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The distance-geometric graph representation adopts a unified scheme(distance) for representing the geometry of three-dimensional(3D) graphs. It isinvariant to rotation and translation of the graph and it reflects pair-wisenode interactions and their generally local nature. To facilitate theincorporation of geometry in deep learning on 3D graphs, we propose amessage-passing graph convolutional network based on the distance-geometricgraph representation: DG-GCN (distance-geometric graph convolution network). Itutilizes continuous-filter convolutional layers, with filter-generatingnetworks, that enable learning of filter weights from distances, therebyincorporating the geometry of 3D graphs in graph convolutions. Our results forthe ESOL and FreeSolv datasets show major improvement over those of standardgraph convolutions. They also show significant improvement over those ofgeometric graph convolutions employing edge weight / edge distance power laws.Our work demonstrates the utility and value of DG-GCN for end-to-end deeplearning on 3D graphs, particularly molecular graphs.

Distance-Geometric Graph Convolutional Network (DG-GCN) for Three-Dimensional (3D) Graphs