arXiv cs.AI· Jorge Luiz Franco, Arthur Queiroz Moura, Moacir Ponti, Amauri Souza·· 11 小时前AI 评分22
消息传递图持续性（MGP）：将消息传递融入图过滤的拓扑描述符
Message-passing graph persistence
AI 导读
研究者提出消息传递图持续性（MGP），将消息传递融入图过滤过程，每个过滤步骤用当前子图更新节点嵌入并关联持续事件，节点嵌入同时决定持续计算中连通分量的代表。MGP 被证明在图同构下不变，且严格强于其所扩展的 PH 类描述符。在表达性基准及多个图分类与回归数据集上，MGP 在多数数据集上优于其他 PH 类描述符。
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