mlsanityData to 14 Oct 2026

RMLR: Extending Multinomial Logistic Regression into General Geometries

arXiv 2409.19433 ↗First posted 28 Sep 2024cs.LG cs.AIcited by 8

Not on the map. Why?

Abstract (arXiv)

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean multinomial logistic regression (MLR) into Riemannian manifolds. However, existing approaches suffer from limited applicability due to their strong reliance on specific geometric properties. This paper proposes a framework for designing Riemannian MLR over general geometries, referred to as RMLR. Our framework only requires minimal geometric properties, thus exhibiting broad applicability and enabling its use with a wide range of geometries. Specifically, we showcase our framework on the Symmetric Positive Definite (SPD) manifold and special orthogonal group, i.e., the set of rotation matrices. On the SPD manifold, we develop five families of SPD MLRs under five types of power-deformed metrics. On rotation matrices we propose Lie MLR based on the popular bi-invariant metric. Extensive experiments on different Riemannian backbone networks validate the effectiveness of our framework.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 33 of its 76 references that are in the map. First posted on arXiv 28 Sep 2024.

Builds on

33 of 76 references.

References · 33

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  4. 2020Accelerating 3D Deep Learning with PyTorch3Dcited by 784
  5. 2016NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysiscited by 686
  6. 2018Hyperbolic Neural Networkscited by 402
  7. 2019Domain-Specific Batch Normalization for Unsupervised Domain Adaptationcited by 197
  8. 2018Riemannian Adaptive Optimization Methodscited by 194
  9. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  10. 2019Mixed-curvature Variational Autoencoderscited by 86
  11. 2018MOABB: Trustworthy algorithm benchmarking for BCIscited by 82
  12. 2019Riemannian batch normalization for SPD neural networkscited by 72
21 more
  1. 2016Building Deep Networks on Grassmann Manifoldscited by 58
  2. 2022SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEGcited by 53
  3. 2016Deep Learning on Lie Groups for Skeleton-based Action Recognitioncited by 42
  4. 2019Deep CNNs Meet Global Covariance Pooling: Better Representation and Generalizationcited by 42
  5. 2015Training Deep Networks with Structured Layers by Matrix Backpropagationcited by 30
  6. 2021GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognitioncited by 27
  7. 2021Why Approximate Matrix Square Root Outperforms Accurate SVD in Global Covariance Pooling?cited by 24
  8. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  9. 2022Riemannian Local Mechanism for SPD Neural Networkscited by 22
  10. 2023Riemannian Residual Neural Networkscited by 21
  11. 2018Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptationcited by 20
  12. 2018A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matricescited by 18
  13. 2023Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approachcited by 18
  14. 2023Adaptive Log-Euclidean Metrics for SPD Matrix Learningcited by 13
  15. 2024Matrix Manifold Neural Networks++cited by 13
  16. 2023Riemannian Multinomial Logistics Regression for SPD Neural Networkscited by 11
  17. 2022On the Eigenvalues of Global Covariance Pooling for Fine-grained Visual Recognitioncited by 10
  18. 2023Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matricescited by 10
  19. 2024Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometrycited by 9
  20. 2024A Lie Group Approach to Riemannian Batch Normalizationcited by 8
  21. 2024Fast and Stable Riemannian Metrics on SPD Manifolds via Cholesky Product Geometrycited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 6.

8 papers.

  1. 2025Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometrycited by 7
  2. 2026Hyperbolic Busemann Neural Networkscited by 5
  3. 2026Beyond Rigid Geometries: The Spline-Pullback Metric for Universal Diffeomorphic SPD Representation Learningcited by 1
  4. 2025Intrinsic-Metric Physics-Informed Neural Networks (IM-PINN) for Reaction-Diffusion Dynamics on Complex Riemannian Manifoldscited by 0
  5. 2026Riemannian Networks over Full-Rank Correlation Matricescited by 0
  6. 2026Riemannian Geometry for Pre-trained Language Model Embeddingscited by 0
  7. 2026LieBN: Batch Normalization over Lie Groupscited by 0
  8. 2026Nested Inductive Bias Framework for SPD Manifold Learningcited by 0