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 this https URL

研究了一种基于图表示的方法，DeepSphere，在球形神经网络上设计卷积需要在效率和旋转等变性之间进行微妙的权衡，并且其性能卓越，甚至好于一些采用各向异性滤波器的方法。

DeepSphere：基于图形的球形 CNN

DeepSphere: a graph-based spherical CNN

Learning equivariant representations is a promising way to reduce sample and
model complexity and improve the generalization performance of deep neural
networks. The spherical CNNs are successful examples, producing
SO(3)-equivariant representations of spherical inputs. There are two main types
of spherical CNNs. The first type lifts the inputs to functions on the rotation
group SO(3) and applies convolutions on the group, which are computationally
expensive since SO(3) has one extra dimension. The second type applies
convolutions directly on the sphere, which are limited to zonal (isotropic)
filters, and thus have limited expressivity. In this paper, we present a new
type of spherical CNN that allows anisotropic filters in an efficient way,
without ever leaving the spherical domain. The key idea is to consider
spin-weighted spherical functions, which were introduced in physics in the
study of gravitational waves. These are complex-valued functions on the sphere
whose phases change upon rotation. We define a convolution between
spin-weighted functions and build a CNN based on it. The spin-weighted
functions can also be interpreted as spherical vector fields, allowing
applications to tasks where the inputs or outputs are vector fields.
Experiments show that our method outperforms previous methods on tasks like
classification of spherical images, classification of 3D shapes and semantic
segmentation of spherical panoramas.

介绍了一种新型球形卷积神经网络，使用自旋加权球形函数，实现在球形空间内的非均向滤波，适用于分类球形图像、3D 形状和球形全景图像的语义分割，并在实验中展现了优越性。