SGRAND: Stochastic Graph Neural Diffusion

In this work, we present Stochastic Graph Neural Diffusion, which approaches deep learning on graphs as a continuous stochastic heat diffusion process. We generalize the Stochastic Heat Equation on the Riemannian manifold to graphs and treat GNNs as a discretization of the Stochastic Heat Conduction Equation on graphs. In our model, the choice of discretization operators for different temporal and spatial operators corresponds to different layer structures and topologies. Our model is generalized to the GRAND model, where the presence of noise through heat conduction significantly increases robustness and alleviates the over-smoothing of GNNs to some extent. We propose several methods for stochastic heat equations on discrete graphs, treating information diffusion on graphs as a heat transfer process. We develop several versions of SGAND and achieve competitive results on many standard graph benchmarks.