# Understanding the Intrinsic Robustness of Image Distributions using Conditional Generative Models

arXiv: https://arxiv.org/abs/2003.00378 · HTML: https://mlsanity.com/paper/2003.00378/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2020.

## Built on by (most cited first, 5 of 5)

- [Robustness in deep learning: The good (width), the bad (depth), and the ugly (initialization)](https://mlsanity.com/paper/2209.07263/) (2022)
- [Benign Overfitting in Adversarially Robust Linear Classification](https://mlsanity.com/paper/2112.15250/) (2021)
- [Improved Estimation of Concentration Under ℓp-Norm Distance Metrics Using Half Spaces](https://mlsanity.com/paper/2103.12913/) (2021)
- [Understanding Intrinsic Robustness Using Label Uncertainty](https://mlsanity.com/paper/2107.03250/) (2021)
- [Robustness bounds on the successful adversarial examples in probabilistic models: Implications from Gaussian processes](https://mlsanity.com/paper/2403.01896/) (2024)

## Abstract (arXiv)

Starting with Gilmer et al. (2018), several works have demonstrated the inevitability of adversarial examples based on different assumptions about the underlying input probability space. It remains unclear, however, whether these results apply to natural image distributions. In this work, we assume the underlying data distribution is captured by some conditional generative model, and prove intrinsic robustness bounds for a general class of classifiers, which solves an open problem in Fawzi et al. (2018). Building upon the state-of-the-art conditional generative models, we study the intrinsic robustness of two common image benchmarks under ℓ2 perturbations, and show the existence of a large gap between the robustness limits implied by our theory and the adversarial robustness achieved by current state-of-the-art robust models. Code for all our experiments is available at https://github.com/xiaozhanguva/Intrinsic-Rob.