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.

翻译：当前超图领域的大部分超图学习方法和基准数据集均通过从图类比进行提升操作获得，导致超图特有特征被遮蔽。本文试图直面该领域的若干待解问题：Q1 同质性概念能否在Hypergraph神经网络（HNNs）中发挥关键作用？Q2 是否可通过审慎处理高阶网络特有特征来改进现有HNN架构？Q3 现有数据集是否为HNNs提供了有意义的基准？为解决这些问题，我们首先基于消息传递（MP）方案提出高阶网络同质性的新概念化框架，统一了高阶网络的分析检验与建模。进而，我们探索了处理HNNs中高阶结构的若干自然但大多未充分研究的策略，例如保持超边依赖的节点表示，或执行节点/超边随机采样，由此推导出迄今最通用的MP公式——MultiSet——以及原始架构设计MultiSetMixer。最后，我们通过大量实验对上述方案进行情境化验证，成功为我们的研究疑问提供了深刻见解。