Neural Discovery of Permutation Subgroups

Karjol, P and Kashyap, R and Prathosh, AP (2023) Neural Discovery of Permutation Subgroups. In: 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023, 25 - 27 April 2023, Valencia, pp. 4668-4678.

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Abstract

We consider the problem of discovering subgroup H of permutation group Sn. Unlike the traditional H-invariant networks wherein H is assumed to be known, we present a method to discover the underlying subgroup, given that it satisfies certain conditions. Our results show that one could discover any subgroup of type Sk(k ≤ n) by learning an Sn-invariant function and a linear transformation. We also prove similar results for cyclic and dihedral subgroups. Finally, we provide a general theorem that can be extended to discover other subgroups of Sn. We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks. Copyright

Item Type:	Conference Paper
Publication:	Proceedings of Machine Learning Research
Publisher:	ML Research Press
Additional Information:	The copyright for this article belongs to the ML Research Press.
Keywords:	Machine learning, Condition; Invariant functions; Numerical experiments; Permutation group; Polynomial regression; Symmetric polynomial, Linear transformations
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	01 Aug 2023 05:07
Last Modified:	01 Aug 2023 05:07
URI:	https://eprints.iisc.ac.in/id/eprint/82746

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