Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classifier-independent Lower-Bounds for Adversarial Robustness   We theoretically analyse the limits of robustness to test-time adversarial
and noisy examples in classification. Our work focuses on deriving bounds which
uniformly apply to all classifiers (i.e all measurable functions from features
to labels) for a given problem. Our contributions are two-fold. (1) We use
optimal transport theory to derive variational formulae for the Bayes-optimal
error a classifier can make on a given classification problem, subject to
adversarial attacks. The optimal adversarial attack is then an optimal
transport plan for a certain binary cost-function induced by the specific
attack model, and can be computed via a simple algorithm based on maximal
matching on bipartite graphs. (2) We derive explicit lower-bounds on the
Bayes-optimal error in the case of the popular distance-based attacks. These
bounds are universal in the sense that they depend on the geometry of the
class-conditional distributions of the data, but not on a particular
classifier. Our results are in sharp contrast with the existing literature,
wherein adversarial vulnerability of classifiers is derived as a consequence of
nonzero ordinary test error.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys