Orbit-Equivariant Graph Neural Networks

Matthew Morris, Bernardo Cuenca Grau, Ian Horrocks

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Keywords: graph neural networks, equivariance, expressivity, graph orbits

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TL;DR: We define orbit-equivariance, a relaxation of equivariance, to enable solving a new class of problems and propose some orbit-equivariant GNNs

Abstract: Equivariance is an important structural property that is captured by architectures such as graph neural networks (GNNs). However, equivariant graph functions cannot produce different outputs for similar nodes, which may be undesirable when the function is trying to optimize some global graph property. In this paper, we define orbit-equivariance, a relaxation of equivariance which allows for such functions whilst retaining important structural inductive biases. We situate the property in the hierarchy of graph functions, define a taxonomy of orbit-equivariant functions, and provide four different ways to achieve non-equivariant GNNs. For each, we analyze their expressivity with respect to orbit-equivariance and evaluate them on two novel datasets, one of which stems from a real-world use-case of designing optimal bioisosteres.

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Primary Area: learning on graphs and other geometries & topologies

Submission Number: 5840