Escaping Oversquashing: Addressable and Support-Aware Global Memory for Message Passing Networks

arXiv:2608.02709v2 Announce Type: replace-cross Abstract: Virtual nodes are a natural tool against oversquashing: they replace long message-passing paths by a two-hop global route. But when many nodes share one global state, that shortcut can become a bottleneck itself. We study two properties of this global memory. First, addressability: under constant-margin address codes and a nonlinearity that amplifies this margin, multiplicative write/read maps provide $M$ selectable memory rows with only $O(\log M)$ address-code dimensions. Cross-attention slots and a constrained $ELU+1$ bilinear memory

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