Riemannian Networks over Full-Rank Correlation Matrices

Ziheng Chen, Xiaojun Wu, Bernhard Schölkopf, Nicu Sebe
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:17467-17507, 2026.

Abstract

Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26fb, title = {{R}iemannian Networks over Full-Rank Correlation Matrices}, author = {Chen, Ziheng and Wu, Xiaojun and Sch\"{o}lkopf, Bernhard and Sebe, Nicu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {17467--17507}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26fb/chen26fb.pdf}, url = {https://proceedings.mlr.press/v306/chen26fb.html}, abstract = {Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.} }
Endnote
%0 Conference Paper %T Riemannian Networks over Full-Rank Correlation Matrices %A Ziheng Chen %A Xiaojun Wu %A Bernhard Schölkopf %A Nicu Sebe %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26fb %I PMLR %P 17467--17507 %U https://proceedings.mlr.press/v306/chen26fb.html %V 306 %X Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlation matrices, a normalized alternative to SPD matrices, remains largely underexplored. This paper introduces Riemannian networks over the correlation manifold, leveraging five recently developed correlation geometries. We systematically extend basic layers, including Multinomial Logistic Regression (MLR), Fully Connected (FC), and convolutional layers, to these geometries. Besides, we present methods for accurate backpropagation for two correlation geometries. Experiments comparing our approach against existing SPD and Grassmannian networks demonstrate its effectiveness.
APA
Chen, Z., Wu, X., Schölkopf, B. & Sebe, N.. (2026). Riemannian Networks over Full-Rank Correlation Matrices. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:17467-17507 Available from https://proceedings.mlr.press/v306/chen26fb.html.

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