The Transferability of Downsamped Sparse Graph Convolutional Networks

TL;DR

This paper analyzes how graph sparsity and topology affect the transferability of downsampling methods in large-scale graph convolutional networks, providing theoretical bounds and experimental validation.

Contribution

It introduces a novel downsampling method based on a sparse random graph model and derives an expected transfer error bound considering sparsity and topology.

Findings

Smaller graph sizes and higher degrees reduce transfer error bound

Increased sampling rates improve transferability

Experimental results confirm theoretical predictions

Abstract

To accelerate the training of graph convolutional networks (GCNs) on real-world large-scale sparse graphs, downsampling methods are commonly employed as a preprocessing step. However, the effects of graph sparsity and topological structure on the transferability of downsampling methods have not been rigorously analyzed or theoretically guaranteed, particularly when the topological structure is affected by graph sparsity. In this paper, we introduce a novel downsampling method based on a sparse random graph model and derive an expected upper bound for the transfer error. Our findings show that smaller original graph sizes, higher expected average degrees, and increased sampling rates contribute to reducing this upper bound. Experimental results validate the theoretical predictions. By incorporating both sparsity and topological similarity into the model, this study establishes an upper bound on the transfer error for downsampling in the training of large-scale sparse graphs and provides insight into the influence of topological structure on transfer performance.