mlsanityData to 14 Oct 2026

A Deep Generative Approach to Stratified Learning

arXiv 2604.10650 ↗First posted 12 Apr 2026stat.ML cs.LGcited by 2

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Abstract (arXiv)

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying dimensionality, intersection singularities, and lack of efficient models in learning the underlying distributions. We provide a deep generative approach to stratified learning by developing two generative frameworks for learning distributions on stratified spaces. The first is a sieve maximum likelihood approach realized via a dimension-aware mixture of variational autoencoders. The second is a diffusion-based framework that explores the score field structure of a mixture. We establish the convergence rates for learning both the ambient and intrinsic distributions, which are shown to be dependent on the intrinsic dimensions and smoothness of the underlying strata. Utilizing the geometry of the score field, we also establish consistency for estimating the intrinsic dimension of each stratum and propose an algorithm that consistently estimates both the number of strata and their dimensions. Theoretical results for both frameworks provide fundamental insights into the interplay of the underlying geometry, the ambient noise level, and deep generative models. Extensive simulations and real dataset applications, such as molecular dynamics, demonstrate the effectiveness of our methods.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 17 of its 56 references that are in the map. First posted on arXiv 12 Apr 2026.

Builds on

17 of 56 references.

References · 17

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2018Understanding disentangling in β-VAEcited by 335
  4. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 315
  5. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 242
  6. 2019Deep ReLU network approximation of functions on a manifoldcited by 74
  7. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensionscited by 65
  8. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 64
  9. 2024ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routingcited by 54
  10. 2024Linear Convergence of Diffusion Models Under the Manifold Hypothesiscited by 45
  11. 2024On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion modelscited by 23
  12. 2025Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularitycited by 17
5 more
  1. 2025Token embeddings violate the manifold hypothesiscited by 16
  2. 2025Unraveling the Localized Latents: Learning Stratified Manifold Structures in LLM Embedding Space with Sparse Mixture-of-Expertscited by 10
  3. 2025On Convolutions, Intrinsic Dimension, and Diffusion Modelscited by 3
  4. 2023Estimating Distributions with Low-dimensional Structures Using Mixtures of Generative Modelscited by 1
  5. 2025Learning collective variables that preserve transition ratescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimensioncited by 0
  2. 2026Nonparametric In-Context Learning under Growing Geometric Complexity: Minimax Optimality and Local Geometry-Adaptivity of Transformerscited by 0