<s>
The	O
random	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
(	O
RNN	O
)	O
is	O
a	O
mathematical	O
representation	O
of	O
an	O
interconnected	O
network	B-Architecture
of	O
neurons	O
or	O
cells	O
which	O
exchange	O
spiking	B-Algorithm
signals	I-Algorithm
.	O
</s>
<s>
It	O
was	O
invented	O
by	O
Erol	O
Gelenbe	O
and	O
is	O
linked	O
to	O
the	O
G-network	O
model	O
of	O
queueing	O
networks	O
as	O
well	O
as	O
to	O
Gene	O
Regulatory	O
Network	B-Architecture
models	O
.	O
</s>
<s>
Each	O
cell	O
state	O
is	O
represented	O
by	O
an	O
integer	O
whose	O
value	O
rises	O
when	O
the	O
cell	O
receives	O
an	O
excitatory	O
spike	B-Algorithm
and	O
drops	O
when	O
it	O
receives	O
an	O
inhibitory	O
spike	B-Algorithm
.	O
</s>
<s>
The	O
spikes	B-Algorithm
can	O
originate	O
outside	O
the	O
network	B-Architecture
itself	O
,	O
or	O
they	O
can	O
come	O
from	O
other	O
cells	O
in	O
the	O
networks	O
.	O
</s>
<s>
Cells	O
whose	O
internal	O
excitatory	O
state	O
has	O
a	O
positive	O
value	O
are	O
allowed	O
to	O
send	O
out	O
spikes	B-Algorithm
of	O
either	O
kind	O
to	O
other	O
cells	O
in	O
the	O
network	B-Architecture
according	O
to	O
specific	O
cell-dependent	O
spiking	O
rates	O
.	O
</s>
<s>
The	O
model	O
has	O
a	O
mathematical	O
solution	O
in	O
steady-state	O
which	O
provides	O
the	O
joint	O
probability	O
distribution	O
of	O
the	O
network	B-Architecture
in	O
terms	O
of	O
the	O
individual	O
probabilities	O
that	O
each	O
cell	O
is	O
excited	O
and	O
able	O
to	O
send	O
out	O
spikes	B-Algorithm
.	O
</s>
<s>
Computing	O
this	O
solution	O
is	O
based	O
on	O
solving	O
a	O
set	O
of	O
non-linear	O
algebraic	O
equations	O
whose	O
parameters	O
are	O
related	O
to	O
the	O
spiking	O
rates	O
of	O
individual	O
cells	O
and	O
their	O
connectivity	O
to	O
other	O
cells	O
,	O
as	O
well	O
as	O
the	O
arrival	O
rates	O
of	O
spikes	B-Algorithm
from	O
outside	O
the	O
network	B-Architecture
.	O
</s>
<s>
a	O
neural	B-Architecture
network	I-Architecture
that	O
is	O
allowed	O
to	O
have	O
complex	O
feedback	O
loops	O
.	O
</s>
<s>
A	O
highly	O
energy-efficient	O
implementation	O
of	O
random	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
was	O
demonstrated	O
by	O
Krishna	O
Palem	O
et	O
al	O
.	O
</s>
<s>
RNNs	O
are	O
also	O
related	O
to	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
,	O
which	O
(	O
like	O
the	O
random	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
)	O
have	O
gradient-based	O
learning	O
algorithms	O
.	O
</s>
<s>
The	O
learning	O
algorithm	O
for	O
an	O
n-node	O
random	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
that	O
includes	O
feedback	O
loops	O
(	O
it	O
is	O
also	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
)	O
is	O
of	O
computational	O
complexity	O
O( n^3	O
)	O
(	O
the	O
number	O
of	O
computations	O
is	O
proportional	O
to	O
the	O
cube	O
of	O
n	O
,	O
the	O
number	O
of	O
neurons	O
)	O
.	O
</s>
<s>
The	O
random	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
can	O
also	O
be	O
used	O
with	O
other	O
learning	O
algorithms	O
such	O
as	O
reinforcement	O
learning	O
.	O
</s>
