mlsanityData to 7 Oct 2026

Learning Globally Smooth Functions on Manifolds

arXiv 2210.00301 ↗First posted 1 Oct 2022cs.LG cs.SY eess.SYcited by 4

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Abstract (arXiv)

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 42 of its 80 references that are in the map. First posted on arXiv 1 Oct 2022.

Builds on

42 of 80 references.

References · 42

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30 more
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Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 1.

4 papers.

  1. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  2. 2024Generalization of Geometric Graph Neural Networks with Lipschitz Loss Functionscited by 6
  3. 2022Convolutional Filtering on Sampled Manifoldscited by 4
  4. 2025Graph Semi-Supervised Learning for Point Classification on Data Manifoldscited by 0