Towards a Spectrum of Graph Convolutional Networks
This addresses the problem of representing complex node dependencies in graph neural networks for researchers and practitioners, though it appears incremental as it builds on existing GCN frameworks.
The paper tackles the limitations of graph convolutional networks (GCNs) by proposing a generalization that uses structural properties of local neighborhoods for aggregation, not just weighted averages, resulting in strictly more expressive models with only a modest increase in parameters and computations.
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.