Multiresolution Graph Variational Autoencoder

In this paper, we propose Multiresolution Graph Networks (MGN) and Multiresolution Graph Variational Autoencoders (MGVAE) to learn and generate graphs in a multiresolution and equivariant manner. At each resolution level, MGN employs higher order message passing to encode the graph while learning to partition it into mutually exclusive clusters and coarsening into a lower resolution. MGVAE constructs a hierarchical generative model based on MGN to variationally autoencode the hierarchy of coarsened graphs. Our proposed framework is end-to-end permutation equivariant with respect to node ordering. Our methods have been successful with several generative tasks including link prediction on citation graphs, unsupervised molecular representation learning to predict molecular properties, molecular generation, general graph generation and graph-based image generation.