TY - GEN
T1 - On learning sets of symmetric elements
AU - Maron, Haggai
AU - Litany, Or
AU - Chechik, Gal
AU - Fetaya, Ethan
N1 - Publisher Copyright: © 2020 37th International Conference on Machine Learning, ICML 2020. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85105168099&partnerID=8YFLogxK
M3 - منشور من مؤتمر
T3 - 37th International Conference on Machine Learning, ICML 2020
SP - 6690
EP - 6700
BT - 37th International Conference on Machine Learning, ICML 2020
A2 - Daume, Hal
A2 - Singh, Aarti
T2 - 37th International Conference on Machine Learning, ICML 2020
Y2 - 13 July 2020 through 18 July 2020
ER -