🚀 This is an ongoing repo, containing resources on Riemannian deep learning.
- Awesome Deep Learning over Riemannian Spaces
- 1 Books
- 2 Papers
- Basic Topology Springer,1983.
- Topology Pearson, 2000.
- An Introduction to Manifolds Springer, 2011.
- Introduction to Smooth Manifolds Springer, 2012.
- Riemannian Geometry Birkhäuser, 1992.
- Introduction to Riemannian Manifolds Springer, 2018.
- Riemannian Geometry Springer, 2006.
- Naive Lie Theory Springer, 2008.
- Lie Groups, Lie Algebras, and Representations Springer, 2015.
- A mathematical introduction to robotic manipulation
- Rotation Averaging IJCV 2013
- Optimization Algorithms on Matrix Manifolds Cambridge University Press, 2023
- An introduction to Optimization on smooth manifolds Princeton University Press, 2008.
🌟 Note: For more on Riemannian optimization, please refer to Awesome-Riemannian-Optimization by Andi Han.
An overview can be found in https://www.manopt.org/manifolds.html
- Learning Riemannian Metrics for Interpolating Animations Openreview 2024
- Riemann2: Learning Riemannian Submanifolds from Riemannian Data AISTATS 2025
- Riemannian Metric Learning: Closer to You than You Imagine Arxiv 2025
- Fast and Simple Computations on Tensors with Log-Euclidean Metrics Reaserch Report 2005
- A Riemannian framework for tensor computing IJCV 2006
- Power Euclidean metrics for covariance matrices with application to diffusion tensor imaging Arxiv 2010
- Riemannian geometry of symmetric positive definite matrices via Cholesky decomposition SIMAX 2019
- On the Bures–Wasserstein distance between positive definite matrices Expositiones Mathematicae 2019
- The geometry of mixed-Euclidean metrics on symmetric positive definite matrices Differential Geometry and its Applications 2022
- O (n)-invariant Riemannian metrics on SPD matrices Linear Algebra and its Applications 2023
- Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry GSI 2023
- Adaptive Log-Euclidean Metrics for SPD Matrix Learning TIP 2024
- Product Geometries on Cholesky Manifolds with Applications to SPD Manifolds Arxiv 2024
- Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices Arxiv 2025
- A Riemannian covariance for manifold-valued data Arxiv 2025
- Learning to Normalize on the SPD Manifold under Bures-Wasserstein geometry CVPR 2025
- The Geometry of Algorithms with Orthogonality Constraints SIMAX 1998
- Schubert varieties and distances between subspaces of different dimensions SIMAX 2016
- A Grassmann Manifold Handbook: Basic Geometry and Computational Aspects Advances in Computational Mathematics 2024
- Left-Invariant Riemannian Geodesics on Spatial Transformation Groups SIIMS 2014
- Optimal Transport on the Lie Group of Roto-translations SIIMS 2024
- Weighted Frechet Means as Convex Combinations in Metric Spaces: Properties and Generalized Median Inequalities Statistics & Probability Letters 2012
- Geodesics, Parallel Transport & One-Parameter Subgroups for Diffeomorphic Image Registration IJCV 2012
- Mathematical Foundations of Geometric Deep Learning 2025
- A Riemannian Network for SPD Matrix Learning AAAI 2017
- Riemannian batch normalization for SPD neural networks NeurIPS 2019
- GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognition ICCV 2021
- Neural Architecture Search of SPD Manifold Networks IJCAI 2021
- Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices NeurIPS 2021
- Riemannian Local Mechanism for SPD Neural Networks AAAI 2023
- SPD Manifold Deep Metric Learning for Image Set Classification TNNLS 2024
- Riemannian Multinomial Logistics Regression for SPD Neural Networks CVPR 2024
- Exploring the Enigma of Neural Dynamics Through A Scattering-Transform Mixer Landscape for Riemannian Manifold ICML 2024
- Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure ICLR 2025
- Building Deep Networks on Grassmann Manifolds AAAI 2018
