Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification regions of deep neural networks   The goal of this paper is to analyze the geometric properties of deep neural
network classifiers in the input space. We specifically study the topology of
classification regions created by deep networks, as well as their associated
decision boundary. Through a systematic empirical investigation, we show that
state-of-the-art deep nets learn connected classification regions, and that the
decision boundary in the vicinity of datapoints is flat along most directions.
We further draw an essential connection between two seemingly unrelated
properties of deep networks: their sensitivity to additive perturbations in the
inputs, and the curvature of their decision boundary. The directions where the
decision boundary is curved in fact remarkably characterize the directions to
which the classifier is the most vulnerable. We finally leverage a fundamental
asymmetry in the curvature of the decision boundary of deep nets, and propose a
method to discriminate between original images, and images perturbed with small
adversarial examples. We show the effectiveness of this purely geometric
approach for detecting small adversarial perturbations in images, and for
recovering the labels of perturbed images.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th