Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adversarial Robustness Against the Union of Multiple Perturbation Models   Owing to the susceptibility of deep learning systems to adversarial attacks,
there has been a great deal of work in developing (both empirically and
certifiably) robust classifiers. While most work has defended against a single
type of attack, recent work has looked at defending against multiple
perturbation models using simple aggregations of multiple attacks. However,
these methods can be difficult to tune, and can easily result in imbalanced
degrees of robustness to individual perturbation models, resulting in a
sub-optimal worst-case loss over the union. In this work, we develop a natural
generalization of the standard PGD-based procedure to incorporate multiple
perturbation models into a single attack, by taking the worst-case over all
steepest descent directions. This approach has the advantage of directly
converging upon a trade-off between different perturbation models which
minimizes the worst-case performance over the union. With this approach, we are
able to train standard architectures which are simultaneously robust against
$\ell_\infty$, $\ell_2$, and $\ell_1$ attacks, outperforming past approaches on
the MNIST and CIFAR10 datasets and achieving adversarial accuracy of 47.0%
against the union of ($\ell_\infty$, $\ell_2$, $\ell_1$) perturbations with
radius = (0.03, 0.5, 12) on the latter, improving upon previous approaches
which achieve 40.6% accuracy.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph