MGP：将消息传递融入图过滤的拓扑描述子方法
Message-passing graph persistence
AI 导读
一篇 arXiv 论文提出 Message-Passing Graph Persistence（MGP），在图过滤的每一步中用当前子图更新节点嵌入，并将其与持续同调事件关联。论文证明 MGP 在图同构下保持不变，且表达能力严格强于其所扩展的基于持久同调（PH）的描述子。在表达性基准及多个图分类与回归数据集上，MGP 在大多数数据集上超越了其他基于 PH 的描述子。
正文 · 原文
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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2611.06801 [cs.LG] |
| (or arXiv:2611.06801v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.06801 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jorge Luiz Franco [view email]
[v1]
Wed, 4 Nov 2026 17:18:34 UTC (131 KB)
来源：arXiv cs.AI · arxiv.org