  Graph Neural Networks (GNNs) have proved to be an effective representation
learning framework for graph-structured data, and have achieved
state-of-the-art performance on many practical predictive tasks, such as node
classification, link prediction and graph classification. Among the variants of
GNNs, Graph Attention Networks (GATs) learn to assign dense attention
coefficients over all neighbors of a node for feature aggregation, and improve
the performance of many graph learning tasks. However, real-world graphs are
often very large and noisy, and GATs are prone to overfitting if not
regularized properly. Even worse, the local aggregation mechanism of GATs may
fail on disassortative graphs, where nodes within local neighborhood provide
more noise than useful information for feature aggregation. In this paper, we
propose Sparse Graph Attention Networks (SGATs) that learn sparse attention
coefficients under an $L_0$-norm regularization, and the learned sparse
attentions are then used for all GNN layers, resulting in an edge-sparsified
graph. By doing so, we can identify noisy/task-irrelevant edges, and thus
perform feature aggregation on most informative neighbors. Extensive
experiments on synthetic and real-world graph learning benchmarks demonstrate
the superior performance of SGATs. In particular, SGATs can remove about
50\%-80\% edges from large assortative graphs, while retaining similar
classification accuracies. On disassortative graphs, SGATs prune majority of
noisy edges and outperform GATs in classification accuracies by significant
margins. Furthermore, the removed edges can be interpreted intuitively and
quantitatively. To the best of our knowledge, this is the first graph learning
algorithm that shows significant redundancies in graphs and edge-sparsified
graphs can achieve similar or sometimes higher predictive performances than
original graphs.
