mlsanityData to 7 Oct 2026

Intrinsic and extrinsic deep learning on manifolds

arXiv 2302.08606 ↗First posted 16 Feb 2023stat.ML cs.LG stat.MEcited by 4

Not on the map. Why?

Abstract (arXiv)

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an equivariant embedding from the manifold to its image in the Euclidean space. Moreover, intrinsic deep neural networks (iDNNs) incorporate the underlying intrinsic geometry of manifolds via exponential and log maps with respect to a Riemannian structure. Consequently, we prove that the empirical risk of the empirical risk minimizers (ERM) of eDNNs and iDNNs converge in optimal rates. Overall, The eDNNs framework is simple and easy to compute, while the iDNNs framework is accurate and fast converging. To demonstrate the utilities of our framework, various simulation studies, and real data analyses are presented with eDNNs and iDNNs.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 17 of its 42 references that are in the map. First posted on arXiv 16 Feb 2023.

Builds on

17 of 42 references.

References · 17

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5 more
  1. 2020Nonconvex sparse regularization for deep neural networks and its optimalitycited by 21
  2. 2018Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learningcited by 19
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 2.

4 papers.

  1. 2024In the Search for Optimal Multi-view Learning Models for Crop Classification with Global Remote Sensing Datacited by 1
  2. 2024Deep Extrinsic Manifold Representation for Vision Taskscited by 0
  3. 2026Rate-optimal neural boundary detection from unlabeled noisy imagescited by 0
  4. 2026IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometrycited by 0