  The success of convolutional networks in learning problems involving planar
signals such as images is due to their ability to exploit the translation
symmetry of the data distribution through weight sharing. Many areas of science
and egineering deal with signals with other symmetries, such as rotation
invariant data on the sphere. Examples include climate and weather science,
astrophysics, and chemistry. In this paper we present spherical convolutional
networks. These networks use convolutions on the sphere and rotation group,
which results in rotational weight sharing and rotation equivariance. Using a
synthetic spherical MNIST dataset, we show that spherical convolutional
networks are very effective at dealing with rotationally invariant
classification problems.
