mlsanityData to 7 Oct 2026

Riemann2: Learning Riemannian Submanifolds from Riemannian Data

arXiv 2503.05540 ↗First posted 7 Mar 2025cs.LG cs.ROcited by 5

Not on the map. Why?

Abstract (arXiv)

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches ignore the underlying geometric constraints or fail to provide meaningful metrics in the latent space. To address these limitations, we propose to learn Riemannian latent representations of such geometric data. To do so, we estimate the pullback metric induced by a Wrapped Gaussian Process Latent Variable Model, which explicitly accounts for the data geometry. This enables us to define geometry-aware notions of distance and shortest paths in the latent space, while ensuring that our model only assigns probability mass to the data manifold. This generalizes previous work and allows us to handle complex tasks in various domains, including robot motion synthesis and analysis of brain connectomes.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 23 of its 59 references that are in the map. First posted on arXiv 7 Mar 2025.

Builds on

23 of 59 references.

References · 23

  1. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  2. 2023Flow Matching on General Geometriescited by 260
  3. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 169
  4. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometrycited by 121
  5. 2022Riemannian Diffusion Modelscited by 120
  6. 2020Normalizing Flows on Tori and Spherescited by 117
  7. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 93
  8. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  9. 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
  10. 2014Metrics for Probabilistic Geometriescited by 28
  11. 2024NRDF: Neural Riemannian Distance Fields for Learning Articulated Pose Priorscited by 27
  12. 2021Learning Riemannian Manifolds for Geodesic Motion Skillscited by 23
11 more
  1. 2020What is a meaningful representation of protein sequences?cited by 22
  2. 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spacescited by 15
  3. 2019Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoderscited by 14
  4. 2021Learning Stable Vector Fields on Lie Groupscited by 12
  5. 2021Uncertainty Estimation Using Riemannian Model Dynamics for Offline Reinforcement Learningcited by 10
  6. 2021Orientation Probabilistic Movement Primitives on Riemannian Manifoldscited by 10
  7. 2024The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphscited by 10
  8. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 9
  9. 2018Active Learning based on Data Uncertainty and Model Sensitivitycited by 7
  10. 2018Probabilistic Riemannian submanifold learning with wrapped Gaussian process latent variable modelscited by 4
  11. 2020How Good are Low-Rank Approximations in Gaussian Process Regression?cited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 1.

5 papers.

  1. 2025Learning Geometry and Topology via Multi-Chart Flowscited by 3
  2. 2025A probabilistic view on Riemannian machine learning models for SPD matricescited by 0
  3. 2025Taxonomy-aware Dynamic Motion Generation on Hyperbolic Manifoldscited by 0
  4. 2025A Likely Geometry of Generative Modelscited by 0
  5. 2026Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methodscited by 0