Mitigating the Curse of Dimensionality for Certified Robustness via Dual Randomized Smoothing

arXiv:2404.09586v1 Announce Type: cross
Abstract: Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of ${\ell_2}$ certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension $d$, proportionally decreasing at a rate of $1/\sqrt{d}$. This paper explores the feasibility of providing ${\ell_2}$ …

arxiv cs.cv cs.lg dimensionality robustness the curse of dimensionality type via