Riemannian Networks over Full-Rank Correlation Matrices
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Computer Science > Machine Learning
Title:Riemannian Networks over Full-Rank Correlation Matrices
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.
| Comments: | Accepted to ICML 2026 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.19073 [cs.LG] |
| (or arXiv:2605.19073v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.19073
arXiv-issued DOI via DataCite (pending registration)
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