Equivariant Hypergraph Diffusion Neural Operators

TL;DR

This paper introduces ED-HNN, a novel hypergraph neural network architecture that effectively models complex higher-order relations, especially in heterophilic hypergraphs, with provable expressiveness and improved efficiency.

Contribution

The paper proposes ED-HNN, a new hypergraph neural network architecture that models continuous equivariant hypergraph diffusion operators with provable expressiveness and efficiency.

Findings

ED-HNN outperforms baseline models on nine real-world hypergraph datasets.

ED-HNN achieves over 2% higher accuracy on four datasets.

ED-HNN is effective in processing heterophilic hypergraphs and deep models.

Abstract

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%$\uparrow$ in prediction accuracy over four datasets therein.