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.
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