Title: Transfer Bound of Graph Convolutional Networks across Arbitrary Sparsity
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph convolutional networks, sparse graphs, convergence, transfer learning

Abstract: Size transfer methods in Graph Convolutional Networks (GCNs) is a common treatment to mitigate the high cost of training on large graphs, by transferring the model trained on randomly sampled smaller graphs. However, the theoretical guarantee of such transfer has only been proved in previous studies for random graphs with fixed sparsity. In practice, downsampled real-world graphs may exhibit multiple sparsity regimes. To fully understand the theoretical performance across arbitrary sparsity, we establish the GCN transferability bound by introducing Stretched Graphon Convolutional Networks (SWNNs) based on the recent generalized graphon model. The bound decomposes into error components arising from expected edge density and graph size, which jointly determine the sparsity. Experiments on real-world networks validate our theoretical findings.

TL;DR: We establish a transfer bound for GCNs across arbitrary sparsity.