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Riemannian Networks over Full-Rank Correlation Matrices

arXiv 2605.19073 ↗First posted 18 May 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 31 of its 55 references that are in the map. First posted on arXiv 18 May 2026.

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31 of 55 references.

References · 31

  1. 2019NTU RGB+D 120: A Large-Scale Benchmark for 3D Human Activity Understandingcited by 533
  2. 2018Hyperbolic Neural Networkscited by 402
  3. 2021Channel-wise Topology Refinement Graph Convolution for Skeleton-Based Action Recognitioncited by 322
  4. 2017First-Person Hand Action Benchmark with RGB-D Videos and 3D Hand Pose Annotationscited by 230
  5. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  6. 2021Fully Hyperbolic Neural Networkscited by 108
  7. 2019Mixed-curvature Variational Autoencoderscited by 86
  8. 2019Trivializations for Gradient-Based Optimization on Manifoldscited by 79
  9. 2019Riemannian batch normalization for SPD neural networkscited by 72
  10. 2016Building Deep Networks on Grassmann Manifoldscited by 58
  11. 2022SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEGcited by 53
  12. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 49
19 more
  1. 2022MAtt: A Manifold Attention Network for EEG Decodingcited by 44
  2. 2016Deep Learning on Lie Groups for Skeleton-based Action Recognitioncited by 42
  3. 2015Training Deep Networks with Structured Layers by Matrix Backpropagationcited by 30
  4. 2020Computationally Tractable Riemannian Manifolds for Graph Embeddingscited by 29
  5. 2022Riemannian Local Mechanism for SPD Neural Networkscited by 22
  6. 2023Riemannian Residual Neural Networkscited by 21
  7. 2023Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approachcited by 18
  8. 2024Matrix Manifold Neural Networks++cited by 13
  9. 2024SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEGcited by 12
  10. 2023Riemannian Multinomial Logistics Regression for SPD Neural Networkscited by 11
  11. 2020A New Parametrization of Correlation Matricescited by 9
  12. 2024Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometrycited by 9
  13. 2024A Lie Group Approach to Riemannian Batch Normalizationcited by 8
  14. 2024RMLR: Extending Multinomial Logistic Regression into General Geometriescited by 8
  15. 2025Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometrycited by 7
  16. 2024Fast and Stable Riemannian Metrics on SPD Manifolds via Cholesky Product Geometrycited by 4
  17. 2024SMLNet: A SPD Manifold Learning Network for Infrared and Visible Image Fusioncited by 4
  18. 2024Schur's Positive-Definite Network: Deep Learning in the SPD cone with structurecited by 3
  19. 2020A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matricescited by 2

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