Beltrami Flow and Neural Diffusion on Graphs

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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Cite

Text

Chamberlain et al. "Beltrami Flow and Neural Diffusion on Graphs." Neural Information Processing Systems, 2021.

Markdown

[Chamberlain et al. "Beltrami Flow and Neural Diffusion on Graphs." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/chamberlain2021neurips-beltrami/)

BibTeX

@inproceedings{chamberlain2021neurips-beltrami,
  title     = {{Beltrami Flow and Neural Diffusion on Graphs}},
  author    = {Chamberlain, Benjamin and Rowbottom, James and Eynard, Davide and Di Giovanni, Francesco and Dong, Xiaowen and Bronstein, Michael},
  booktitle = {Neural Information Processing Systems},
  year      = {2021},
  url       = {https://mlanthology.org/neurips/2021/chamberlain2021neurips-beltrami/}
}