Symmetry Regularization
Name
CBMM-Memo-063.pdf
Size
6.1 MB
Format
Adobe PDF
Checksum (MD5)
464577b5b98f105768dbb5401e6d4810
Author(s)
Anselmi, Fabio
Evangelopoulos, Georgios
Rosasco, Lorenzo
Poggio, Tomaso
Date Issued
May 26, 2017
Publisher
Center for Brains, Minds and Machines (CBMM)
Series/Report no.
CBMM Memo Series;063
Abstract
The properties of a representation, such as smoothness, adaptability, generality, equivari- ance/invariance, depend on restrictions imposed during learning. In this paper, we propose using data symmetries, in the sense of equivalences under transformations, as a means for learning symmetry- adapted representations, i.e., representations that are equivariant to transformations in the original space. We provide a sufficient condition to enforce the representation, for example the weights of a neural network layer or the atoms of a dictionary, to have a group structure and specifically the group structure in an unlabeled training set. By reducing the analysis of generic group symmetries to per- mutation symmetries, we devise an analytic expression for a regularization scheme and a permutation invariant metric on the representation space. Our work provides a proof of concept on why and how to learn equivariant representations, without explicit knowledge of the underlying symmetries in the data.
Subjects
invariance
learning symmetry
regularization
Terms of Use
Attribution-NonCommercial-ShareAlike 3.0 United States
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