Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Approximation with Sparse Neural Networks and Applications   We use deep sparsely connected neural networks to measure the complexity of a
function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory
requirement for storing the neural networks. We also introduce representation
system - a countable collection of functions to guide neural networks, since
approximation theory with representation system has been well developed in
Mathematics. We then prove the fundamental bound theorem, implying a quantity
intrinsic to the function class itself can give information about the
approximation ability of neural networks and representation system. We also
provides a method for transferring existing theories about approximation by
representation systems to that of neural networks, greatly amplifying the
practical values of neural networks. Finally, we use neural networks to
approximate B-spline functions, which are used to generate the B-spline curves.
Then, we analyse the complexity of a class called $\beta$ cartoon-like
functions using rate-distortion theory and wedgelets construction.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int