As LLM agents evolve into collaborative multi-agent systems, their memory requirements grow rapidly in complexity. This position paper frames multi-agent memory as a computer architecture problem. We distinguish shared and distributed memory paradigms, propose a three-layer memory hierarchy (I/O, cache, and memory), and identify two critical protocol gaps: cache sharing across agents and structured memory access control. We argue that the most pressing open challenge is multi-agent memory consistency. Our architectural framing provides a foundation for building reliable, scalable multi-agent systems.

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