Understanding Noise-Augmented Training for Randomized Smoothing

Published: 30 Apr 2023, Last Modified: 30 Jun 2023Accepted by TMLREveryoneRevisionsBibTeX
Authors that are also TMLR Expert Reviewers: ~Jeremias_Sulam1
Abstract: Randomized smoothing is a technique for providing provable robustness guarantees against adversarial attacks while making minimal assumptions about a classifier. This method relies on taking a majority vote of any base classifier over multiple noise-perturbed inputs to obtain a smoothed classifier, and it remains the tool of choice to certify deep and complex neural network models. Nonetheless, non-trivial performance of such smoothed classifier crucially depends on the base model being trained on noise-augmented data, i.e., on a smoothed input distribution. While widely adopted in practice, it is still unclear how this noisy training of the base classifier precisely affects the risk of the robust smoothed classifier, leading to heuristics and tricks that are poorly understood. In this work we analyze these trade-offs theoretically in a binary classification setting, proving that these common observations are not universal. We show that, without making stronger distributional assumptions, no benefit can be expected from predictors trained with noise-augmentation, and we further characterize distributions where such benefit is obtained. Our analysis has direct implications to the practical deployment of randomized smoothing, and we illustrate some of these via experiments on CIFAR-10 and MNIST, as well as on synthetic datasets.
Certifications: Expert Certification
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: N/A
Video: https://youtu.be/LzIoT5pX7pQ
Code: https://github.com/ambarpal/randomized-smoothing
Supplementary Material: pdf
Assigned Action Editor: ~Jinwoo_Shin1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 773