Using and Abusing Equivariance

Investigating Differences between Exact and Approximate Equivariance in Computer Vision

Master thesis (2023)

Authors

T.F. Edixhoven Electrical Engineering, Mathematics and Computer Science

Contributors

J.C. van Gemert Pattern Recognition and Bioinformatics - EEMCS (supervisor 1)
W.P. Brinkman Interactive Intelligence - EEMCS (coach)
A. Lengyel Pattern Recognition and Bioinformatics - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Tom Edixhoven
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Published Date

27-01-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this work we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on the 2D roto-translation group and investigate the impact of broken equivariance on network performance. We show that changing the input dimension of a network by as little as a single pixel can be enough for commonly used architectures to become approximately equivariant, rather than exactly. We investigate the impact of networks not being exactly equivariant and find that approximately equivariant networks generalise significantly worse to unseen symmetries compared to their exactly equivariant counterparts. However, when the symmetries in the training data are not identical to the symmetries of the network, we find that approximately equivariant networks are able to relax their own equivariant constraints, causing them to match or outperform exactly equivariant networks on common benchmark datasets.