Multiresolution Equivariant Graph Variational Autoencoder

In this paper, we propose Multiresolution Equivariant Graph Variational Autoencoders (MGVAE), the first <PRE_TAG>hierarchical generative model</POST_TAG> to learn and generate graphs in a multiresolution and equivariant manner. At each resolution level, MGVAE employs higher order message passing to encode the graph while learning to partition it into mutually exclusive clusters and coarsening into a lower resolution that eventually creates a hierarchy of latent distributions. MGVAE then constructs a <PRE_TAG>hierarchical generative model</POST_TAG> to variationally decode into a hierarchy of coarsened <PRE_TAG>graphs</POST_TAG>. Importantly, our proposed framework is end-to-end permutation <PRE_TAG>equivariant</POST_TAG> with respect to node ordering. MGVAE achieves competitive results with several generative tasks including general graph generation, molecular generation, unsupervised molecular representation learning to predict molecular properties, link prediction on citation <PRE_TAG>graphs</POST_TAG>, and graph-based image generation.