  We analyze the role of rotational equivariance in convolutional neural
networks (CNNs) applied to spherical images. We compare the performance of the
group equivariant networks known as S2CNNs and standard non-equivariant CNNs
trained with an increasing amount of data augmentation. The chosen
architectures can be considered baseline references for the respective design
paradigms. Our models are trained and evaluated on single or multiple items
from the MNIST or FashionMNIST dataset projected onto the sphere. For the task
of image classification, which is inherently rotationally invariant, we find
that by considerably increasing the amount of data augmentation and the size of
the networks, it is possible for the standard CNNs to reach at least the same
performance as the equivariant network. In contrast, for the inherently
equivariant task of semantic segmentation, the non-equivariant networks are
consistently outperformed by the equivariant networks with significantly fewer
parameters. We also analyze and compare the inference latency and training
times of the different networks, enabling detailed tradeoff considerations
between equivariant architectures and data augmentation for practical problems.
The equivariant spherical networks used in the experiments are available at
https://github.com/JanEGerken/sem_seg_s2cnn .
