  Recent advances in representation learning on graphs, mainly leveraging graph
convolutional networks, have brought a substantial improvement on many
graph-based benchmark tasks. While novel approaches to learning node embeddings
are highly suitable for node classification and link prediction, their
application to graph classification (predicting a single label for the entire
graph) remains mostly rudimentary, typically using a single global pooling step
to aggregate node features or a hand-designed, fixed heuristic for hierarchical
coarsening of the graph structure. An important step towards ameliorating this
is differentiable graph coarsening---the ability to reduce the size of the
graph in an adaptive, data-dependent manner within a graph neural network
pipeline, analogous to image downsampling within CNNs. However, the previous
prominent approach to pooling has quadratic memory requirements during training
and is therefore not scalable to large graphs. Here we combine several recent
advances in graph neural network design to demonstrate that competitive
hierarchical graph classification results are possible without sacrificing
sparsity. Our results are verified on several established graph classification
benchmarks, and highlight an important direction for future research in
graph-based neural networks.
