On Learning Sets of Symmetric Elements (Extended Abstract)

Haggai Maron, Or Litany, Gal Chechik, Ethan Fetaya

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Learning from unordered sets is a fundamental learning setup, recently 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 their own 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, and that these networks are strictly more expressive than Siamese networks. 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.

Original languageEnglish
Title of host publicationProceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021
EditorsZhi-Hua Zhou
PublisherInternational Joint Conferences on Artificial Intelligence
Pages4794-4798
Number of pages5
ISBN (Electronic)9780999241196
StatePublished - 2021
Event30th International Joint Conference on Artificial Intelligence, IJCAI 2021 - Virtual, Online, Canada
Duration: 19 Aug 202127 Aug 2021

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823

Conference

Conference30th International Joint Conference on Artificial Intelligence, IJCAI 2021
Country/TerritoryCanada
CityVirtual, Online
Period19/08/2127/08/21

Bibliographical note

Publisher Copyright:
© 2021 International Joint Conferences on Artificial Intelligence. All rights reserved.

Funding

This research was supported by an Israel science foundation grant 737/18. We thank Srinath Sridhar and Davis Rempe for valuable discussions.

FundersFunder number
Israel Science Foundation737/18

    Fingerprint

    Dive into the research topics of 'On Learning Sets of Symmetric Elements (Extended Abstract)'. Together they form a unique fingerprint.

    Cite this