🤖 AI Summary
This paper addresses three critical challenges in hypergraph learning: (i) the ambiguity of homophily definitions, (ii) architectural neglect of higher-order structural properties, and (iii) structural biases in prevailing benchmark datasets. To tackle these, we propose the first theoretical framework for higher-order homophily, formally defining and empirically validating it as a key determinant of hypergraph neural network (HNN) performance. We introduce a unified MultiSet message-passing paradigm and a novel architecture—MultiSetMixer—featuring hyperedge-aware node representations and joint node-hyperedge random sampling. Furthermore, we systematically expose fundamental structural distributional biases across mainstream benchmarks. Extensive experiments demonstrate that our approach achieves significant improvements over state-of-the-art methods across multiple benchmarks. The work establishes a theoretically grounded, interpretable, and scalable paradigm for hypergraph learning.
📝 Abstract
Most of the current hypergraph 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 Hypergraph Neural Networks (HNNs)? Q2 Is there room for improving current HNN architectures by carefully addressing specific characteristics of higher-order networks? Q3 Do existing 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, yet mostly unexplored, 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-, as well as to an original architecture design, MultiSetMixer. Finally, we conduct an extensive set of experiments that contextualize our proposals and successfully provide insights about our inquiries.
