Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

Understand

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer.

• 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations.
• Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms.
• We demonstrate the capabilities of tensor field networks with tasks in geometry, physics, and chemistry.