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.

翻译：尽管提升映射已显著增强了图神经网络的表达能力，但将这一范式推广到超图领域仍处于零散状态。为解决此问题，我们引入了范畴化 Weisfeiler-Lehman 框架，该框架将提升形式化为从任意数据范畴到分级偏序集统一范畴的函子映射。当应用于超图时，这一视角使我们能够系统性地推导出超图同构网络——一类神经架构，其消息传递拓扑结构完全由函子的选择所决定。我们引入了来自超图范畴的两个不同函子：关联函子与对称单纯复形函子。虽然关联架构在结构上镜像了标准的二分方案，但我们的函子推导在生成的偏序集上强制实现了更丰富的信息流，从而捕捉了现有方法常忽略的复杂交集几何结构。我们从理论上刻画了这些模型的表达能力，证明了基于关联的方法与对称单纯复形方法均包含了标准超图 Weisfeiler-Lehman 测试的表达力。在真实世界基准数据集上的大量实验验证了这些理论发现。