Normalizing Flows on Tori and Spheres

Danilo Jimenez Rezende, George Papamakarios, Sebastien Racaniere, Michael Albergo, Gurtej Kanwar, Phiala Shanahan, Kyle Cranmer
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:8083-8092, 2020.

Abstract

Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-rezende20a, title = {Normalizing Flows on Tori and Spheres}, author = {Rezende, Danilo Jimenez and Papamakarios, George and Racaniere, Sebastien and Albergo, Michael and Kanwar, Gurtej and Shanahan, Phiala and Cranmer, Kyle}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {8083--8092}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/rezende20a/rezende20a.pdf}, url = {https://proceedings.mlr.press/v119/rezende20a.html}, abstract = {Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.} }
Endnote
%0 Conference Paper %T Normalizing Flows on Tori and Spheres %A Danilo Jimenez Rezende %A George Papamakarios %A Sebastien Racaniere %A Michael Albergo %A Gurtej Kanwar %A Phiala Shanahan %A Kyle Cranmer %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-rezende20a %I PMLR %P 8083--8092 %U https://proceedings.mlr.press/v119/rezende20a.html %V 119 %X Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.
APA
Rezende, D.J., Papamakarios, G., Racaniere, S., Albergo, M., Kanwar, G., Shanahan, P. & Cranmer, K.. (2020). Normalizing Flows on Tori and Spheres. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:8083-8092 Available from https://proceedings.mlr.press/v119/rezende20a.html.

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