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

This paper proposes a generalized version of SO(3)-equivariant architectures including Spherical CNN. By utilizing the algebraic properties of Fourier transform and the tools in non-commutative harmonic analysis, the authors are able to construct (and prove) a most generalized version of SO(3)-equivariant architecture. Specifically, it only requires that, when an input image is rotated, each fragment (i.e., the output, Fourier coefficient vectors) of each layer will be multiplied by a Wigner-D matrix. To include non-linearities without performing inverse Fourier transform, the authors propose to use Clebsch-Gordon transformation. The experiments show that the proposed CG-Net can outperform Spherical CNN in several tasks.