Empirically Measuring Concentration: Fundamental Limits on Intrinsic Robustness
Saeed Mahloujifar, Xiao Zhang, Mohammad Mahmoody, David Evans
Abstract
Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018b), show that if the inputs are drawn from a concentrated metric probability space, then adversarial examples with small perturbation are inevitable. A concentrated space has the property that any subset with Ω(1) (e.g.,1/100) measure, according to the imposed distribution, has small distance to almost all (e.g., 99/100) of the points in the space. It is not clear, however, whether these theoretical results apply to actual distributions such as images. This paper presents a method for empirically measuring and bounding the concentration of a concrete dataset which is proven to converge to the actual concentration. We use it to empirically estimate the intrinsic robustness to and L
BibTeX
@inproceedings{NEURIPS2019_46f76a4b,
author = {Mahloujifar, Saeed and Zhang, Xiao and Mahmoody, Mohammad and Evans, David},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Empirically Measuring Concentration: Fundamental Limits on Intrinsic Robustness},
url = {https://proceedings.neurips.cc/paper_files/paper/2019/file/46f76a4bda9a9579eab38a8f6eabcda1-Paper.pdf},
volume = {32},
year = {2019}
}