Abstract. We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended
data augmentation in order to tackle it. We model 3D data with multivalued spherical functions and we propose a novel spherical convolutional
network that implements exact convolutions on the sphere by realizing
them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel
pooling on the spectral domain and our operations are independent of the
underlying spherical resolution throughout the network. We show that
networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in
standard retrieval and classification benchmarks