General E(2)-Equivariant Steerable CNNs

2019/11/19 by Maurice Weiler, Weiler, Maurice, Gabriele Cesa +1 · 52 citations
Computer Science · Engineering · Neuroscience · #Advanced Neural Network Applications #Brain Tumor Detection and Classification #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #Geophysical Methods and Applications #Image and Video Processing (eess.IV) #Machine Learning (cs.LG) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1911.08251

openalex publication_date 2019/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for planar images. Here we give a general description of E(2)-equivariant convolutions in the framework of Steerable CNNs. The theory of Steerable CNNs thereby yields constraints on the convolution kernels which depend on group representations describing the transformation laws of feature spaces. We show that these constraints for arbitrary group representations can be reduced to constraints under irreducible representations. A general solution of the kernel space constraint is given for arbitrary representations of the Euclidean group E(2) and its subgroups. We implement a wide range of previously proposed and entirely new equivariant network architectures and extensively compare their performances. E(2)-steerable convolutions are further shown to yield remarkable gains on CIFAR-10, CIFAR-100 and STL-10 when used as a drop-in replacement for non-equivariant convolutions.

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