On the Latent Information Geometry of the Grassmann Manifold

Lorenzo Cazzella, Søren Hauberg, Georgios Arvanitidis, Matteo Matteucci
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1306-1314, 2026.

Abstract

Modeling linear subspaces and relations among them naturally arises in several applications in signal processing, computer vision, and system identification. In this paper, we investigate the latent information geometry of deep generative models that output linear subspaces. Such subspaces are members of the Grassmann manifold, which we model with a matrix Bingham distribution as a likelihood. We derive the Fisher-Rao metric on the statistical manifold of the matrix Bingham parameters, and propose pulling this back to the latent space to achieve uncertainty-aware and identifiable latent representations. We provide numerical results assessing the meaningfulness of the achieved latent subspace representations on a relevant vehicular wireless communications scenario.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-cazzella26a, title = { On the Latent Information Geometry of the Grassmann Manifold }, author = {Cazzella, Lorenzo and Hauberg, S{\o}ren and Arvanitidis, Georgios and Matteucci, Matteo}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1306--1314}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/cazzella26a/cazzella26a.pdf}, url = {https://proceedings.mlr.press/v300/cazzella26a.html}, abstract = { Modeling linear subspaces and relations among them naturally arises in several applications in signal processing, computer vision, and system identification. In this paper, we investigate the latent information geometry of deep generative models that output linear subspaces. Such subspaces are members of the Grassmann manifold, which we model with a matrix Bingham distribution as a likelihood. We derive the Fisher-Rao metric on the statistical manifold of the matrix Bingham parameters, and propose pulling this back to the latent space to achieve uncertainty-aware and identifiable latent representations. We provide numerical results assessing the meaningfulness of the achieved latent subspace representations on a relevant vehicular wireless communications scenario. } }
Endnote
%0 Conference Paper %T On the Latent Information Geometry of the Grassmann Manifold %A Lorenzo Cazzella %A Søren Hauberg %A Georgios Arvanitidis %A Matteo Matteucci %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-cazzella26a %I PMLR %P 1306--1314 %U https://proceedings.mlr.press/v300/cazzella26a.html %V 300 %X Modeling linear subspaces and relations among them naturally arises in several applications in signal processing, computer vision, and system identification. In this paper, we investigate the latent information geometry of deep generative models that output linear subspaces. Such subspaces are members of the Grassmann manifold, which we model with a matrix Bingham distribution as a likelihood. We derive the Fisher-Rao metric on the statistical manifold of the matrix Bingham parameters, and propose pulling this back to the latent space to achieve uncertainty-aware and identifiable latent representations. We provide numerical results assessing the meaningfulness of the achieved latent subspace representations on a relevant vehicular wireless communications scenario.
APA
Cazzella, L., Hauberg, S., Arvanitidis, G. & Matteucci, M.. (2026). On the Latent Information Geometry of the Grassmann Manifold . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1306-1314 Available from https://proceedings.mlr.press/v300/cazzella26a.html.

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