  Graph Neural Networks (GNNs) achieve an impressive performance on structured
graphs by recursively updating the representation vector of each node based on
its neighbors, during which parameterized transformation matrices should be
learned for the node feature updating. However, existing propagation schemes
are far from being optimal since they do not fully utilize the relational
information between nodes. We propose the information maximizing graph neural
networks (IGNN), which maximizes the mutual information between edge states and
transform parameters. We reformulate the mutual information as a differentiable
objective via a variational approach. We compare our model against several
recent variants of GNNs and show that our model achieves the state-of-the-art
performance on multiple tasks including quantum chemistry regression on QM9
dataset, generalization capability from QM9 to larger molecular graphs, and
prediction of molecular bioactivities relevant for drug discovery. The IGNN
model is based on an elegant and fundamental idea in information theory as
explained in the main text, and it could be easily generalized beyond the
contexts of molecular graphs considered in this work. To encourage more future
work in this area, all datasets and codes used in this paper will be released
for public access.
