On the Universality of Rotation Equivariant Point Cloud Networks

Nadav Dym; Haggai Maron

ICLR 2021poster104 citations

On the Universality of Rotation Equivariant Point Cloud Networks

Abstract

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. We then use these conditions to show that two recently suggested models, Tensor field Networks and SE3-Transformers, are universal, and for devising two other novel universal architectures.

3D deep learningRotation invarianceInvariant and equivariant deep networksUniversal approximationPoint clouds

BibTeX

@inproceedings{
dym2021on,
title={On the Universality of Rotation Equivariant Point Cloud Networks},
author={Nadav Dym and Haggai Maron},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=6NFBvWlRXaG}
}