Group invariant machine learning by fundamental domain projections

Benjamin Aslan, Daniel Platt, David Sheard
Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 197:181-218, 2023.

Abstract

We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), finding an improvement in accuracy versus others in the literature.

Cite this Paper

BibTeX
@InProceedings{pmlr-v197-aslan23a, title = {Group invariant machine learning by fundamental domain projections}, author = {Aslan, Benjamin and Platt, Daniel and Sheard, David}, booktitle = {Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {181--218}, year = {2023}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Di Bernardo, Arianna and Miolane, Nina}, volume = {197}, series = {Proceedings of Machine Learning Research}, month = {03 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v197/aslan23a/aslan23a.pdf}, url = {https://proceedings.mlr.press/v197/aslan23a.html}, abstract = {We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), finding an improvement in accuracy versus others in the literature.} }
Endnote
%0 Conference Paper %T Group invariant machine learning by fundamental domain projections %A Benjamin Aslan %A Daniel Platt %A David Sheard %B Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2023 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Arianna Di Bernardo %E Nina Miolane %F pmlr-v197-aslan23a %I PMLR %P 181--218 %U https://proceedings.mlr.press/v197/aslan23a.html %V 197 %X We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), finding an improvement in accuracy versus others in the literature.
APA
Aslan, B., Platt, D. & Sheard, D.. (2023). Group invariant machine learning by fundamental domain projections. Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 197:181-218 Available from https://proceedings.mlr.press/v197/aslan23a.html.

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