Beltrami Flow and Neural Diffusion on Graphs
This work addresses the challenge of improving graph neural networks for researchers and practitioners in machine learning, though it appears incremental as it generalizes existing methods.
The authors tackled the problem of graph representation learning by proposing a novel class of graph neural networks based on the discretised Beltrami flow, which jointly evolves node features and graph topology, achieving state-of-the-art results on several benchmarks.
We propose a novel class of graph neural networks based on the discretised 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 and topology evolution. The resulting model generalises many popular graph neural networks and achieves state-of-the-art results on several benchmarks.