Hypergraph neural diffusion networks

We present the Hypergraph Neural Diffusion Networks (HNDiffN) for learning node embedding and hyperedge embedding in hypergraphs. The main novelty lies in developing a continuous-time diffusion equation defined on nodes and hyperedges in hypergraphs suitably. With the resulting system of well-posed differential equations, well-established numerical differential equation schemes can be employed to devise various families of neural networks with desirable stability properties. We also point out some similarities between diffusion on hypergraphs and staggered grid formulations in computational fluid dynamics to provide an alternative interpretation of the proposed hypergraph model. Experimental results fully demonstrate that HNDiffN performs consistently better than all baseline methods on specific evaluation indicators when solving numerous semi-supervised classification problems. Moreover, the experiments show that the prediction accuracy remains steady as the network depth increases, whereas other graph-based and hypergraph-based baseline models deteriorate. This is attributed to the fact that differential equation approach yields much better controlled network gradients, which helps to overcome the depth dilemma and retain rather decent stability.