On learning sets of symmetric elements

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. 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 pointclouds.

Original languageEnglish
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
Pages6690-6700
Number of pages11
ISBN (Electronic)9781713821120
StatePublished - 2020
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: 13 Jul 202018 Jul 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020
VolumePartF168147-9

Conference

Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online
Period13/07/2018/07/20

All Science Journal Classification (ASJC) codes

  • Software
  • Human-Computer Interaction
  • Computational Theory and Mathematics

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