@article {2900,
	title = {Symmetry Regularization},
	number = {063},
	year = {2017},
	month = {05/2017},
	abstract = {<p>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.</p>
},
	author = {F. Anselmi and Georgios Evangelopoulos and Lorenzo Rosasco and Tomaso Poggio}
}
