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Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

Machine Learning 2023-05-09 v2

Abstract

To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.

Keywords

Cite

@article{arxiv.2203.03934,
  title  = {Nonlinear Isometric Manifold Learning for Injective Normalizing Flows},
  author = {Eike Cramer and Felix Rauh and Alexander Mitsos and Raúl Tempone and Manuel Dahmen},
  journal= {arXiv preprint arXiv:2203.03934},
  year   = {2023}
}

Comments

11 pages, 7 figures, 4 tables

R2 v1 2026-06-24T10:05:41.594Z