Similarity Group Equivariant Convolutional Networks

Xinhua Zhang, Ganesh Sundaramoorthi

Keywords: Group Convolution, Group Equivariance, Similarity Transformation, Continuous Transformation, Translation, Rotation, Scaling, Reflection

TL;DR: We implemented deep group convolutional networks that are similarity equivariant by using a Fourier analysis approach.

Abstract:

We introduce similarity group equivariant convolutional networks (SECNNs), designed to achieve continuous translation, rotation and scale equivariance, or discrete similarity group equivariance that involves discrete Dihedral group. The networks are implemented as steerable CNNs by employing a steerable and approximately shiftable and scalable basis for continuous translating, rotating and scaling convolution kernels within a five-dimensional position-orientation-scale-reflection space.
Our results demonstrate that SECNNs attain state-of-the-art results on translated, rotated and scaled MNIST datasets. SECNNs also achieve the accuracy of other leading group equivariant networks on CIFAR10/100,
while being equivariant to the full range of the similarity group in comparison to existing state of the art, which is equivariant to only sub-groups of the similarity group.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 8014