Virtual nodes give message-passing neural networks a simple global communication route, but the standard node--VN--node pipeline compresses the graph into one homogeneous state and broadcasts it identically to every node. Building on the Two-Radius analysis of Mishayev et al., we ask how auxiliary virtual memory can relieve this finite-capacity bottleneck without self-attention.

We identify two requirements. First, the global memory should be factorized into independently writable and readable states: this can be achieved using addressable cross-attention slots.

Second, addressability alone does not preserve multiplicity, because softmax attention is invariant to uniform replication. Inserting each slot query as a private key/value anchor recovers the discarded normalization mass and yields, on bounded color domains, an injective multiset representation able to implement a 1-WL refinement.

Experiments on multiplicity-aware Two-Radius, motif counting, and constrained link-set prediction support this addressable and cardinality-preserving virtual memory at (O(nMd)) arithmetic cost.