Neural Discovery of Permutation Subgroups

Pavan Karjol, Rohan Kashyap, Prathosh AP
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 $S_n$. 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 $S_k (k \leq n)$ by learning an $S_n$-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 $S_n$. We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-karjol23a, title = {Neural Discovery of Permutation Subgroups}, author = {Karjol, Pavan and Kashyap, Rohan and {AP}, Prathosh}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {4668--4678}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/karjol23a/karjol23a.pdf}, url = {https://proceedings.mlr.press/v206/karjol23a.html}, abstract = {We consider the problem of discovering subgroup $H$ of permutation group $S_n$. 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 $S_k (k \leq n)$ by learning an $S_n$-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 $S_n$. We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks.} }
Endnote
%0 Conference Paper %T Neural Discovery of Permutation Subgroups %A Pavan Karjol %A Rohan Kashyap %A Prathosh AP %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-karjol23a %I PMLR %P 4668--4678 %U https://proceedings.mlr.press/v206/karjol23a.html %V 206 %X We consider the problem of discovering subgroup $H$ of permutation group $S_n$. 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 $S_k (k \leq n)$ by learning an $S_n$-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 $S_n$. We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks.
APA
Karjol, P., Kashyap, R. & AP, P.. (2023). Neural Discovery of Permutation Subgroups. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:4668-4678 Available from https://proceedings.mlr.press/v206/karjol23a.html.

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