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Contributed Talk 4: Directional Graph Networks
Dominique Beaini · Saro Passaro · Vincent Létourneau · Will Hamilton · Gabriele Corso · Pietro Liò

Fri Dec 11 07:18 AM -- 07:23 AM (PST) @
in Differential Geometry meets Deep Learning (DiffGeo4DL) »

In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection and rotation on the underlying directional field.

Author Information

Dominique Beaini (Invivo AI)
Saro Passaro (University of Cambridge)
Vincent Létourneau (InVivo AI)
Will Hamilton (McGill)
Gabriele Corso (University of Cambridge)
Pietro Liò (University of Cambridge)

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