HGNNv2: Stable Hypergraph Neural Networks

Hypergraph neural networks (HGNNs) are widely used models for analyzing higher-order relational data. HGNNs suffer from the rapid performance degradation with increasing layers. Hypergraph dynamic system (HDS) is a potential way to deal with this challenge. However, hypergraph dynamic system is confined to a time-continuous isotropic model, lacking positional information in the structural space of the hypergraph. In contrast, anisotropic diffusion can capture structural space differences among vertices, providing a more precise representation of the information propagation process in hypergraph structures than isotropic diffusion. In this paper, we introduce HGNNv2, a stable hypergraph neural network, which is built as a hypergraph dynamic system with partial differential equation (PDE). This model incorporates a position-aware anisotropic diffusion term and an external control term. We further present the vertex-rooted subtree method to determine anisotropic diffusion intensity. HGNNv2 has properties that vertices occupying equivalent positions in the structural space share equivalent structural labels and positional features. Experiments on 6 hypergraph datasets and 3 graph datasets reveal that HGNNv2 outperforms all 12 compared methods. HGNNv2 is capable of achieving stable final representations and task accuracy even under noisy conditions. HGNNv2 achieves stable performance with fewer layers than hypergraph dynamic systems employing isotropic diffusion. We provide feature visualizations to illustrate the evolution of representations.