GRAND: Graph Neural Diffusion
This work addresses common challenges in graph learning for researchers and practitioners, offering a principled framework for developing more stable and effective GNNs.
The authors tackled the problem of designing deep graph neural networks that avoid issues like oversmoothing and bottlenecks by modeling them as discretizations of continuous diffusion processes, achieving competitive results on standard benchmarks.
We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks.