Geometric Graph Representations and Geometric Graph Convolutions for\n Deep Learning on Three-Dimensional (3D) Graphs

The geometry of three-dimensional (3D) graphs, consisting of nodes and edges,\nplays a crucial role in many important applications. An excellent example is\nmolecular graphs, whose geometry influences important properties of a molecule\nincluding its reactivity and biological activity. To facilitate the\nincorporation of geometry in deep learning on 3D graphs, we define three types\nof geometric graph representations: positional, angle-geometric and\ndistance-geometric. For proof of concept, we use the distance-geometric graph\nrepresentation for geometric graph convolutions. Further, to utilize standard\ngraph convolution networks, we employ a simple edge weight / edge distance\ncorrelation scheme, whose parameters can be fixed using reference values or\ndetermined through Bayesian hyperparameter optimization. The results of\ngeometric graph convolutions, for the ESOL and Freesol datasets, show\nsignificant improvement over those of standard graph convolutions. Our work\ndemonstrates the feasibility and promise of incorporating geometry, using the\ndistance-geometric graph representation, in deep learning on 3D graphs.\n