# Lipschitz Networks and Distributional Robustness

arXiv: https://arxiv.org/abs/1809.01129 · HTML: https://mlsanity.com/paper/1809.01129/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2018.

## Built on by (most cited first, 6 of 6)

- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Spectral Bias in Practice: The Role of Function Frequency in Generalization](https://mlsanity.com/paper/2110.02424/) (2021)
- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Miti-DETR: Object Detection based on Transformers with Mitigatory Self-Attention Convergence](https://mlsanity.com/paper/2112.13310/) (2021)
- [What training reveals about neural network complexity](https://mlsanity.com/paper/2106.04186/) (2021)
- [Sinkhorn doubly stochastic attention rank decay analysis](https://mlsanity.com/paper/2604.07925/) (2026)

## Abstract (arXiv)

Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class rich enough to include deep neural networks by a regularised empirical risk involving the Lipschitz constant of the model. This allows us to interpretand quantify the robustness properties of a deep neural network. As an application we show the distributionally robust risk upperbounds the adversarial training risk.