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On the Expressive Power of Geometric Graph Neural Networks
Cristian Bodnar · Chaitanya K. Joshi · Simon Mathis · Taco Cohen · Pietro Liò

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in Symmetry and Geometry in Neural Representations (NeurReps) »
Event URL: https://openreview.net/forum?id=fzjd0rW81a- »

We propose a geometric version of the Weisfeiler-Leman graph isomorphism test (GWL) for discriminating geometric graphs while respecting the underlying symmetries such as permutation, rotation, and translation.We use GWL to characterise the expressive power of Graph Neural Networks (GNNs) for geometric graphs and provide formal results for the following: (1) What geometric graphs can and cannot be distinguished by GNNs invariant or equivariant to spatial symmetries;(2) Equivariant GNNs are strictly more powerful than their invariant counterparts.

Keywords: Expressive Power · geometric graph neural networks

Author Information

Cristian Bodnar (University of Cambridge)
Chaitanya K. Joshi (University of Cambridge)
Simon Mathis (University of Cambridge)
Taco Cohen (Qualcomm AI Research)

Taco Cohen is a machine learning research scientist at Qualcomm AI Research in Amsterdam and a PhD student at the University of Amsterdam, supervised by prof. Max Welling. He was a co-founder of Scyfer, a company focussed on active deep learning, acquired by Qualcomm in 2017. He holds a BSc in theoretical computer science from Utrecht University and a MSc in artificial intelligence from the University of Amsterdam (both cum laude). His research is focussed on understanding and improving deep representation learning, in particular learning of equivariant and disentangled representations, data-efficient deep learning, learning on non-Euclidean domains, and applications of group representation theory and non-commutative harmonic analysis, as well as deep learning based source compression. He has done internships at Google Deepmind (working with Geoff Hinton) and OpenAI. He received the 2014 University of Amsterdam thesis prize, a Google PhD Fellowship, ICLR 2018 best paper award for “Spherical CNNs”, and was named one of 35 innovators under 35 in Europe by MIT in 2018.

Pietro Liò (University of Cambridge)

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