On the Universality of Rotation Equivariant Point Cloud Networks
This provides foundational insights for researchers in fields like computer vision and chemistry, though it is incremental as it builds on existing models.
The paper tackled the problem of understanding the approximation capabilities of rotation equivariant neural networks for point clouds, and proved that certain architectures are universal approximators.
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.