Beltrami Flow and Neural Diffusion on Graphs

Benjamin Paul Chamberlain, James Rowbottom, Davide Eynard, Francesco Di Giovanni, Xiaowen Dong, Michael M. Bronstein

Keywords: Geometric Deep Learning, Graph Neural Network, Diffusion

TL;DR: A generalisation of Graph Neural Networks using Beltrami Flow that jointly diffuses features and positional encodings

Abstract:

We propose a novel class of graph neural networks based on the discretized Beltrami flow, a non-Euclidean diffusion PDE.
In our model, node features are supplemented with positional encodings derived from the graph topology and jointly evolved by the Beltrami flow, producing simultaneously continuous feature learning, topology evolution.
The resulting model generalizes many popular graph neural networks and achieves state-of-the-art results on several benchmarks.

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Code: https://github.com/twitter-research/graph-neural-pde

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.09443/code)