Efficient Generalized Spherical CNNs

TL;DR

This paper introduces a generalized framework for spherical CNNs that reduces computational complexity, enabling larger models that achieve state-of-the-art accuracy on spherical data tasks.

Contribution

It presents new strictly equivariant layers with lower complexity, integrating them into a unified framework for more efficient spherical CNNs.

Findings

New layers reduce complexity from O(C^2L^5) to O(CL^3 log L)

Hybrid models achieve state-of-the-art accuracy

Models are more parameter-efficient and scalable

Abstract

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.