Gauge Equivariant Convolutional Networks and the Icosahedral CNN
T. Cohen, M. Weiler, B. Kicanaoglu, and M. Welling. (2019)cite arxiv:1902.04615Comment: To appear in the Proceedings of the International Conference on Machine Learning (ICML), 2019.
Abstract
The principle of equivariance to symmetry transformations enables a
theoretically grounded approach to neural network architecture design.
Equivariant networks have shown excellent performance and data efficiency on
vision and medical imaging problems that exhibit symmetries. Here we show how
this principle can be extended beyond global symmetries to local gauge
transformations. This enables the development of a very general class of
convolutional neural networks on manifolds that depend only on the intrinsic
geometry, and which includes many popular methods from equivariant and
geometric deep learning.
We implement gauge equivariant CNNs for signals defined on the surface of the
icosahedron, which provides a reasonable approximation of the sphere. By
choosing to work with this very regular manifold, we are able to implement the
gauge equivariant convolution using a single conv2d call, making it a highly
scalable and practical alternative to Spherical CNNs. Using this method, we
demonstrate substantial improvements over previous methods on the task of
segmenting omnidirectional images and global climate patterns.
Description
[1902.04615] Gauge Equivariant Convolutional Networks and the Icosahedral CNN
%0 Journal Article
%1 cohen2019gauge
%A Cohen, Taco S.
%A Weiler, Maurice
%A Kicanaoglu, Berkay
%A Welling, Max
%D 2019
%K deep-learning equivariance robustness symmetry theory
%T Gauge Equivariant Convolutional Networks and the Icosahedral CNN
%U http://arxiv.org/abs/1902.04615
%X The principle of equivariance to symmetry transformations enables a
theoretically grounded approach to neural network architecture design.
Equivariant networks have shown excellent performance and data efficiency on
vision and medical imaging problems that exhibit symmetries. Here we show how
this principle can be extended beyond global symmetries to local gauge
transformations. This enables the development of a very general class of
convolutional neural networks on manifolds that depend only on the intrinsic
geometry, and which includes many popular methods from equivariant and
geometric deep learning.
We implement gauge equivariant CNNs for signals defined on the surface of the
icosahedron, which provides a reasonable approximation of the sphere. By
choosing to work with this very regular manifold, we are able to implement the
gauge equivariant convolution using a single conv2d call, making it a highly
scalable and practical alternative to Spherical CNNs. Using this method, we
demonstrate substantial improvements over previous methods on the task of
segmenting omnidirectional images and global climate patterns.
@article{cohen2019gauge,
abstract = {The principle of equivariance to symmetry transformations enables a
theoretically grounded approach to neural network architecture design.
Equivariant networks have shown excellent performance and data efficiency on
vision and medical imaging problems that exhibit symmetries. Here we show how
this principle can be extended beyond global symmetries to local gauge
transformations. This enables the development of a very general class of
convolutional neural networks on manifolds that depend only on the intrinsic
geometry, and which includes many popular methods from equivariant and
geometric deep learning.
We implement gauge equivariant CNNs for signals defined on the surface of the
icosahedron, which provides a reasonable approximation of the sphere. By
choosing to work with this very regular manifold, we are able to implement the
gauge equivariant convolution using a single conv2d call, making it a highly
scalable and practical alternative to Spherical CNNs. Using this method, we
demonstrate substantial improvements over previous methods on the task of
segmenting omnidirectional images and global climate patterns.},
added-at = {2019-05-01T23:17:22.000+0200},
author = {Cohen, Taco S. and Weiler, Maurice and Kicanaoglu, Berkay and Welling, Max},
biburl = {https://www.bibsonomy.org/bibtex/260b94dde318d059e918fb42bb30e1892/kirk86},
description = {[1902.04615] Gauge Equivariant Convolutional Networks and the Icosahedral CNN},
interhash = {1c37256cb4859958f660049921465917},
intrahash = {60b94dde318d059e918fb42bb30e1892},
keywords = {deep-learning equivariance robustness symmetry theory},
note = {cite arxiv:1902.04615Comment: To appear in the Proceedings of the International Conference on Machine Learning (ICML), 2019},
timestamp = {2019-05-01T23:17:22.000+0200},
title = {Gauge Equivariant Convolutional Networks and the Icosahedral CNN},
url = {http://arxiv.org/abs/1902.04615},
year = 2019
}