- A Grassmannian Manifold Self-Attention Network for Signal Classification IJCAI 2024
- Human Action Recognition by Representing 3D Skeletons as Points in a Lie Group CVPR 2014
- Rolling rotations for recognizing human actions from 3d skeletal data CVPR 2016
- Deep Learning on Lie Groups for Skeleton-based Action Recognition CVPR 2017
- Hyperplane margin classifiers on the multinomial manifold ICML 2004
- Hyperbolic entailment cones for learning hierarchical embeddings ICML 2018
- Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry ICML 2018
- Hyperbolic Neural Networks NeurIPS 2018
- Poincaré GloVe: Hyperbolic Word Embeddings ICLR 2019
- Hyperbolic Attention Networks ICLR 2019
- Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders NeurIPS 2019
- Mixed-curvature Variational Autoencoders ICLR 2020
- Hyperbolic Neural Networks++ ICLR 2021
- Differentiating through the Fréchet Mean ICML 2020
- Curvature Generation in Hyperbolic Spaces for Few-Shot Learning ICCV 2021
- Fully Hyperbolic Neural Networks ACL 2022
- Nested hyperbolic spaces for dimensionality reduction and hyperbolic nn design CVPR 2022
- Hyperbolic Feature Augmentation via Distribution Estimation and Infinite Sampling on Manifolds NeurIPS 2022
- Random Laplacian Features for Learning with Hyperbolic Space ICLR 2023
- Poincaré ResNet ICCV 2023
- Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space NeurIPS 2023
- Fully Hyperbolic Convolutional Neural Networks for Computer Vision ICLR 2024
- Hyperbolic Kernel Convolution: A Generic Framework LOG 2024
- Hyperbolic Deep Learning in Computer Vision: A Survey IJCV 2024
- Lorentzian Residual Neural Networks KDD 2025
- Cartan Networks: Group theoretical Hyperbolic Deep Learning 2025
- HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules 2025
- Computationally Tractable Riemannian Manifolds for Graph Embeddings AAAI 2021
- Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis TNNLS 2023
- Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices ECML 2023
- Hyperbolic Graph Convolutional Neural Networks NeurIPS 2019
- Hyperbolic Graph Neural Networks NeurIPS 2019
- Constant Curvature Graph Convolutional Networks ICML 2020
- A Hyperbolic-to-Hyperbolic Graph Convolutional Network CVPR 2021
- LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering ICML 2024
- Spiking Graph Neural Network on Riemannian Manifolds NeurIPS 2024
- A Mixed-Curvature Graph Diffusion Model CIKM 2024
- Pioneer: Physics-informed Riemannian Graph ODE for Entropy-increasing Dynamics AAAI 2025
- RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry WWW 2025
- Hyperbolic Deep Learning for Foundation Models: A Survey KDD 2025
-
Dilated Convolutional Neural Networks for Sequential Manifold-valued Data ICCV 2019
-
A General Theory of Equivariant CNNs on Homogeneous Spaces NeurIPS 2019
-
ManifoldNet: A Deep Neural Network for Manifold-Valued Data With Applications TPAMI 2020
-
ManifoldNorm: Extending normalizations on Riemannian Manifolds Arxiv 2020
-
A Gyrovector Space Approach for Symmetric Positive Semi-definite Matrix Learning ECCV 2022
-
The Gyro-Structure of Some Matrix Manifolds NeurIPS 2022
-
Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approach ICML 2023
-
Riemannian Residual Neural Networks NeurIPS 2023
-
Matrix Manifold Neural Networks++ ICLR 2024
-
A Lie Group Approach to Riemannian Batch Normalization ICLR 2024
-
RMLR: Extending Multinomial Logistic Regression into General Geometries NeurIPS 2024
-
Gyrogroup Batch Normalization ICLR 2025
-
Neural Networks on Symmetric Spaces of Noncompact Type ICLR 2025
-
GyroAtt: A Gyro Attention Framework for Matrix Manifolds Openreview 2025
- Riemannian score-based generative modelling NeurIPS 2022
- Riemannian Diffusion Models NeurIPS 2022
- SE (3) diffusion model with application to protein backbone generation ICML 2023
