[2505.08087] Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry

Computer Science > Machine Learning arXiv:2505.08087 (cs) [Submitted on 12 May 2025 (v1), last revised 26 Feb 2026 (this version, v3)] Title:Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry Authors:Willem Diepeveen, Deanna Needell View a PDF of the paper titled Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry, by Willem Diepeveen and 1 other authors View PDF HTML (experimental) Abstract:Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data through learning Riemannian geometry algorithms can achieve improved performance and interpretability in tasks like clustering, dimensionality reduction, and interpolation. In particular, learned pullback geometry has recently undergone transformative developments that now make it scalable to learn and scalable to evaluate, which further opens the door for principled non-linear data analysis and interpretable machine learning. However, there are still steps to be taken when considering real-world multi-modal data. This work focuses on addressing distortions and modeling errors that can arise in the multi-modal setting and proposes to alleviate both challenges through isometrizing the learned Riemannian structure and balancing regularity and expressivit...