Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
This work addresses the challenge of orientation invariance in 3D data processing for applications in geometry, physics, and chemistry, representing a novel method for a known bottleneck.
The paper tackles the problem of achieving rotation and translation equivariance in neural networks for 3D point clouds by introducing tensor field networks, which use spherical harmonics-based filters to guarantee equivariance at every layer and eliminate the need for data augmentation.
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.