title: Detecting Adversarial Examples Is (Nearly) As Hard As Classifying Them
abstract: Making classifiers robust to adversarial examples is challenging. 
  Thus, many defenses tackle the seemingly easier task of \emph{detecting} perturbed inputs.
  
  We show a barrier towards this goal. We prove a general \emph{hardness reduction} between detection and classification of adversarial examples: given a robust detector for attacks at distance $\epsilon$ (in some metric), we show how to build a similarly robust (but inefficient) \emph{classifier} for attacks at distance $\epsilon/2$---and vice-versa.
  
  Our reduction is computationally inefficient, and thus cannot be used to build practical classifiers. Instead, it is a useful sanity check to test whether empirical detection results imply something much stronger than the authors presumably anticipated.
  
  To illustrate, we revisit $14$ empirical detector defenses published over the past years. For $12/14$ defenses, we show that the claimed detection results imply an inefficient classifier with robustness far beyond the state-of-the-art--- thus casting some doubts on the results' validity.
  
  Finally, we show that our reduction applies in both directions: a robust classifier for attacks at distance $\epsilon/2$ implies an inefficient robust detector at distance $\epsilon$. Thus, we argue that robust classification and robust detection should be regarded as (near)-equivalent problems.
authors: Florian Tramer
hIndex: Florian Tramer 29