# An Improved Uniform Convergence Bound with Fat-Shattering Dimension

arXiv: https://arxiv.org/abs/2307.06644 · HTML: https://mlsanity.com/paper/2307.06644/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [Approximation beats concentration? An approximation view on inference with smooth radial kernels](https://mlsanity.com/paper/1801.03437/) (2018)
- [Improved Generalization Bounds for Adversarially Robust Learning](https://mlsanity.com/paper/1810.02180/) (2018)
- [2 Notes on Classes with Vapnik-Chervonenkis Dimension 1](https://mlsanity.com/paper/1507.05307/) (2015)
- [Prediction, Learning, Uniform Convergence, and Scale-sensitive Dimensions](https://mlsanity.com/paper/2304.11059/) (2023)
- [Metric Entropy Duality and the Sample Complexity of Outcome Indistinguishability](https://mlsanity.com/paper/2203.04536/) (2022)

## Built on by (most cited first, 3 of 3)

- [Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means](https://mlsanity.com/paper/2506.14673/) (2025)
- [Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data](https://mlsanity.com/paper/2509.00924/) (2025)
- [Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale](https://mlsanity.com/paper/2605.13684/) (2026)

## 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.