A Unified Framework for Discovering Discrete Symmetries

Pavan Karjol, Rohan Kashyap, Aditya Gopalan, A. P. Prathosh
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:793-801, 2024.

Abstract

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear, matrix-valued and non-linear functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the non-linear functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the matrix-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-karjol24a, title = {A Unified Framework for Discovering Discrete Symmetries}, author = {Karjol, Pavan and Kashyap, Rohan and Gopalan, Aditya and Prathosh, A. P.}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {793--801}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/karjol24a/karjol24a.pdf}, url = {https://proceedings.mlr.press/v238/karjol24a.html}, abstract = {We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear, matrix-valued and non-linear functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the non-linear functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the matrix-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.} }
Endnote
%0 Conference Paper %T A Unified Framework for Discovering Discrete Symmetries %A Pavan Karjol %A Rohan Kashyap %A Aditya Gopalan %A A. P. Prathosh %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-karjol24a %I PMLR %P 793--801 %U https://proceedings.mlr.press/v238/karjol24a.html %V 238 %X We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear, matrix-valued and non-linear functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the non-linear functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the matrix-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.
APA
Karjol, P., Kashyap, R., Gopalan, A. & Prathosh, A.P.. (2024). A Unified Framework for Discovering Discrete Symmetries. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:793-801 Available from https://proceedings.mlr.press/v238/karjol24a.html.

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