Multiresolution Equivariant Graph Variational Autoencoder

TL;DR

This paper introduces MGVAE, a hierarchical, multiresolution, and permutation-equivariant graph variational autoencoder that effectively learns and generates complex graph structures across multiple tasks.

Contribution

It presents the first hierarchical generative model for graphs that operates in a multiresolution and equivariant manner, enabling diverse graph-related applications.

Findings

Achieves competitive results in graph and molecular generation

Effective in unsupervised molecular property prediction

Performs well in link prediction and image generation tasks

Abstract

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.