Natural Graph Networks

TL;DR

This paper introduces the concept of naturality as a more general and flexible framework than equivariance for graph neural networks, enabling scalable and well-defined graph processing.

Contribution

It generalizes the theoretical foundation of graph networks from equivariance to naturality, and proposes scalable local natural graph networks with practical implementation.

Findings

Natural graph networks are more flexible than traditional equivariant networks.

The proposed natural network achieves good performance on benchmarks.

Local natural graph networks match the scalability of message passing methods.

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.