Convolutional Networks for Spherical Signals

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.