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Starting with Gilmer et al. (2018), several works have demonstrated theinevitability of adversarial examples based on different assumptions about theunderlying input probability space. It remains unclear, however, whether theseresults apply to natural image distributions. In this work, we assume theunderlying data distribution is captured by some conditional generative model,and prove intrinsic robustness bounds for a general class of classifiers, whichsolves an open problem in Fawzi et al. (2018). Building upon thestate-of-the-art conditional generative models, we study the intrinsicrobustness of two common image benchmarks under $\ell_2$ perturbations, andshow the existence of a large gap between the robustness limits implied by ourtheory and the adversarial robustness achieved by current state-of-the-artrobust models. Code for all our experiments is available athttps://github.com/xiaozhanguva/Intrinsic-Rob.

Understanding the Intrinsic Robustness of Image Distributions using Conditional Generative Models