Understanding convolution on graphs via energies

2 code implementations • 22 Jun 2022 • Francesco Di Giovanni, James Rowbottom, Benjamin P. Chamberlain, Thomas Markovich, Michael M. Bronstein

We do so by showing that linear graph convolutions with symmetric weights minimize a multi-particle energy that generalizes the Dirichlet energy; in this setting, the weight matrices induce edge-wise attraction (repulsion) through their positive (negative) eigenvalues, thereby controlling whether the features are being smoothed or sharpened.

Inductive Bias Node Classification

Equivariant Mesh Attention Networks

1 code implementation • 21 May 2022 • Sourya Basu, Jose Gallego-Posada, Francesco Viganò, James Rowbottom, Taco Cohen

Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research.

Inductive Bias

Graph-Coupled Oscillator Networks

1 code implementation • 4 Feb 2022 • T. Konstantin Rusch, Benjamin P. Chamberlain, James Rowbottom, Siddhartha Mishra, Michael M. Bronstein

This demonstrates that the proposed framework mitigates the oversmoothing problem.

Beltrami Flow and Neural Diffusion on Graphs

1 code implementation • NeurIPS 2021 • Benjamin Paul Chamberlain, James Rowbottom, Davide Eynard, Francesco Di Giovanni, Xiaowen Dong, Michael M Bronstein

We propose a novel class of graph neural networks based on the discretised Beltrami flow, a non-Euclidean diffusion PDE.

GRAND: Graph Neural Diffusion

1 code implementation • NeurIPS Workshop DLDE 2021 • Benjamin Paul Chamberlain, James Rowbottom, Maria Gorinova, Stefan Webb, Emanuele Rossi, Michael M. Bronstein

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE.

Graph Learning