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On Learning Sets of Symmetric Elements
Haggai Maron · Or Litany · Gal Chechik · Ethan Fetaya

Tue Jul 14 10:00 AM -- 10:45 AM & Tue Jul 14 11:00 PM -- 11:45 PM (PDT) @ Virtual #None

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.

Author Information

Haggai Maron (NVIDIA Research)

I am a Research Scientist at NVIDIA Research. My main fields of interest are machine learning, optimization, and shape analysis. More specifically, I am working on applying deep learning to irregular domains (e.g., graphs, point clouds, and surfaces) and graph/shape matching problems. I completed my Ph.D. in 2019 at the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science under the supervision of Prof. Yaron Lipman.

Or Litany (Stanford University)
Gal Chechik (NVIDIA / Bar-Ilan University)
Ethan Fetaya (Bar-Ilan University)

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