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.

本论文旨在探讨超图学习方法和基准数据集的一些悬而未决的问题，其中提出了一种新的同质性概念，探索了高阶网络结构和动态的分析框架，并引入了 MultiSet 框架重新定义 Hypergraph Neural Networks。