<s>
An	O
echo	B-Algorithm
state	I-Algorithm
network	I-Algorithm
(	O
ESN	O
)	O
is	O
a	O
type	O
of	O
reservoir	B-Algorithm
computer	I-Algorithm
that	O
uses	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
with	O
a	O
sparsely	O
connected	O
hidden	O
layer	O
(	O
with	O
typically	O
1%	O
connectivity	O
)	O
.	O
</s>
<s>
The	O
connectivity	O
and	O
weights	O
of	O
hidden	O
neurons	B-Algorithm
are	O
fixed	O
and	O
randomly	O
assigned	O
.	O
</s>
<s>
The	O
weights	O
of	O
output	O
neurons	B-Algorithm
can	O
be	O
learned	O
so	O
that	O
the	O
network	O
can	O
produce	O
or	O
reproduce	O
specific	O
temporal	O
patterns	O
.	O
</s>
<s>
The	O
main	O
interest	O
of	O
this	O
network	O
is	O
that	O
although	O
its	O
behaviour	O
is	O
non-linear	O
,	O
the	O
only	O
weights	O
that	O
are	O
modified	O
during	O
training	O
are	O
for	O
the	O
synapses	O
that	O
connect	O
the	O
hidden	O
neurons	B-Algorithm
to	O
output	O
neurons	B-Algorithm
.	O
</s>
<s>
Some	O
publicly	O
available	O
implementations	O
of	O
ESNs	O
are	O
:	O
(	O
i	O
)	O
aureservoir	O
:	O
an	O
efficient	O
C++	O
library	O
for	O
various	O
kinds	O
of	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
with	O
python/numpy	O
bindings	O
;	O
and	O
(	O
ii	O
)	O
Matlab	O
code	O
:	O
an	O
efficient	O
matlab	O
for	O
an	O
echo	B-Algorithm
state	I-Algorithm
network	I-Algorithm
,	O
(	O
iii	O
)	O
ReservoirComputing.jl	O
:	O
an	O
efficient	O
Julia-based	O
implementation	O
of	O
various	O
types	O
of	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
,	O
and	O
(	O
iv	O
)	O
pyESN	O
:	O
simple	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
in	O
Python	O
.	O
</s>
<s>
The	O
Echo	B-Algorithm
State	I-Algorithm
Network	I-Algorithm
(	O
ESN	O
)	O
belongs	O
to	O
the	O
Recurrent	B-Algorithm
Neural	I-Algorithm
Network	I-Algorithm
(	O
RNN	O
)	O
family	O
and	O
provide	O
their	O
architecture	O
and	O
supervised	O
learning	O
principle	O
.	O
</s>
<s>
Unlike	O
Feedforward	O
Neural	O
Networks	O
,	O
Recurrent	B-Algorithm
Neural	I-Algorithm
Networks	I-Algorithm
are	O
dynamic	O
systems	O
and	O
not	O
functions	O
.	O
</s>
<s>
Recurrent	B-Algorithm
Neural	I-Algorithm
Networks	I-Algorithm
are	O
typically	O
used	O
for	O
:	O
Learn	O
dynamical	O
process	O
:	O
signal	O
treatment	O
in	O
engineering	O
and	O
telecommunications	O
,	O
vibration	O
analysis	O
,	O
seismology	O
,	O
control	O
of	O
engines	O
and	O
generators	O
.	O
</s>
<s>
Another	O
feature	O
of	O
the	O
ESN	O
is	O
the	O
autonomous	O
operation	O
in	O
prediction	O
:	O
if	O
the	O
Echo	B-Algorithm
State	I-Algorithm
Network	I-Algorithm
is	O
trained	O
with	O
an	O
input	O
that	O
is	O
a	O
backshifted	O
version	O
of	O
the	O
output	O
,	O
then	O
it	O
can	O
be	O
used	O
for	O
signal	O
generation/prediction	O
by	O
using	O
the	O
previous	O
output	O
as	O
input	O
.	O
</s>
<s>
The	O
main	O
idea	O
of	O
ESNs	O
is	O
tied	O
to	O
Liquid	B-Algorithm
State	I-Algorithm
Machines	I-Algorithm
(	O
LSM	O
)	O
,	O
which	O
were	O
independently	O
and	O
simultaneously	O
developed	O
with	O
ESNs	O
by	O
Wolfgang	O
Maass	O
.	O
</s>
<s>
LSMs	O
,	O
ESNs	O
and	O
the	O
newly	O
researched	O
Backpropagation	O
Decorrelation	O
learning	O
rule	O
for	O
RNNs	O
are	O
more	O
and	O
more	O
summarized	O
under	O
the	O
name	O
Reservoir	B-Algorithm
Computing	I-Algorithm
.	O
</s>
<s>
An	O
early	O
clear	O
formulation	O
of	O
the	O
reservoir	B-Algorithm
computing	I-Algorithm
idea	O
is	O
due	O
to	O
K	O
.	O
Kirby	O
,	O
who	O
disclosed	O
this	O
concept	O
in	O
a	O
largely	O
forgotten	O
conference	O
contribution	O
.	O
</s>
<s>
The	O
first	O
formulation	O
of	O
the	O
reservoir	B-Algorithm
computing	I-Algorithm
idea	O
known	O
today	O
stems	O
from	O
L	O
.	O
Schomaker	O
,	O
who	O
described	O
how	O
a	O
desired	O
target	O
output	O
can	O
be	O
obtained	O
from	O
an	O
RNN	O
by	O
learning	O
to	O
combine	O
signals	O
from	O
a	O
randomly	O
configured	O
ensemble	O
of	O
spiking	O
neural	O
oscillators	O
.	O
</s>
<s>
Echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
can	O
be	O
built	O
in	O
different	O
ways	O
.	O
</s>
<s>
Other	O
variants	O
of	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
seek	O
to	O
change	O
the	O
formulation	O
to	O
better	O
match	O
common	O
models	O
of	O
physical	O
systems	O
,	O
such	O
as	O
those	O
typically	O
those	O
defined	O
by	O
differential	O
equations	O
.	O
</s>
<s>
Work	O
in	O
this	O
direction	O
includes	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
which	O
partially	O
include	O
physical	O
models	O
,	O
hybrid	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
,	O
and	O
continuous-time	O
echo	B-Algorithm
state	I-Algorithm
networks	I-Algorithm
.	O
</s>
