Natural Graph Networks

Abstract

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

Published at NeurIPS 2020

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• Improving the Expressiveness of $K$-hop Message-Passing GNNs by Injecting Contextualized Substructure Information
• Category Theory in Machine Learning
• Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes
• Weisfeiler and Lehman Go Cellular: CW Networks
• Quiver Signal Processing (QSP)
• Kähler Geometry of Quiver Varieties and Machine Learning