  Recent work in graph neural networks (GNNs) has led to improvements in
molecular activity and property prediction tasks. Unfortunately, GNNs often
fail to capture the relative importance of interactions between molecular
substructures, in part due to the absence of efficient intermediate pooling
steps. To address these issues, we propose LaPool (Laplacian Pooling), a novel,
data-driven, and interpretable hierarchical graph pooling method that takes
into account both node features and graph structure to improve molecular
representation. We benchmark LaPool on molecular graph prediction and
understanding tasks and show that it outperforms recent GNNs. Interestingly,
LaPool also remains competitive on non-molecular tasks. Both quantitative and
qualitative assessments are done to demonstrate LaPool's improved
interpretability and highlight its potential benefits in drug design. Finally,
we demonstrate LaPool's utility for the generation of valid and novel molecules
by incorporating it into an adversarial autoencoder.
