方向发展。关键的是，中心化网络中的“快速稳定”意味着更快锁定至一个碎片化平台期，而非达成全局共识——这一特性可用于生成分歧观点。我们进一步发现一种由记忆调节的速度-统一性权衡：中心化网络始终比去中心化网络保留更多竞争性惯例，但其稳定速度高度依赖于记忆深度。在智能体层面，网络内分析表明，高介数桥接节点承受中介惩罚，而处于局部聚类邻域的智能体则能实现更高的协调成功率。最后，为寻找可解析的生成机制，我们发现智能体的选择行为能被虚拟博弈良好刻画，表明其采用基于信念而非基于奖励的适应策略。实际启示在于：记忆深度与通信拓扑应协同设计，而非孤立优化。