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Neural Discovery of Permutation Subgroups
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:4668-4678, 2023.
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.