$G^3$: Representation Learning and Generation for Geometric Graphs

A geometric graph is a graph equipped with geometric information (i.e., node coordinates). A notable example is molecular graphs, where the combinatorial bonding is supplement with atomic coordinates that determine the three-dimensional structure. This work proposes a generative model for geometric graphs, capitalizing on the complementary information of structure and geometry to learn the underlying distribution. The proposed model, Geometric Graph Generator (G$^3$), orchestrates graph neural networks and point cloud models in a nontrivial manner under an autoencoding framework. Additionally, we augment this framework with a normalizing flow so that one can effectively sample from the otherwise intractable latent space. G$^3$ can be used in computer-aided drug discovery, where seeking novel and optimal molecular structures is critical. As a representation learning approach, the interaction of the graph structure and the geometric point cloud also improve significantly the performance of downstream tasks, such as molecular property prediction. We conduct a comprehensive set of experiments to demonstrate that G$^3$ learns more accurately the distribution of given molecules and helps identify novel molecules with better properties of interest.