Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High Dimensional Spaces, Deep Learning and Adversarial Examples   In this paper, we analyze deep learning from a mathematical point of view and
derive several novel results. The results are based on intriguing mathematical
properties of high dimensional spaces. We first look at perturbation based
adversarial examples and show how they can be understood using topological and
geometrical arguments in high dimensions. We point out mistake in an argument
presented in prior published literature, and we present a more rigorous,
general and correct mathematical result to explain adversarial examples in
terms of topology of image manifolds. Second, we look at optimization
landscapes of deep neural networks and examine the number of saddle points
relative to that of local minima. Third, we show how multiresolution nature of
images explains perturbation based adversarial examples in form of a stronger
result. Our results state that expectation of $L_2$-norm of adversarial
perturbations is $O\left(\frac{1}{\sqrt{n}}\right)$ and therefore shrinks to 0
as image resolution $n$ becomes arbitrarily large. Finally, by incorporating
the parts-whole manifold learning hypothesis for natural images, we investigate
the working of deep neural networks and root causes of adversarial examples and
discuss how future improvements can be made and how adversarial examples can be
eliminated.

24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess