Efficient Generalized Spherical CNNs
This work addresses computational bottlenecks for researchers and practitioners in computer vision and natural sciences analyzing spherical data, offering incremental improvements to existing methods.
The paper tackles the high computational cost of strictly equivariant spherical CNNs, which limits their use, by developing two new layers with reduced complexity from O(C^2L^5) to O(CL^4) and O(CL^3 log L), enabling more expressive models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmarks.
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical CNN framework that encompasses various existing approaches and allows them to be leveraged alongside each other. The only existing non-linear spherical CNN layer that is strictly equivariant has complexity $\mathcal{O}(C^2L^5)$, where $C$ is a measure of representational capacity and $L$ the spherical harmonic bandlimit. Such a high computational cost often prohibits the use of strictly equivariant spherical CNNs. We develop two new strictly equivariant layers with reduced complexity $\mathcal{O}(CL^4)$ and $\mathcal{O}(CL^3 \log L)$, making larger, more expressive models computationally feasible. Moreover, we adopt efficient sampling theory to achieve further computational savings. We show that these developments allow the construction of more expressive hybrid models that achieve state-of-the-art accuracy and parameter efficiency on spherical benchmark problems.