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Graph Neural Networks for Geometric Graphs

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Geometric graphs are spatially embedded graphs used to model systems in biochemistry, physical simulations and multiagent robotics. Importantly, graph attributes transform along with global Euclidean transformations or symmetries of the system, such as rotations, reflections, and translation. Graph Neural Networks (GNNs) with global symmetries ‘baked in’ have emerged as the architecture of choice for geometric graphs. This talk will introduce two classes of Geometric GNNs: (1) Equivariant GNNs, which use both scalar and geometric features that are equivariant to global symmetries; and (2) Invariant GNNs, which only reason locally via invariant scalars such as distances and angles. Additionally, we will study the expressive power of the two classes of Geometric GNNs from the perspective of distinguishing geometric graphs, i.e. graph isomorphism testing. We will introduce a Geometric Weisfeiler-Leman graph isomorphism test (GWL). We will then use the GWL framework to formally show that equivariant GNNs have greater expressive power than invariant GNNs, as they enable propagating geometric information beyond local neighbourhoods and compositionally build long-range interactions.

This talk is based on the paper ”On the Expressive Power of Geometric Graph Neural Networks”, by Chaitanya K. Joshi (x), Cristian Bodnar (x), Simon V. Mathis, Taco Cohen, and Pietro LiĆ², to be presented as an Oral at the NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representations.

This talk is part of the Artificial Intelligence Research Group Talks (Computer Laboratory) series.

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