Geometric Graph Representations and Geometric Graph Convolutions for Deep Learning on Three-Dimensional (3D) Graphs
This work addresses the challenge of leveraging geometric information in 3D graphs for applications like molecular property prediction, though it appears incremental as it builds on existing graph convolution methods.
The authors tackled the problem of incorporating geometry into deep learning on 3D graphs, such as molecular graphs, by defining geometric graph representations and using distance-geometric representations for convolutions, resulting in significant improvements over standard graph convolutions on ESOL and Freesol datasets.
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule including its reactivity and biological activity. To facilitate the incorporation of geometry in deep learning on 3D graphs, we define three types of geometric graph representations: positional, angle-geometric and distance-geometric. For proof of concept, we use the distance-geometric graph representation for geometric graph convolutions. Further, to utilize standard graph convolution networks, we employ a simple edge weight / edge distance correlation scheme, whose parameters can be fixed using reference values or determined through Bayesian hyperparameter optimization. The results of geometric graph convolutions, for the ESOL and Freesol datasets, show significant improvement over those of standard graph convolutions. Our work demonstrates the feasibility and promise of incorporating geometry, using the distance-geometric graph representation, in deep learning on 3D graphs.