Learning from unordered sets is a fundamental learning setup, which is
attracting increasing attention. Research in this area has focused on the case
where elements of the set are represented by feature vectors, and far less
emphasis has been given to the common case where set elements themselves adhere
to certain symmetries. That case is relevant to numerous applications, from
deblurring image bursts to multi-view 3D shape recognition and reconstruction.
In this paper, we present a principled approach to learning sets of general
symmetric elements. We first characterize the space of linear layers that are
equivariant both to element reordering and to the inherent symmetries of
elements, like translation in the case of images. We further show that networks
that are composed of these layers, called Deep Sets for Symmetric elements
layers (DSS), are universal approximators of both invariant and equivariant
functions. DSS layers are also straightforward to implement. Finally, we show
that they improve over existing set-learning architectures in a series of
experiments with images, graphs, and point-clouds.
Description
[2002.08599] On Learning Sets of Symmetric Elements
%0 Journal Article
%1 maron2020learning
%A Maron, Haggai
%A Litany, Or
%A Chechik, Gal
%A Fetaya, Ethan
%D 2020
%K deep-learning learning sets symmetry
%T On Learning Sets of Symmetric Elements
%U http://arxiv.org/abs/2002.08599
%X Learning from unordered sets is a fundamental learning setup, which is
attracting increasing attention. Research in this area has focused on the case
where elements of the set are represented by feature vectors, and far less
emphasis has been given to the common case where set elements themselves adhere
to certain symmetries. That case is relevant to numerous applications, from
deblurring image bursts to multi-view 3D shape recognition and reconstruction.
In this paper, we present a principled approach to learning sets of general
symmetric elements. We first characterize the space of linear layers that are
equivariant both to element reordering and to the inherent symmetries of
elements, like translation in the case of images. We further show that networks
that are composed of these layers, called Deep Sets for Symmetric elements
layers (DSS), are universal approximators of both invariant and equivariant
functions. DSS layers are also straightforward to implement. Finally, we show
that they improve over existing set-learning architectures in a series of
experiments with images, graphs, and point-clouds.
@article{maron2020learning,
abstract = {Learning from unordered sets is a fundamental learning setup, which is
attracting increasing attention. Research in this area has focused on the case
where elements of the set are represented by feature vectors, and far less
emphasis has been given to the common case where set elements themselves adhere
to certain symmetries. That case is relevant to numerous applications, from
deblurring image bursts to multi-view 3D shape recognition and reconstruction.
In this paper, we present a principled approach to learning sets of general
symmetric elements. We first characterize the space of linear layers that are
equivariant both to element reordering and to the inherent symmetries of
elements, like translation in the case of images. We further show that networks
that are composed of these layers, called Deep Sets for Symmetric elements
layers (DSS), are universal approximators of both invariant and equivariant
functions. DSS layers are also straightforward to implement. Finally, we show
that they improve over existing set-learning architectures in a series of
experiments with images, graphs, and point-clouds.},
added-at = {2020-02-23T23:32:32.000+0100},
author = {Maron, Haggai and Litany, Or and Chechik, Gal and Fetaya, Ethan},
biburl = {https://www.bibsonomy.org/bibtex/21ed44b4977a35665d5fd3c77be697112/kirk86},
description = {[2002.08599] On Learning Sets of Symmetric Elements},
interhash = {ad35e661dca977a0cbfefd1219822d90},
intrahash = {1ed44b4977a35665d5fd3c77be697112},
keywords = {deep-learning learning sets symmetry},
note = {cite arxiv:2002.08599},
timestamp = {2020-02-23T23:32:49.000+0100},
title = {On Learning Sets of Symmetric Elements},
url = {http://arxiv.org/abs/2002.08599},
year = 2020
}