Neural Discovery of Permutation Subgroups
Pavan Karjol, Rohan Kashyap, Prathosh A P

TL;DR
This paper introduces a method to discover hidden permutation subgroups within the symmetric group by learning invariant functions and transformations, with theoretical guarantees and practical experiments demonstrating effectiveness.
Contribution
It presents a novel approach to identify permutation subgroups from data, extending previous invariant network methods to discover unknown subgroups like cyclic and dihedral groups.
Findings
Successfully discovers subgroups of type S_k, cyclic, and dihedral groups.
Theoretical proofs establish conditions under which subgroups can be identified.
Numerical experiments validate the method on image-digit sum and polynomial regression tasks.
Abstract
We consider the problem of discovering subgroup of permutation group . Unlike the traditional -invariant networks wherein 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 by learning an -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 . We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks.
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Taxonomy
TopicsAlzheimer's disease research and treatments
