  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 may limit their accessibility, or
are tied to specific input data types and network architectures. In this paper,
we introduce a general framework built on top of what we call Vector Neuron
representations for creating SO(3)-equivariant neural networks for pointcloud
processing. Extending neurons from 1D scalars to 3D vectors, our vector neurons
enable a simple mapping of SO(3) actions to latent spaces thereby providing a
framework for building equivariance in common neural operations -- including
linear layers, non-linearities, pooling, and normalizations. Due to their
simplicity, vector neurons are versatile and, as we demonstrate, can be
incorporated into diverse network architecture backbones, allowing them to
process geometry inputs in arbitrary poses. Despite its simplicity, our method
performs comparably well in accuracy and generalization with other more complex
and specialized state-of-the-art methods on classification and segmentation
tasks. We also show for the first time a rotation equivariant reconstruction
network.
