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

Abstract

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

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