  Graph neural networks (GNNs), which learn the representation of a node by
aggregating its neighbors, have become an effective computational tool in
downstream applications. Over-smoothing is one of the key issues which limit
the performance of GNNs as the number of layers increases. It is because the
stacked aggregators would make node representations converge to
indistinguishable vectors. Several attempts have been made to tackle the issue
by bringing linked node pairs close and unlinked pairs distinct. However, they
often ignore the intrinsic community structures and would result in sub-optimal
performance. The representations of nodes within the same community/class need
be similar to facilitate the classification, while different classes are
expected to be separated in embedding space. To bridge the gap, we introduce
two over-smoothing metrics and a novel technique, i.e., differentiable group
normalization (DGN). It normalizes nodes within the same group independently to
increase their smoothness, and separates node distributions among different
groups to significantly alleviate the over-smoothing issue. Experiments on
real-world datasets demonstrate that DGN makes GNN models more robust to
over-smoothing and achieves better performance with deeper GNNs.
