A Unified Framework for Discovering Discrete Symmetries

Karjol, P and Kashyap, R and Gopalan, A and Prathosh, AP (2024) A Unified Framework for Discovering Discrete Symmetries. In: International Conference on Artificial Intelligence and Statistics, AISTATS 2024, 2 May 2024through 4 May 2024, Valencia, pp. 793-801.

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Abstract

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear, matrix-valued and non-linear functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the non-linear functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the matrix-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach. Copyright 2024 by the author(s).

Item Type:	Conference Paper
Publication:	Proceedings of Machine Learning Research
Publisher:	ML Research Press
Additional Information:	The copyright for this article belongs to ML Research Press.
Keywords:	Artificial intelligence; Matrix algebra, Discrete symmetry; Gradient-descent; Learn+; Linear matrix; Matrix-valued functions; Multiarmed bandits (MABs); Nonlinear functions; Novel architecture; Symmetrics; Unified framework, Gradient methods
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	13 Aug 2024 06:15
Last Modified:	13 Aug 2024 06:15
URI:	http://eprints.iisc.ac.in/id/eprint/85278

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