Parameter Efficient Node Classification on Homophilic Graphs

Deep Learning on Graphs was recently made possible with the introduction of Graph Neural Networks (GNNs). GNNs use learnable diffusion processes to propagate information through the graph and improve performance on downstream tasks. However, learning this diffusion process can be expensive in terms of memory and computation. While much research has gone into making these models more expressive and able to capture more complex patterns, in practice, edges in common benchmarking datasets often encode similarity of nodes with respect to the downstream task. This property is called homophily. We argue that for these homophilic graphs, learnable diffusion processes and large receptive fields are not required to achieve competitive performance. We propose Graph Non-Parametric Diffusion (GNPD) a method that outperforms traditional GNNs using only 2 linear models and non-parameteric diffusion. Our method takes ideas from Correct & Smooth (C&S) and the Scalable Inception Graph Network (SIGN) and combines them to create a simpler model that outperforms both of them on several datasets. Our method achieves unmatched parameter efficiency, competing with models with two orders of magnitude more parameters. Additionally GNPD can also forego spectral embeddings which are the computational bottleneck of the C&S method.