Message-passing graph persistence

Experiments show that MGP outperforms other PH-based descriptors on most of these datasets. It comes from a paper posted to arXiv on 5 November 2026. Message-passing graph neural networks (GNNs) are limited in expressive power by the one-dimensional Weisfeiler-Leman test. Persistent homology (PH) provides topological descriptors that can complement GNN representations, but existing approaches typically compute persistence separately from the representation learning process. In this paper, we introduce Message-Passing Graph Persistence (MGP), a family of topological descriptors that incorporates message passing into graph filtrations. At each filtration step, node embeddings are updated using the current subgraph and associated with persistence events. These embeddings also determine the representatives of connected components during persistence computation. We prove that MGP is invariant under graph isomorphism and that it is strictly more expressive than the PH-based descriptors it extends. We evaluate MGP on an expressivity benchmark and on several graph classification and regression datasets.

Why it counts

Experiments show that MGP outperforms other PH-based descriptors on most of these datasets.

Sources

Primary source: primary source

What is not known

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