- Exploring Data Geometry for Continual Learning CVPR 2023
- Scaling Riemannian Diffusion Models NeurIPS 2023
- Flow Matching on General Geometries ICLR 2024
- Hyperbolic Geometric Latent Diffusion Model for Graph Generation ICML 2024
- Generative Modeling on Lie Groups via Euclidean Generalized Score Matching Arxiv 2025
- Hyperbolic Wasserstein Distance for Shape Indexing TPAMI 2019
- Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals ICML 2023
- Hyperbolic sliced-Wasserstein via geodesic and horospherical projections ICMLW 2023
- Spherical Sliced-Wasserstein ICLR 2023
- Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds JMLR 2025
- Spherical Manifold Guided Diffusion Model for Panoramic Image Generation CVPR 2025
- HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations ICLR 2023
- Hyperbolic learning with synthetic captions for open-world detection CVPR 2024
- Geometry-Aware Deep Learning for 3D Skeleton-Based Motion Prediction WACV 2025
- Hyperbolic Uncertainty-Aware Few-Shot Incremental Point Cloud Segmentation CVPR 2025
- Deep Change Monitoring: A Hyperbolic Representative Learning Framework and a Dataset for Long-term Fine-grained Tree Change Detection CVPR 2025
- Hyperbolic Category Discovery CVPR 2025
- Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning ICCV 2025
- Kernel Pooling for Convolutional Neural Networks CVPR 2017
- Towards Faster Training of Global Covariance Pooling Networks by Iterative Matrix Square Root Normalization CVPR 2018
- DeepKSPD: Learning Kernel-matrix-based SPD Representation for Fine-grained Image Recognition ECCV 2018
- Deep CNNs Meet Global Covariance Pooling: Better Representation and Generalization TPAMI 2020
- Orthogonal SVD Covariance Conditioning and Latent Disentanglement TPAMI 2022
- Fast Differentiable Matrix Square Root and Inverse Square Root TPAMI 2022
- On the Eigenvalues of Global Covariance Pooling for Fine-grained Visual Recognition TPAMI 2022
- Learning partial correlation based deep visual representation for image classification CVPR 2023
- Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry ICLR 2025
- Revitalizing SVD for Global Covariance Pooling: Halley’s Method to Overcome Over-Flattening NeurIPS 2025
- Riemannian High-Order Pooling for Brain Foundation Models ICLR 2026
- Compositional Entailment Learning for Hyperbolic Vision-Language Models ICLR 2025
- Hyperbolic Safety-Aware Vision-Language Models CVPR 2025
- Galaxy Walker: Geometry-aware VLMs For Galaxy-scale Understanding CVPR 2025
- HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Experts 2025
- HyperVLM: Hyperbolic Space Guided Vision Language Modeling for Hierarchical Multi-Modal Understanding CVPRW 2025
- Hyperbolic Deep Learning for Foundation Models: A Survey KDD 2025
- Understanding Fine-tuning CLIP for Open-vocabulary Semantic Segmentation in Hyperbolic Space CVPR 2025
- Hyperbolic Fine-tuning for Large Language Models 2025
- MAtt: A Manifold Attention Network for EEG Decoding NeurIPS 2022
- Deep Optimal Transport for Domain Adaptation on SPD Manifolds AI 2025
- SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG NeurIPS 2024
- Deep Geodesic Canonical Correlation Analysis for Covariance-Based Neuroimaging Data ICLR 2024
- Exploring the Enigma of Neural Dynamics Through A Scattering-Transform Mixer Landscape for Riemannian Manifold ICML 2024
- GeoMind: A Geometric Neural Network of State Space Model for Understanding Brain Dynamics on Riemannian Manifold Openreview 2025
- SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG ICLR 2025
- Hyperbolic Genome Embeddings ICLR 2025
- SPD Learning for Covariance-Based Neuroimaging Analysis: Perspectives, Methods, and Challenges 2025
- Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry 2025
- Riemannian High-Order Pooling for Brain Foundation Models ICLR 2026