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.
@article{arxiv.2106.10934,
title = {GRAND: Graph Neural Diffusion},
author = {Benjamin Paul Chamberlain and James Rowbottom and Maria Gorinova and Stefan Webb and Emanuele Rossi and Michael M. Bronstein},
journal= {arXiv preprint arXiv:2106.10934},
year = {2021}
}
Comments
15 pages, 4 figures. Proceedings of the 38th International Conference on Machine Learning, PMLR 139, 2021. Copyright 2021 by the author(s)