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

TL;DR

Tensor field networks are a novel type of neural network designed for 3D point cloud data that are equivariant to rotations, translations, and permutations, enabling more efficient learning without data augmentation.

Contribution

The paper introduces tensor field neural networks that are locally equivariant to 3D transformations and use spherical harmonics-based filters, advancing geometric deep learning.

Findings

Effective in geometry, physics, and chemistry tasks

Eliminate need for data augmentation in 3D orientation recognition

Handle scalars, vectors, and tensors within the network

Abstract

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.