  The distance-geometric graph representation adopts a unified scheme
(distance) for representing the geometry of three-dimensional(3D) graphs. It is
invariant to rotation and translation of the graph and it reflects pair-wise
node interactions and their generally local nature. To facilitate the
incorporation of geometry in deep learning on 3D graphs, we propose a
message-passing graph convolutional network based on the distance-geometric
graph representation: DG-GCN (distance-geometric graph convolution network). It
utilizes continuous-filter convolutional layers, with filter-generating
networks, that enable learning of filter weights from distances, thereby
incorporating the geometry of 3D graphs in graph convolutions. Our results for
the ESOL and FreeSolv datasets show major improvement over those of standard
graph convolutions. They also show significant improvement over those of
geometric graph convolutions employing edge weight / edge distance power laws.
Our work demonstrates the utility and value of DG-GCN for end-to-end deep
learning on 3D graphs, particularly molecular graphs.
