An Improved Uniform Convergence Bound with Fat-Shattering Dimension
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Abstract (arXiv)
The fat-shattering dimension characterizes the uniform convergence property of real-valued functions. The state-of-the-art upper bounds feature a multiplicative squared logarithmic factor on the sample complexity, leaving an open gap with the existing lower bound. We provide an improved uniform convergence bound that closes this gap.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 5 of its 23 references that are in the map. First posted on arXiv 13 Jul 2023.
Builds on
5 of 23 references.
References · 5
- 2018Approximation beats concentration? An approximation view on inference with smooth radial kernelscited by 33
- 2018Improved Generalization Bounds for Adversarially Robust Learningcited by 22
- 20152 Notes on Classes with Vapnik-Chervonenkis Dimension 1cited by 12
- 2023Prediction, Learning, Uniform Convergence, and Scale-sensitive Dimensionscited by 12
- 2022Metric Entropy Duality and the Sample Complexity of Outcome Indistinguishabilitycited by 7
Built on by
Citing papers per year: 2025: 2; 2026: 1.
3 papers.
- 2025Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Meanscited by 4
- 2025Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Datacited by 1
- 2026Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scalecited by 1
- 2026Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale13 May 2026
- 2025Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data31 Aug 2025
- 2025Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means17 Jun 2025