Addressable Virtual Nodes Enhance Message Passing Neural Networks

A new arXiv paper (2608.02709) proposes a method to improve message-passing neural networks by using addressable virtual nodes as global memory. The standard virtual node approach compresses the graph into a single homogeneous state, which limits capacity. The authors, building on the Two-Radius analysis by Mishayev et al., identify two requirements: factorizing global memory into independently writable and readable states via addressable cross-attention slots, and preserving multiplicity by inserting each slot query as a private key/value anchor. This recovers normalization mass and yields an injective multiset representation on bounded color domains, enabling 1-WL refinement. Experiments on multiplicity-aware Two-Radius tasks demonstrate the effectiveness of the method.