  Despite much research, Graph Neural Networks (GNNs) still do not display the
favorable scaling properties of other deep neural networks such as
Convolutional Neural Networks and Transformers. Previous work has identified
issues such as oversmoothing of the latent representation and have suggested
solutions such as skip connections and sophisticated normalization schemes.
Here, we propose a different approach that is based on a stratification of the
graph nodes. We provide motivation that the nodes in a graph can be stratified
into those with a low degree and those with a high degree and that the two
groups are likely to behave differently. Based on this motivation, we modify
the Graph Neural Network (GNN) architecture so that the weight matrices are
learned, separately, for the nodes in each group. This simple-to-implement
modification seems to improve performance across datasets and GNN methods. To
verify that this increase in performance is not only due to the added capacity,
we also perform the same modification for random splits of the nodes, which
does not lead to any improvement.
