Multiresolution Equivariant Graph Variational Autoencoder
This addresses the need for scalable and permutation-equivariant graph generative models, with incremental improvements in specific domains.
The paper tackles the problem of learning and generating graphs in a hierarchical, multiresolution manner by proposing MGVAE, which achieves competitive results in tasks like graph and molecular generation, link prediction, and image generation.
In this paper, we propose Multiresolution Equivariant Graph Variational Autoencoders (MGVAE), the first hierarchical generative model 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 hierarchical generative model to variationally decode into a hierarchy of coarsened graphs. Importantly, our proposed framework is end-to-end permutation equivariant 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 graphs, and graph-based image generation.