Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Echo state networks are universal   This paper shows that echo state networks are universal uniform approximants
in the context of discrete-time fading memory filters with uniformly bounded
inputs defined on negative infinite times. This result guarantees that any
fading memory input/output system in discrete time can be realized as a simple
finite-dimensional neural network-type state-space model with a static linear
readout map. This approximation is valid for infinite time intervals. The proof
of this statement is based on fundamental results, also presented in this work,
about the topological nature of the fading memory property and about reservoir
computing systems generated by continuous reservoir maps.

29
The categories of this paper are: funct-an
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom