Title: Hypergraph-Native Message Passing: An Incidence-Centric Perspective
Primary area: learning on graphs and other geometries & topologies
Keywords: Hypergraph Neural Networks, Message Passing, Hyperedge-Dependent Labelling, Node Classification

Abstract: While hypergraphs encapsulate higher-order interactions among entities and transcend the pairwise connections characteristic of traditional graphs, their prevailing learning approaches predominantly inherit from graph neural networks, adhering to the established message passing paradigm.
These methods frequently conceptualizes hyperedges as special nodes, facilitating the transmission of aggregated messages through hyperedges instead of direct messages between adjacent nodes.
Such a paradigm is prone to information loss, especially in the context of large hyperedges that bridge a heterophilic array of nodes.
To mitigate this shortcoming and enhance high-order message passing, we propose the Hypergraph-native Message Passing (HMP) framework, which leverages full-rank interactions among the incidences along the underlying hypergraph and its dual.
In contrast to the conventional node-centric approaches, this incidence-centric perspective adeptly manages incidence-level tasks, such as hyperedge-dependent labelling, and seamlessly integrates virtual incidences for both hyperedge- and node-level tasks.
Empirical evaluations demonstrate that HMP achieves a substantial improvement over state-of-the-art methods on 6 hyperedge-dependent labelling benchmarks, with an increase in accuracy ranging from 2.3% to 28.9%, while also delivering competitive results on 13 node classification benchmarks.
Code to reproduce all our experiments is available.

TL;DR: A state-of-the-art hypergraph learning method that exploits the high-order structures of hypergraphs for incidence-, hyperedge-, and node-leval tasks