mlsanityData to 14 Oct 2026

Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation

arXiv 1603.03236 ↗First posted 10 Mar 2016cs.MS cs.LG math.OCcited by 94

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Abstract (arXiv)

Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable manifold. While many optimization problems are of the described form, technicalities of differential geometry and the laborious calculation of derivatives pose a significant barrier for experimenting with these methods. We introduce Pymanopt (available at https://pymanopt.github.io), a toolbox for optimization on manifolds, implemented in Python, that---similarly to the Manopt Matlab toolbox---implements several manifold geometries and optimization algorithms. Moreover, we lower the barriers to users further by using automated differentiation for calculating derivative information, saving users time and saving them from potential calculation and implementation errors.

Key facts. Cited by 94 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Mar 2016.

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Citing papers per year: 2021: 23; 2022: 11; 2023: 16; 2024: 20; 2025: 14; 2026: 10.

94 papers.

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  1. 2022SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEGcited by 53
  2. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  3. 2021On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometrycited by 32
  4. 2021Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronizationcited by 30
  5. 2024NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priorscited by 27
  6. 2023HaLP: Hallucinating Latent Positives for Skeleton-based Self-Supervised Learning of Actionscited by 25
  7. 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
  8. 2023A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifoldcited by 21
  9. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  10. 2024Symmetry Discovery Beyond Affine Transformationscited by 15
  11. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  12. 2024Guiding Neural Collapse: Optimising Towards the Nearest Simplex Equiangular Tight Framecited by 14
38 more
  1. 2022Federated Learning on Riemannian Manifoldscited by 13
  2. 2021Interactive Dimensionality Reduction for Comparative Analysiscited by 12
  3. 2022Riemannian Hamiltonian methods for min-max optimization on manifoldscited by 12
  4. 2023Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Spacecited by 11
  5. 2021Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometrycited by 10
  6. 2025SECA: Semantically Equivalent and Coherent Attacks for Eliciting LLM Hallucinationscited by 9
  7. 2021Manifold optimization for non-linear optimal transport problemscited by 8
  8. 2022Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patternscited by 8
  9. 2023Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policiescited by 8
  10. 2023Alignment of Density Maps in Wasserstein Distancecited by 8
  11. 2021Entangled Kernels -- Beyond Separabilitycited by 7
  12. 2022NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learningcited by 7
  13. 2023Medoid splits for efficient random forests in metric spacescited by 7
  14. 2021Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifoldscited by 6
  15. 2021Optimization on manifolds: A symplectic approachcited by 6
  16. 2025Riemann2: Learning Riemannian Submanifolds from Riemannian Datacited by 6
  17. 2025SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challengescited by 6
  18. 2025Geometric Neural Distance Fields for Learning Human Motion Priorscited by 6
  19. 2021Bayesian Quadrature on Riemannian Data Manifoldscited by 5
  20. 2021tensorflow-riemopt: A Library for Optimization on Riemannian Manifoldscited by 5
  21. 2021Simulation-based Bayesian inference for multi-fingered robotic graspingcited by 5
  22. 2021Topologically Regularized Data Embeddingscited by 5
  23. 2021NCVX: A User-Friendly and Scalable Package for Nonconvex Optimization in Machine Learningcited by 5
  24. 2024Fun with Flags: Robust Principal Directions via Flag Manifoldscited by 5
  25. 2024Meta-Learning with Generalized Ridge Regression: High-dimensional Asymptotics, Optimality and Hyper-covariance Estimationcited by 5
  26. 2024Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Datacited by 5
  27. 2024An Overview of the Burer-Monteiro Method for Certifiable Robot Perceptioncited by 5
  28. 2025Wrapped Gaussian on the manifold of Symmetric Positive Definite Matricescited by 5
  29. 2025Riemannian Optimization on Relaxed Indicator Matrix Manifoldcited by 5
  30. 2022Manifold Free Riemannian Optimizationcited by 4
  31. 2023Reinforcement Learning with Exogenous States and Rewardscited by 4
  32. 2023Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structurescited by 4
  33. 2024Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithmcited by 4
  34. 2023Gradient-Based Spectral Embeddings of Random Dot Product Graphscited by 3
  35. 2021A Riemannian Newton Trust-Region Method for Fitting Gaussian Mixture Modelscited by 2
  36. 2021Faster Randomized Methods for Orthogonality Constrained Problemscited by 2
  37. 2021Nonlinear matrix recovery using optimization on the Grassmann manifoldcited by 2
  38. 2024On the Role of Initialization on the Implicit Bias in Deep Linear Networkscited by 2

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