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This research introduces Message-Passing Graph Persistence (MGP), a novel framework that integrates topological descriptors directly into the message-passing mechanism of graph neural networks to overcome expressivity limitations. By coupling node embeddings with persistence events during filtration, the method achieves strictly higher representational power than existing approaches while maintaining isomorphism invariance. Empirical results on classification and regression benchmarks demonstrate that MGP consistently outperforms standard persistent homology-based descriptors.
Message-passing graph persistence
arXiv:2611.06801v1 Announce Type: cross Abstract: 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. Experiments show that MGP outperforms other PH-based descriptors on most of these datasets.
Abstract: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. Experiments show that MGP outperforms other PH-based descriptors on most of these datasets.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
arXiv:2611.06801 [cs.LG]
(or arXiv:2611.06801v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.06801 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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