Vector Neurons: A General Framework for SO(3)-Equivariant Networks

Understand

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.