Neural Discovery of Permutation Subgroups
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 23 of its 35 references that are in the map. First posted on arXiv 11 Sep 2023.
Builds on
23 of 35 references.
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11 more
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Citing papers per year: 2023: 1; 2024: 1.
2 papers.