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

TL;DR

This paper introduces geometric graph representations and convolution methods for 3D graphs, demonstrating improved performance in molecular property prediction tasks by incorporating geometric information.

Contribution

It defines three types of geometric graph representations and employs distance-geometric convolution with a simple edge weighting scheme, advancing deep learning on 3D graph data.

Findings

Significant performance improvements on ESOL and Freesol datasets

Feasibility of incorporating geometric information into deep learning models

Distance-geometric representation enhances graph convolution effectiveness

Abstract

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.