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

• DOI: 10.48550/arxiv.1802.08219
• Publication Date: 2018-01-01
• Authors: Nathaniel Thomas; Tess Smidt; Steven Kearnes; Lusann Yang; Li Li; Kai Kohlhoff; Patrick Riley
• Keywords: Equivariant map

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