Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design

Most of the current learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This paper attempts to confront some pending questions in that regard: Q1 Can the concept of homophily play a crucial role in Hyper-graph Neural Networks (HNNs)? Q2 How do models that employ unique characteristics of higher-order networks perform compared to lifted models? Q3 Do well-established hypergraph datasets provide a meaningful benchmark for HNNs? To address them, we first introduce a novel conceptualization of homophily in higher-order networks based on a Message Passing (MP) scheme, unifying both the analytical examination and the modeling of higher-order networks. Further, we investigate some natural strategies for processing higher-order structures within HNNs (such as keeping hyperedge-dependent node representations or performing node/hyperedge stochastic samplings), leading us to the most general MP formulation up to date –MultiSet. Finally, we conduct an extensive set of experiments that contextualize our proposals.