  Spherical CNNs generalize CNNs to functions on the sphere, by using spherical
convolutions as the main linear operation. The most accurate and efficient way
to compute spherical convolutions is in the spectral domain (via the
convolution theorem), which is still costlier than the usual planar
convolutions. For this reason, applications of spherical CNNs have so far been
limited to small problems that can be approached with low model capacity. In
this work, we show how spherical CNNs can be scaled for much larger problems.
To achieve this, we make critical improvements including novel variants of
common model components, an implementation of core operations to exploit
hardware accelerator characteristics, and application-specific input
representations that exploit the properties of our model. Experiments show our
larger spherical CNNs reach state-of-the-art on several targets of the QM9
molecular benchmark, which was previously dominated by equivariant graph neural
networks, and achieve competitive performance on multiple weather forecasting
tasks. Our code is available at
https://github.com/google-research/spherical-cnn.
