Weisfeiler and Lehman Go Categorical
Seongjin Choi, Gahee Kim, Se-Young Yun

TL;DR
This paper introduces a categorical framework for hypergraph neural networks, deriving new architectures with enhanced expressivity and validating their effectiveness through theoretical analysis and experiments.
Contribution
It formalizes hypergraph neural networks using category theory, deriving new architectures with proven expressive power and demonstrating their advantages empirically.
Findings
The proposed models subsume the expressive power of the standard Hypergraph Weisfeiler-Lehman test.
The incidence-based architecture captures complex intersection geometries.
Experimental results validate the theoretical expressivity improvements.
Abstract
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…
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Taxonomy
TopicsAdvanced Graph Neural Networks · Graph Theory and Algorithms · Topological and Geometric Data Analysis
