# A Chain Rule for the Expected Suprema of Bernoulli Processes

arXiv: https://arxiv.org/abs/2304.14474 · HTML: https://mlsanity.com/paper/2304.14474/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 8 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 3 of 3)

- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [A chain rule for the expected suprema of Gaussian processes](https://mlsanity.com/paper/1411.2635/) (2014)

## Built on by (most cited first, 1 of 1)

- [On Generalization Bounds for Neural Networks with Low Rank Layers](https://mlsanity.com/paper/2411.13733/) (2024)

## Abstract (arXiv)

We obtain an upper bound on the expected supremum of a Bernoulli process indexed by the image of an index set under a uniformly Lipschitz function class in terms of properties of the index set and the function class, extending an earlier result of Maurer for Gaussian processes. The proof makes essential use of recent results of Bednorz and Latala on the boundedness of Bernoulli processes.