A Simple and Universal Rotation Equivariant Point-cloud Network

TL;DR

This paper introduces a simpler rotation-equivariant point-cloud network that maintains universality in approximating equivariant functions, demonstrating competitive performance on ModelNet40.

Contribution

It proposes a simpler architecture with proven universality guarantees for rotation equivariance in 3D point-cloud learning.

Findings

Achieves universality similar to Tensor Field Networks

Performs well on ModelNet40 dataset

Provides open-source code for reproducibility

Abstract

Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any equivariant function. In this paper we suggest a much simpler architecture, prove that it enjoys the same universality guarantees and evaluate its performance on Modelnet40. The code to reproduce our experiments is available at \url{https://github.com/simpleinvariance/UniversalNetwork}