GrAE ScaLE: Grassmannian AutoEncoder for Scalable Linearly-invariant Embeddings

Tegan Emerson, Tim Marrinan, Audun D Myers, Sarah McGuire Scullen
Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), PMLR 334(2):345-363, 2026.

Abstract

Supervised learning and generation on subspace-valued data remain difficult in practice, since existing techniques for embeddings of points on the Grassmann manifold can be costly and difficult to scale. In this work, we introduce the Grassmannian Autoencoder (GrAE), an autoencoder architecture designed for subspace-valued data, together with a variational extension, the Grassmannian Variational Autoencoder (GrVAE). These architectures produce informative, robust, low-dimensional latent representations with improved computational scalability. We demonstrate our approaches across three novel subspace datasets designed to help disambiguate failure modes and support benchmarking for future subspace-learning architectures. Our GrAE architectures{’} compact latent representations offer an efficient and expressive alternative for supervised learning on the Grassmann manifold and a practical step toward scalable subspace learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v334-emerson26b, title = {GrAE ScaLE: Grassmannian AutoEncoder for Scalable Linearly-invariant Embeddings}, author = {Emerson, Tegan and Marrinan, Tim and Myers, Audun D and Scullen, Sarah McGuire}, booktitle = {Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026)}, pages = {345--363}, year = {2026}, editor = {Berman, Eddie and Bernárdez, Guillermo and Chen, Samantha and Cloninger, Alex and Doster, Timothy and Emerson, Tegan and Grigsby, J. Elisenda and Kvinge, Henry and Lawrence, Hannah and Marrinan, Tim and Myers, Audun and Papillon, Mathilde and Tahmasebi, Behrooz and Telyatnikov, Lev and Walters, Robin and Weber, Melanie and Xie, YuQing and Yeats, Eric}, volume = {334}, number = {2}, series = {Proceedings of Machine Learning Research}, month = {18--20 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v334/main/assets/emerson26b/emerson26b.pdf}, url = {https://proceedings.mlr.press/v334/emerson26b.html}, abstract = {Supervised learning and generation on subspace-valued data remain difficult in practice, since existing techniques for embeddings of points on the Grassmann manifold can be costly and difficult to scale. In this work, we introduce the Grassmannian Autoencoder (GrAE), an autoencoder architecture designed for subspace-valued data, together with a variational extension, the Grassmannian Variational Autoencoder (GrVAE). These architectures produce informative, robust, low-dimensional latent representations with improved computational scalability. We demonstrate our approaches across three novel subspace datasets designed to help disambiguate failure modes and support benchmarking for future subspace-learning architectures. Our GrAE architectures{’} compact latent representations offer an efficient and expressive alternative for supervised learning on the Grassmann manifold and a practical step toward scalable subspace learning.} }
Endnote
%0 Conference Paper %T GrAE ScaLE: Grassmannian AutoEncoder for Scalable Linearly-invariant Embeddings %A Tegan Emerson %A Tim Marrinan %A Audun D Myers %A Sarah McGuire Scullen %B Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026) %C Proceedings of Machine Learning Research %D 2026 %E Eddie Berman %E Guillermo Bernárdez %E Samantha Chen %E Alex Cloninger %E Timothy Doster %E Tegan Emerson %E J. Elisenda Grigsby %E Henry Kvinge %E Hannah Lawrence %E Tim Marrinan %E Audun Myers %E Mathilde Papillon %E Behrooz Tahmasebi %E Lev Telyatnikov %E Robin Walters %E Melanie Weber %E YuQing Xie %E Eric Yeats %F pmlr-v334-emerson26b %I PMLR %P 345--363 %U https://proceedings.mlr.press/v334/emerson26b.html %V 334 %N 2 %X Supervised learning and generation on subspace-valued data remain difficult in practice, since existing techniques for embeddings of points on the Grassmann manifold can be costly and difficult to scale. In this work, we introduce the Grassmannian Autoencoder (GrAE), an autoencoder architecture designed for subspace-valued data, together with a variational extension, the Grassmannian Variational Autoencoder (GrVAE). These architectures produce informative, robust, low-dimensional latent representations with improved computational scalability. We demonstrate our approaches across three novel subspace datasets designed to help disambiguate failure modes and support benchmarking for future subspace-learning architectures. Our GrAE architectures{’} compact latent representations offer an efficient and expressive alternative for supervised learning on the Grassmann manifold and a practical step toward scalable subspace learning.
APA
Emerson, T., Marrinan, T., Myers, A.D. & Scullen, S.M.. (2026). GrAE ScaLE: Grassmannian AutoEncoder for Scalable Linearly-invariant Embeddings. Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), in Proceedings of Machine Learning Research 334(2):345-363 Available from https://proceedings.mlr.press/v334/emerson26b.html.

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