  Designing a convolution for a spherical neural network requires a delicate
tradeoff between efficiency and rotation equivariance. DeepSphere, a method
based on a graph representation of the sampled sphere, strikes a controllable
balance between these two desiderata. This contribution is twofold. First, we
study both theoretically and empirically how equivariance is affected by the
underlying graph with respect to the number of vertices and neighbors. Second,
we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art
performance and demonstrates the efficiency and flexibility of this
formulation. Perhaps surprisingly, comparison with previous work suggests that
anisotropic filters might be an unnecessary price to pay. Our code is available
at https://github.com/deepsphere
