Hypergraph Dynamic System

Recently, hypergraph neural networks (HGNNs) exhibit the potential to tackle tasks with high-order correlations and have achieved success in many tasks. However, existing evolution on the hypergraph has poor controllability and lacks sufficient theoretical support (like dynamic systems), thus yielding sub-optimal performance. One typical scenario is that only one or two layers of HGNNs can achieve good results and more layers lead to degeneration of performance. Under such circumstances, it is important to increase the controllability of HGNNs. In this paper, we first introduce hypergraph dynamic systems (HDS), which bridge hypergraphs and dynamic systems and characterize the continuous dynamics of representations. We then propose a control-diffusion hypergraph dynamic system by an ordinary differential equation (ODE). We design a multi-layer HDS$^{ode}$ as a neural implementation, which contains control steps and diffusion steps. HDS$^{ode}$ has the properties of controllability and stabilization and is allowed to capture long-range correlations among vertices. Experiments on $9$ datasets demonstrate HDS$^{ode}$ beat all compared methods. HDS$^{ode}$ achieves stable performance with increased layers and solves the poor controllability of HGNNs. We also provide the feature visualization of the evolutionary process to demonstrate the controllability and stabilization of HDS$^{ode}$.