Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network

TL;DR

This paper introduces Clebsch-Gordan Nets, a spherical convolutional neural network that leverages Fourier space and the Clebsch-Gordan transform for improved rotation-invariant learning on spherical data, simplifying implementation and enhancing performance.

Contribution

It proposes a novel neural network architecture using the Clebsch-Gordan transform as the sole nonlinearity, simplifying implementation and extending group invariance beyond rotations.

Findings

Achieves improved performance over previous spherical CNNs.

Simplifies implementation by avoiding repeated Fourier transforms.

Extensible to invariance under other compact groups.

Abstract

Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler. An unusual feature of the proposed architecture is that it uses the Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding repeated forward and backward Fourier transforms. The underlying ideas of the paper generalize to constructing neural networks that are invariant to the action of other compact groups.