Towards a Spectrum of Graph Convolutional Networks

TL;DR

This paper explores the limitations of existing graph convolutional networks and proposes a more expressive generalization that adapts to local neighborhood structures, enhancing their ability to model complex node dependencies.

Contribution

It introduces a novel generalization of GCNs that uses structural properties for aggregation, increasing expressiveness with minimal additional computational cost.

Findings

More expressive than standard GCNs

Equivalent to standard convolutions on grid graphs

Requires only modest increase in parameters

Abstract

We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis of GCNs with the help of the corresponding computation graphs, we propose a generalization of existing GCNs where the aggregation operations are (a) determined by structural properties of the local neighborhood graphs and (b) not restricted to weighted averages. We show that the proposed approach is strictly more expressive while requiring only a modest increase in the number of parameters and computations. We also show that the proposed generalization is identical to standard convolutional layers when applied to regular grid graphs.