论文标题
关于旋转模棱两可的点云网络的普遍性
On the Universality of Rotation Equivariant Point Cloud Networks
论文作者
论文摘要
点云上的学习功能在许多领域都有应用，包括计算机视觉，计算机图形，物理和化学。最近，人们对神经体系结构的兴趣日益浓厚，这些神经体系结构是对点云的所有三种形状保留转换的不变或等效的：翻译，旋转和置换。 在本文中，我们介绍了这些架构的近似能力的首次研究。我们首先基于对均等多项式空间的新表征，为e夫式体系结构提供了两个足够的条件，可以具有通用近似特性。然后，我们使用这些条件表明，最近建议的两个模型是通用的，并设计了另外两个新型的通用体系结构。
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.
