On the Universality of Rotation Equivariant Point Cloud Networks

Understand

Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry.

• Recently, there has been a growing interest in neural architectures that are invariant or equivariant to all three shape-preserving transformations of point clouds: translation, rotation, and permutation.
• In this paper, we present a first study of the approximation power of these architectures.
• We first derive two sufficient conditions for an equivariant architecture to have the universal approximation property, based on a novel characterization of the space of equivariant polynomials.