Abstract
How do two agents invent a shared language from scratch? In a Lewis signaling game, a sender and receiver must coordinate on a code using only their interaction history. We study five memory architectures across varying channel configurations with LLM agents and find that memory architecture matters more than channel capacity. Agents with a persistent private notebook benefit from surplus channel capacity and avoid the high-capacity collapse seen in stateless agents, achieving the most reliable coordination ( at capacity = 25). Stateless agents peak at moderate capacity and then degrade as the vocabulary grows beyond what a rolling context window can track The notebook externalizes learned conventions, freeing agents from having to re-derive codes each round. An information bottleneck-inspired argument predicts an optimal capacity equal to the number of objects. Instead, the bottleneck (capacity = 8) proves to be a fragility point, and surplus capacity is generally better. We show that channel capacity alone cannot predict coordination; memory architecture determines whether agents turn interaction history into stable conventions, and both dimensions are needed to understand how signals become language.