Neural Sheaf Diffusion for deep learning on graphs
Graph Neural Networks (GNNs) are connected to diffusion equations that exchange information between the nodes of a graph. Being purely topological objects, graphs are implicitly assumed to have trivial geometry. Using a more general construction called cellular sheaves, we can endow the graph with a learnable geometric structure. We show that diffusion processes on cellular sheaves can solve any node classification task and can provide new insights about over-smoothing, the problem of dealing with heterophilic data, and the expressive power of GNNs.