Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, simultaneously leading to overshadowing hypergraph network foundations. This paper attempts to confront some pending questions in that regard: Can the concept of homophily play a crucial role in Hypergraph Neural Networks (HGNNs), similar to its significance in graph-based research? Is there room for improving current hypergraph architectures and methodologies? (e.g. by carefully addressing the specific characteristics of higher-order networks) Do existing datasets provide a meaningful benchmark for HGNNs? Diving into the details, this paper proposes a novel conceptualization of homophily in higher-order networks based on a message passing scheme; this approach harmonizes the analytical frameworks of datasets and architectures, offering a unified perspective for exploring and interpreting complex, higher-order network structures and dynamics. Further, we propose MultiSet, a novel message passing framework that redefines HGNNs by allowing hyperedge-dependent node representations, as well as introduce a novel architecture MultiSetMixer that leverages a new hyperedge sampling strategy. Finally, we provide an extensive set of experiments that contextualize our proposals and lead to valuable insights in hypergraph representation learning.

翻译：当前超图领域中的大多数学习方法和基准数据集均通过从图类比中提升得到，这同时导致了超图网络基础被遮蔽的问题。本文试图解决与之相关的几个悬而未决的问题：同质性概念能否在超图神经网络（HGNNs）中发挥类似其在图研究中重要性？是否有可能改进现有超图架构与方法？（例如通过审慎应对高阶网络的特定特性）现有数据集能否为HGNNs提供有意义的基准？深入细节，本文提出了一种基于消息传递方案的高阶网络同质性新概念化方法；该方法协调了数据集与架构的分析框架，为探索和解释复杂高阶网络结构与动态提供了统一视角。进一步地，我们提出MultiSet——一种通过允许超边依赖的节点表示来重新定义HGNNs的新型消息传递框架，同时引入利用新型超边采样策略的架构MultiSetMixer。最终，我们通过大量实验验证了所提方法的可行性，并为超图表示学习提供了宝贵见解。