Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design

TL;DR

This paper introduces a unified message passing framework for hypergraph neural networks, emphasizing the role of homophily and proposing new architectures and strategies to better capture hypergraph characteristics, supported by extensive experiments.

Contribution

It presents a novel conceptualization of homophily in hypergraphs, a general message passing formulation called MultiSet, and a new architecture named MultiSetMixer, addressing gaps in current HNN approaches.

Findings

Homophily significantly influences HNN performance.

The MultiSet formulation generalizes existing message passing schemes.

MultiSetMixer outperforms previous models on benchmark tasks.

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.