On the Expressive Power of Geometric Graph Neural NetworksDownload PDF

Published: 24 Nov 2022, Last Modified: 12 Mar 2024LoG 2022 PosterReaders: Everyone
Keywords: Geometric Deep Learning, Graph Neural Networks
TL;DR: We propose a geometric version of the Weisfeler-Leman graph isomorphism test to study the expressive power of GNNs for geometric graphs.
Abstract: The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the lens of the Weisfeiler-Leman (WL) graph isomorphism test. Yet, many graphs in scientific and engineering applications come embedded in Euclidean space with an additional notion of geometric isomorphism, which is not covered by the WL framework. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of GNNs that are invariant or equivariant to physical symmetries in terms of the classes of geometric graphs they can distinguish. This allows us to formalise the advantages of equivariant GNN layers over invariant ones: equivariant GNNs have greater expressive power as they enable propagating geometric information beyond local neighbourhoods, while invariant GNNs cannot distinguish graphs that are locally similar, highlighting their inability to compute global geometric quantities.
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Software: https://bit.ly/geometric-wl
Video: https://youtu.be/VKj5wzZsoK4
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