# A Spectral View of Adversarially Robust Features

arXiv: https://arxiv.org/abs/1811.06609 · HTML: https://mlsanity.com/paper/1811.06609/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2018.

## Built on by (most cited first, 4 of 4)

- [Can we achieve robustness from data alone?](https://mlsanity.com/paper/2207.11727/) (2022)
- [It Is All About Data: A Survey on the Effects of Data on Adversarial Robustness](https://mlsanity.com/paper/2303.09767/) (2023)
- [Wavelets Beat Monkeys at Adversarial Robustness](https://mlsanity.com/paper/2304.09403/) (2023)
- [Contrastive Spectral Rectification: Test-Time Defense towards Zero-shot Adversarial Robustness of CLIP](https://mlsanity.com/paper/2601.19210/) (2026)

## Abstract (arXiv)

Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features. Specifically, given a dataset and metric of interest, the goal is to return a function (or multiple functions) that 1) is robust to adversarial perturbations, and 2) has significant variation across the datapoints. We establish strong connections between adversarially robust features and a natural spectral property of the geometry of the dataset and metric of interest. This connection can be leveraged to provide both robust features, and a lower bound on the robustness of any function that has significant variance across the dataset. Finally, we provide empirical evidence that the adversarially robust features given by this spectral approach can be fruitfully leveraged to learn a robust (and accurate) model.