Vector Neurons: A General Framework for SO(3)-Equivariant Networks
This provides a simpler and more versatile approach to rotation-equivariant networks for 3D deep learning, addressing a bottleneck in handling arbitrary poses in geometry inputs.
The authors tackled the problem of creating rotation-equivariant neural networks for 3D point cloud processing by introducing Vector Neurons, a general framework that extends neurons to 3D vectors, achieving comparable accuracy and generalization to state-of-the-art methods on classification and segmentation tasks.
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.