Equivariance versus Augmentation for Spherical Images

Abstract

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 will be made available at https: //github.com/JanEGerken/sem_seg_s2cnn.

Geometric deep learning and equivariant neural networks

“…Group equivariant CNNs on S 2 were studied in Cohen et al (2018) by implementing efficient Fourier analysis on M = S 2 and G = SO(3). In Gerken et al (2022) the performance of group equivariant CNNs on S 2 was compared to standard nonequivariant CNNs trained with data augmentation. For the task of semantic segmentation it was demonstrated that the non-equivariant networks are consistently outperformed by the equivariant networks with considerably fewer parameters.…”

Lattice Gauge Equivariant Convolutional Neural Networks

“…Group convolutional layers thus commute with group transformations. In certain applications where larger symmetries are important, these networks have been shown to further improve performance compared to networks exhibiting less symmetry [12,13]. From a physical perspective, the symmetries considered in CNNs and, more generally, in G-CNNs are analogous to global symmetries of lattice field theories, which has led to numerous applications of CNNs in high energy physics (see [14] for a review).…”