将图神经网络的提升机制扩展到超图,构建更强大的超图模型。
Weisfeiler and Lehman Go Categorical
- 用范畴论统一建模超图信息传递,通过函子定义消息传递结构。
- 提出两种新架构,表达能力超越传统超图同构测试。
- 适合对超图表示学习有深度需求的研究者使用。
尽管提升映射显著增强了图神经网络的表达能力,但将其推广至超图仍不完整。为此,本文提出类别化的Weisfeiler-Lehman框架,将提升视为从任意数据范畴到分级偏序集范畴的函子映射。应用于超图时,该视角可系统推导出超图同构网络家族,其消息传递拓扑严格由函子选择决定。本文引入两类来自超图范畴的函子:关联函子与对称单纯复形函子。关联架构在结构上类似标准二分图方案,但函子推导强制在生成的偏序集中实现更丰富的信息流动,捕捉现有方法常忽略的复杂交集几何。理论分析表明,两种架构的表达能力均超过标准超图Weisfeiler-Lehman测试。在真实世界基准上的大量实验验证了这些理论结果。
原文摘要 · Abstract (English)
While lifting map has significantly enhanced the expressivity of graph neural networks, extending this paradigm to hypergraphs remains fragmented. To address this, we introduce the categorical Weisfeiler-Lehman framework, which formalizes lifting as a functorial mapping from an arbitrary data category to the unifying category of graded posets. When applied to hypergraphs, this perspective allows us to systematically derive Hypergraph Isomorphism Networks, a family of neural architectures where the message passing topology is strictly determined by the choice of functor. We introduce two distinct functors from the category of hypergraphs: an incidence functor and a symmetric simplicial complex functor. While the incidence architecture structurally mirrors standard bipartite schemes, our functorial derivation enforces a richer information flow over the resulting poset, capturing complex intersection geometries often missed by existing methods. We theoretically characterize the expressivity of these models, proving that both the incidence-based and symmetric simplicial approaches subsume the expressive power of the standard Hypergraph Weisfeiler-Lehman test. Extensive experiments on real-world benchmarks validate these theoretical findings.
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