mlsanityData to 14 Oct 2026

geomstats: a Python Package for Riemannian Geometry in Machine Learning

arXiv 1805.08308 ↗First posted 21 May 2018cs.LG cs.MS stat.MLcited by 71

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Abstract (arXiv)

We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively unit-tested implementations of these manifolds, together with useful Riemannian metrics and associated Exponential and Logarithm maps. The corresponding geodesic distances provide a range of intuitive choices of Machine Learning loss functions. We also give the corresponding Riemannian gradients. The operations implemented in geomstats are available with different computing backends such as numpy, tensorflow and keras. We have enabled GPU implementation and integrated geomstats manifold computations into keras deep learning framework. This paper also presents a review of manifolds in machine learning and an overview of the geomstats package with examples demonstrating its use for efficient and user-friendly Riemannian geometry.

Key facts. Cited by 71 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 May 2018.

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Citing papers per year: 2021: 10; 2022: 14; 2023: 15; 2024: 9; 2025: 13; 2026: 10.

71 papers.

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  1. 2022Riemannian Score-Based Generative Modellingcited by 219
  2. 2021Generalized Shape Metrics on Neural Representationscited by 112
  3. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  4. 2021Universal Approximation Under Constraints is Possible with Transformerscited by 32
  5. 2021GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognitioncited by 27
  6. 2023Geometric Autoencoders -- What You See is What You Decodecited by 23
  7. 2023A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifoldcited by 21
  8. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  9. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  10. 2024Symmetry Discovery Beyond Affine Transformationscited by 15
  11. 2022Small Transformers Compute Universal Metric Embeddingscited by 12
  12. 2025HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modulescited by 12
38 more
  1. 2023Geometric Neural Diffusion Processescited by 10
  2. 2025SECA: Semantically Equivalent and Coherent Attacks for Eliciting LLM Hallucinationscited by 9
  3. 2022Differentially Private Fr'echet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices with log-Euclidean Metriccited by 8
  4. 2021Closed-form geodesics and trust-region method to calculate Riemannian logarithms on Stiefel and its quotient manifoldscited by 7
  5. 2022NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learningcited by 7
  6. 2023Fast hyperboloid decision tree algorithmscited by 7
  7. 2023Learning Distributions on Manifolds with Free-Form Flowscited by 7
  8. 2023HypLL: The Hyperbolic Learning Librarycited by 6
  9. 2024Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantificationcited by 6
  10. 2025Riemann2: Learning Riemannian Submanifolds from Riemannian Datacited by 6
  11. 2025SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challengescited by 6
  12. 2021tensorflow-riemopt: A Library for Optimization on Riemannian Manifoldscited by 5
  13. 2021NCVX: A User-Friendly and Scalable Package for Nonconvex Optimization in Machine Learningcited by 5
  14. 2022Neural Networks as Paths through the Space of Representationscited by 5
  15. 2023Differential geometry with extreme eigenvalues in the positive semidefinite conecited by 5
  16. 2024BlackDAN: A Black-Box Multi-Objective Approach for Effective and Contextual Jailbreaking of Large Language Modelscited by 5
  17. 2024Stiefel Flow Matching for Moment-Constrained Structure Elucidationcited by 5
  18. 2026Riemannian MeanFlow for One-Step Generation on Manifoldscited by 5
  19. 2022Asymptotic Theory of Geometric and Adaptive k-Means Clusteringcited by 4
  20. 2022Universal Prototype Transport for Zero-Shot Action Recognition and Localizationcited by 4
  21. 2023Embedded Feature Similarity Optimization with Specific Parameter Initialization for 2D/3D Medical Image Registrationcited by 4
  22. 2023Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structurescited by 4
  23. 2025ShapeEmbed: a self-supervised learning framework for 2D contour quantificationcited by 4
  24. 2022Near out-of-distribution detection for low-resolution radar micro-Doppler signaturescited by 3
  25. 2022Parametric information geometry with the package Geomstatscited by 3
  26. 2025Learning Geometry and Topology via Multi-Chart Flowscited by 3
  27. 2025On the Wasserstein Geodesic Principal Component Analysis of probability measurescited by 3
  28. 2022Geometric Learning of Hidden Markov Models via a Method of Moments Algorithmcited by 2
  29. 2024Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical modelscited by 2
  30. 2024Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metricscited by 2
  31. 2025Towards Understanding the Shape of Representations in Protein Language Modelscited by 2
  32. 2025Geometric Moment Alignment for Domain Adaptation via Siegel Embeddingscited by 2
  33. 2026Parallelised Differentiable Straightest Geodesics for 3D Meshescited by 2
  34. 2021Riemannian Geometry with differentiable ambient space and metric operatorcited by 1
  35. 2021Riemannian Functional Map Synchronization for Probabilistic Partial Correspondence in Shape Networkscited by 1
  36. 2022Riemannian data-dependent randomized smoothing for neural networks certificationcited by 1
  37. 2022Rieoptax: Riemannian Optimization in JAXcited by 1
  38. 2022k-Means Clustering for Persistent Homologycited by 1

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