mlsanityData to 14 Oct 2026

Learning Geometry and Topology via Multi-Chart Flows

arXiv 2505.24665 ↗First posted 30 May 2025cs.LGcited by 3

Not on the map. Why?

Abstract (arXiv)

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if the manifold has a non-trivial topology, it can never be correctly learned using a single flow. Instead multiple flows must be `glued together'. In this paper, we first propose the general training scheme for learning such a collection of flows, and secondly we develop the first numerical algorithms for computing geodesics on such manifolds. Empirically, we demonstrate that this leads to highly significant improvements in topology estimation.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 37 of its 71 references that are in the map. First posted on arXiv 30 May 2025.

Builds on

37 of 71 references.

References · 37

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2016Density estimation using Real NVPcited by 2,042
  3. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  4. 2015Automatic differentiation in machine learning: a surveycited by 855
  5. 2019Neural Spline Flowscited by 596
  6. 2018Pyro: Deep Universal Probabilistic Programmingcited by 380
  7. 2023Flow Matching on General Geometriescited by 265
  8. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 174
  9. 2019Topological Autoencoderscited by 127
  10. 2020Flows for simultaneous manifold learning and density estimationcited by 118
  11. 2020Normalizing Flows on Tori and Spherescited by 117
  12. 2019Semi-Supervised Learning with Normalizing Flowscited by 76
25 more
  1. 2019NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transportcited by 74
  2. 2018geomstats: a Python Package for Riemannian Geometry in Machine Learningcited by 71
  3. 2023normflows: A PyTorch Package for Normalizing Flowscited by 56
  4. 2021Rectangular Flows for Manifold Learningcited by 50
  5. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  6. 2021Resampling Base Distributions of Normalizing Flowscited by 42
  7. 2019Chart Auto-Encoders for Manifold Structured Datacited by 33
  8. 2022Diagnosing and Fixing Manifold Overfitting in Deep Generative Modelscited by 28
  9. 2023Free-form Flows: Make Any Architecture a Normalizing Flowcited by 26
  10. 2023Lifting Architectural Constraints of Injective Flowscited by 18
  11. 2018Accelerating Natural Gradient with Higher-Order Invariancecited by 17
  12. 2018Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)cited by 17
  13. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 17
  14. 2019Semi-Conditional Normalizing Flows for Semi-Supervised Learningcited by 15
  15. 2018Geodesic Clustering in Deep Generative Modelscited by 14
  16. 2021Density estimation on smooth manifolds with normalizing flowscited by 11
  17. 2022VQ-Flows: Vector Quantized Local Normalizing Flowscited by 10
  18. 2020Intrinsic persistent homology via density-based metric learningcited by 9
  19. 2024Pulling back symmetric Riemannian geometry for data analysiscited by 8
  20. 2024Pullback Flow Matching on Data Manifoldscited by 8
  21. 2025Riemann2: Learning Riemannian Submanifolds from Riemannian Datacited by 6
  22. 2022Neural Implicit Manifold Learning for Topology-Aware Density Estimationcited by 5
  23. 2022Quantifying Extrinsic Curvature in Neural Manifoldscited by 5
  24. 2021Spread Flows for Manifold Modellingcited by 4
  25. 2023Mixture Modeling with Normalizing Flows for Spherical Density Estimationcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Learning the Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou Trajectories: A Nonlinear Approach using a Deep Autoencoder Modelcited by 0
  2. 2026Reparameterization through Coverings and Topological Weight Priorscited by 0
  3. 2026Beyond Unimodal Bases: Pullback Geometry for Multimodal Datacited by 0