Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Geometry of Adversarial Examples   Adversarial examples are a pervasive phenomenon of machine learning models
where seemingly imperceptible perturbations to the input lead to
misclassifications for otherwise statistically accurate models. We propose a
geometric framework, drawing on tools from the manifold reconstruction
literature, to analyze the high-dimensional geometry of adversarial examples.
In particular, we highlight the importance of codimension: for low-dimensional
data manifolds embedded in high-dimensional space there are many directions off
the manifold in which to construct adversarial examples. Adversarial examples
are a natural consequence of learning a decision boundary that classifies the
low-dimensional data manifold well, but classifies points near the manifold
incorrectly. Using our geometric framework we prove (1) a tradeoff between
robustness under different norms, (2) that adversarial training in balls around
the data is sample inefficient, and (3) sufficient sampling conditions under
which nearest neighbor classifiers and ball-based adversarial training are
robust.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin