Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating smooth functions by deep neural networks with sigmoid
  activation function   We study the power of deep neural networks (DNNs) with sigmoid activation
function. Recently, it was shown that DNNs approximate any $d$-dimensional,
smooth function on a compact set with a rate of order $W^{-p/d}$, where $W$ is
the number of nonzero weights in the network and $p$ is the smoothness of the
function. Unfortunately, these rates only hold for a special class of sparsely
connected DNNs. We ask ourselves if we can show the same approximation rate for
a simpler and more general class, i.e., DNNs which are only defined by its
width and depth. In this article we show that DNNs with fixed depth and a width
of order $M^d$ achieve an approximation rate of $M^{-2p}$. As a conclusion we
quantitatively characterize the approximation power of DNNs in terms of the
overall weights $W_0$ in the network and show an approximation rate of
$W_0^{-p/d}$. This more general result finally helps us to understand which
network topology guarantees a special target accuracy.

15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int