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2. On the Universality of Rotation Equivariant Point Cloud Networks
 
 # On the Universality of Rotation Equivariant Point Cloud Networks

  ![](/sites/default/files/styles/wide/public/publications/rep.png?itok=h75zxJ2b)

 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 are universal, and for devising two other novel universal architectures.



 ## Authors



Nadav Dym (Duke University)

[Haggai Maron](/person/haggai-maron)

 

 

 ## Publication Date



Sunday, April 4, 2021

 

 ## Published in



[ICLR 2021](https://arxiv.org/abs/2010.02449)

 

 ## Research Area



[Artificial Intelligence and Machine Learning ](/research-area/machine-learning-artificial-intelligence)