Abstract: We consider representation learning from 3D graphs in which each node is
associated with a spatial position in 3D. This is an under explored area of
research, and a principled framework is currently lacking. In this work, we
propose a generic framework, known as the 3D graph network (3DGN), to provide a
unified interface at different levels of granularity for 3D graphs. Built on
3DGN, we propose the spherical message passing (SMP) as a novel and specific
scheme for realizing the 3DGN framework in the spherical coordinate system
(SCS). We conduct formal analyses and show that the relative location of each
node in 3D graphs is uniquely defined in the SMP scheme. Thus, our SMP
represents a complete and accurate architecture for learning from 3D graphs in
the SCS. We derive physically-based representations of geometric information
and propose the SphereNet for learning representations of 3D graphs. We show
that existing 3D deep models can be viewed as special cases of the SphereNet.
Experimental results demonstrate that the use of complete and accurate 3D
information in 3DGN and SphereNet leads to significant performance improvements
in prediction tasks.