Learning Lie Group Symmetry Transformations with Neural Networks

Alex Gabel, Victoria Klein, Riccardo Valperga, Jeroen S. W. Lamb, Kevin Webster, Rick Quax, Efstratios Gavves
Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), PMLR 221:50-59, 2023.

Abstract

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks require prior knowledge of the symmetries of the task at hand, this work focuses on discovering and characterising unknown symmetries present in the dataset, namely, Lie group symmetry transformations beyond the traditional ones usually considered in the field (rotation, scaling, and translation). Specifically, we consider a scenario in which a dataset has been transformed by a one-parameter subgroup of transformations with different parameter values for each data point. Our goal is to characterise the transformation group and the distribution of the parameter values, even when they aren’t small or the transformation group isn’t one of the traditional ones. The results showcase the effectiveness of the approach in both these settings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v221-gabel23a, title = {Learning Lie Group Symmetry Transformations with Neural Networks}, author = {Gabel, Alex and Klein, Victoria and Valperga, Riccardo and Lamb, Jeroen S. W. and Webster, Kevin and Quax, Rick and Gavves, Efstratios}, booktitle = {Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML)}, pages = {50--59}, year = {2023}, editor = {Doster, Timothy and Emerson, Tegan and Kvinge, Henry and Miolane, Nina and Papillon, Mathilde and Rieck, Bastian and Sanborn, Sophia}, volume = {221}, series = {Proceedings of Machine Learning Research}, month = {28 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v221/gabel23a/gabel23a.pdf}, url = {https://proceedings.mlr.press/v221/gabel23a.html}, abstract = {The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks require prior knowledge of the symmetries of the task at hand, this work focuses on discovering and characterising unknown symmetries present in the dataset, namely, Lie group symmetry transformations beyond the traditional ones usually considered in the field (rotation, scaling, and translation). Specifically, we consider a scenario in which a dataset has been transformed by a one-parameter subgroup of transformations with different parameter values for each data point. Our goal is to characterise the transformation group and the distribution of the parameter values, even when they aren’t small or the transformation group isn’t one of the traditional ones. The results showcase the effectiveness of the approach in both these settings.} }
Endnote
%0 Conference Paper %T Learning Lie Group Symmetry Transformations with Neural Networks %A Alex Gabel %A Victoria Klein %A Riccardo Valperga %A Jeroen S. W. Lamb %A Kevin Webster %A Rick Quax %A Efstratios Gavves %B Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) %C Proceedings of Machine Learning Research %D 2023 %E Timothy Doster %E Tegan Emerson %E Henry Kvinge %E Nina Miolane %E Mathilde Papillon %E Bastian Rieck %E Sophia Sanborn %F pmlr-v221-gabel23a %I PMLR %P 50--59 %U https://proceedings.mlr.press/v221/gabel23a.html %V 221 %X The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks require prior knowledge of the symmetries of the task at hand, this work focuses on discovering and characterising unknown symmetries present in the dataset, namely, Lie group symmetry transformations beyond the traditional ones usually considered in the field (rotation, scaling, and translation). Specifically, we consider a scenario in which a dataset has been transformed by a one-parameter subgroup of transformations with different parameter values for each data point. Our goal is to characterise the transformation group and the distribution of the parameter values, even when they aren’t small or the transformation group isn’t one of the traditional ones. The results showcase the effectiveness of the approach in both these settings.
APA
Gabel, A., Klein, V., Valperga, R., Lamb, J.S.W., Webster, K., Quax, R. & Gavves, E.. (2023). Learning Lie Group Symmetry Transformations with Neural Networks. Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), in Proceedings of Machine Learning Research 221:50-59 Available from https://proceedings.mlr.press/v221/gabel23a.html.

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