Exploiting Learned Symmetries in Group Equivariant Convolutions

TL;DR

This paper analyzes learned symmetries in Group Equivariant Convolutions, revealing redundancies and proposing an efficient decomposition into depthwise separable convolutions that maintains equivariance, leading to improved performance.

Contribution

It introduces a method to decompose GConvs into depthwise separable convolutions, reducing parameters and computation while preserving equivariance.

Findings

Redundancies in learned filter parameters of GConvs

Decomposition into depthwise separable convolutions maintains equivariance

Improved performance and data efficiency demonstrated on two datasets

Abstract

Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and find certain conditions under which they become highly redundant. We show that GConvs can be efficiently decomposed into depthwise separable convolutions while preserving equivariance properties and demonstrate improved performance and data efficiency on two datasets. All code is publicly available at github.com/Attila94/SepGrouPy.