# On the Universality of Rotation Equivariant Point Cloud Networks

@article{Dym2020OnTU, title={On the Universality of Rotation Equivariant Point Cloud Networks}, author={Nadav Dym and Haggai Maron}, journal={ArXiv}, year={2020}, volume={abs/2010.02449} }

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…

## 34 Citations

### ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Clouds

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A novel neural network architecture is proposed for processing 2D point clouds and its universality for approximating functions exhibiting any continuous rotation equivariant and permutation invariant function is proved.

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Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that…

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### Barron’s Theorem for Equivariant Networks

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This work demonstrates that for some commonly used groups, there exist smooth subclasses of functions — analogous to Barron classes offunction — which can be efficiently approximated using invariant architectures, thereby providing approximation results that are not only invariant, but efficient.

### Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces

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We introduce a uniﬁed framework for group equivariant networks on homogeneous spaces derived from a Fourier perspective. We consider tensor-valued feature ﬁelds, before and after a convolutional…

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