Understanding the Intrinsic Robustness of Image Distributions using Conditional Generative Models
This work addresses a foundational open problem in adversarial machine learning by providing theoretical insights into robustness limits for image data, which is significant for researchers and practitioners in AI security, though it is incremental in building on prior theoretical frameworks.
The paper tackles the problem of understanding the intrinsic robustness limits of natural image distributions to adversarial perturbations, proving theoretical bounds using conditional generative models and showing a large gap between these limits and current state-of-the-art robust models on common image benchmarks under ℓ₂ perturbations.
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 $\ell_2$ 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.