  Graph neural networks (GNNs) have achieved great success on various tasks and
fields that require relational modeling. GNNs aggregate node features using the
graph structure as inductive biases resulting in flexible and powerful models.
However, GNNs remain hard to interpret as the interplay between node features
and graph structure is only implicitly learned. In this paper, we propose a
novel method called Kedge for explicitly sparsifying the underlying graph by
removing unnecessary neighbors. Our key idea is based on a tractable method for
sparsification using the Hard Kumaraswamy distribution that can be used in
conjugation with any GNN model. Kedge learns edge masks in a modular fashion
trained with any GNN allowing for gradient based optimization in an end-to-end
fashion. We demonstrate through extensive experiments that our model Kedge can
prune a large proportion of the edges with only a minor effect on the test
accuracy. Specifically, in the PubMed dataset, Kedge learns to drop more than
80% of the edges with an accuracy drop of merely 2% showing that graph
structure has only a small contribution in comparison to node features.
Finally, we also show that Kedge effectively counters the over-smoothing
phenomena in deep GNNs by maintaining good task performance with increasing GNN
layers.
