Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Provable approximation properties for deep neural networks   We discuss approximation of functions using deep neural nets. Given a
function $f$ on a $d$-dimensional manifold $\Gamma \subset \mathbb{R}^m$, we
construct a sparsely-connected depth-4 neural network and bound its error in
approximating $f$. The size of the network depends on dimension and curvature
of the manifold $\Gamma$, the complexity of $f$, in terms of its wavelet
description, and only weakly on the ambient dimension $m$. Essentially, our
network computes wavelet functions, which are computed from Rectified Linear
Units (ReLU)

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph