Beltrami Flow and Neural Diffusion on Graphs

Part of Advances in Neural Information Processing Systems 34 (NeurIPS 2021)

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


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.