  Convolutional neural networks (CNNs) constructed natively on the sphere have
been developed recently and shown to be highly effective for the analysis of
spherical data. While an efficient framework has been formulated, spherical
CNNs are nevertheless highly computationally demanding; typically they cannot
scale beyond spherical signals of thousands of pixels. We develop scattering
networks constructed natively on the sphere that provide a powerful
representational space for spherical data. Spherical scattering networks are
computationally scalable and exhibit rotational equivariance, while their
representational space is invariant to isometries and provides efficient and
stable signal representations. By integrating scattering networks as an
additional type of layer in the generalized spherical CNN framework, we show
how they can be leveraged to scale spherical CNNs to the high-resolution data
typical of many practical applications, with spherical signals of many tens of
megapixels and beyond.
