<s>
A	O
Bayesian	O
Confidence	O
Propagation	O
Neural	B-Architecture
Network	I-Architecture
(	O
BCPNN	B-Algorithm
)	O
is	O
an	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
inspired	O
by	O
Bayes	O
 '	O
theorem	O
,	O
which	O
regards	O
neural	O
computation	O
and	O
processing	O
as	O
probabilistic	O
inference	O
.	O
</s>
<s>
This	O
probabilistic	O
neural	B-Architecture
network	I-Architecture
model	I-Architecture
can	O
also	O
be	O
run	O
in	O
generative	O
mode	O
to	O
produce	O
spontaneous	O
activations	O
and	O
temporal	O
sequences	O
.	O
</s>
<s>
The	O
basic	O
model	O
is	O
a	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
comprising	O
neural	O
units	O
with	O
continuous	O
activation	O
,	O
having	O
a	O
bias	O
representing	O
prior	O
,	O
and	O
being	O
connected	O
by	O
Bayesian	O
weights	O
in	O
the	O
form	O
of	O
point-wise	B-General_Concept
mutual	I-General_Concept
information	I-General_Concept
.	O
</s>
<s>
The	O
original	O
network	O
has	O
been	O
extended	O
to	O
a	O
modular	O
structure	O
of	O
minicolumns	O
and	O
hypercolumns	B-General_Concept
,	O
representing	O
discrete	O
coded	O
features	O
or	O
attributes	O
.	O
</s>
<s>
The	O
units	O
can	O
also	O
be	O
connected	O
as	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
(	O
losing	O
the	O
strict	O
interpretation	O
of	O
their	O
activations	O
as	O
probabilities	O
)	O
but	O
becoming	O
a	O
possible	O
abstract	O
model	O
of	O
biological	O
neural	B-Architecture
networks	I-Architecture
and	O
associative	O
memory	O
.	O
</s>
<s>
BCPNN	B-Algorithm
has	O
been	O
used	O
for	O
machine	O
learning	O
classification	O
and	O
data	B-Application
mining	I-Application
,	O
for	O
example	O
for	O
discovery	O
of	O
adverse	O
drug	O
reactions	O
.	O
</s>
<s>
The	O
BCPNN	B-Algorithm
learning	O
rule	O
has	O
also	O
been	O
used	O
to	O
model	O
biological	O
synaptic	O
plasticity	O
and	O
intrinsic	O
excitability	O
in	O
large-scale	O
spiking	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
(	O
SNN	B-Algorithm
)	O
models	O
of	O
cortical	O
associative	O
memory	O
and	O
reward	O
learning	O
in	O
Basal	O
ganglia	O
.	O
</s>
<s>
The	O
BCPNN	B-Algorithm
network	O
architecture	O
is	O
modular	O
in	O
terms	O
of	O
hypercolumns	B-General_Concept
and	O
minicolumns	O
.	O
</s>
<s>
The	O
latter	O
turns	O
the	O
negative	O
BCPNN-weights	O
formed	O
between	O
neurons	O
with	O
anti-correlated	O
activity	O
into	O
di-synaptic	O
inhibition	O
.	O
</s>
<s>
Lateral	O
inhibition	O
within	O
the	O
hypercolumn	B-General_Concept
makes	O
it	O
a	O
soft	O
winner-take-all	B-Algorithm
module	O
.	O
</s>
<s>
Looking	O
at	O
real	O
cortex	O
,	O
the	O
number	O
of	O
minicolumns	O
within	O
a	O
hypercolumn	B-General_Concept
is	O
on	O
the	O
order	O
of	O
a	O
hundred	O
,	O
which	O
makes	O
the	O
activity	O
sparse	O
,	O
at	O
the	O
level	O
of	O
1%	O
or	O
less	O
,	O
given	O
that	O
hypercolumns	B-General_Concept
can	O
also	O
be	O
silent	O
.	O
</s>
<s>
A	O
BCPNN	B-Algorithm
network	O
with	O
a	O
size	O
of	O
the	O
human	O
neocortex	O
would	O
have	O
a	O
couple	O
of	O
million	O
hypercolumns	B-General_Concept
,	O
partitioned	O
into	O
some	O
hundred	O
areas	O
.	O
</s>
<s>
In	O
addition	O
to	O
sparse	O
activity	O
,	O
a	O
large-scale	O
BCPNN	B-Algorithm
would	O
also	O
have	O
very	O
sparse	O
connectivity	O
,	O
given	O
that	O
the	O
real	O
cortex	O
is	O
sparsely	O
connected	O
at	O
the	O
level	O
of	O
0.01	O
-	O
0.001	O
%	O
on	O
average	O
.	O
</s>
<s>
The	O
BCPNN	B-Algorithm
learning	O
rule	O
was	O
derived	O
from	O
Bayes	O
rule	O
and	O
is	O
Hebbian	O
such	O
that	O
neural	O
units	O
with	O
activity	O
correlated	O
over	O
time	O
get	O
excitatory	O
connections	O
between	O
them	O
whereas	O
anti-correlation	O
generates	O
inhibition	O
and	O
lack	O
of	O
correlation	O
gives	O
zero	O
connections	O
.	O
</s>
<s>
BCPNN	B-Algorithm
represents	O
a	O
straight-forward	O
way	O
of	O
deriving	O
a	O
neural	B-Architecture
network	I-Architecture
from	O
Bayes	O
rule	O
.	O
</s>
<s>
There	O
has	O
been	O
proposals	O
for	O
a	O
biological	O
interpretation	O
of	O
the	O
BCPNN	B-Algorithm
learning	O
rule	O
.	O
</s>
<s>
The	O
cortex	O
inspired	O
modular	O
architecture	O
of	O
BCPNN	B-Algorithm
has	O
been	O
the	O
basis	O
for	O
several	O
spiking	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
models	O
of	O
cortex	O
aimed	O
at	O
studying	O
its	O
associative	O
memory	O
functions	O
.	O
</s>
<s>
In	O
these	O
models	O
,	O
minicolumns	O
comprise	O
about	O
30	O
model	O
pyramidal	O
cells	O
and	O
a	O
hypercolumn	B-General_Concept
comprises	O
ten	O
or	O
more	O
such	O
minicolumns	O
and	O
a	O
population	O
of	O
basket	O
cells	O
that	O
mediate	O
local	O
feedback	O
inhibition	O
.	O
</s>
<s>
A	O
modelled	O
network	O
is	O
composed	O
of	O
about	O
ten	O
or	O
more	O
such	O
hypercolumns	B-General_Concept
.	O
</s>
<s>
Connectivity	O
is	O
excitatory	O
within	O
minicolumns	O
and	O
support	O
feedback	O
inhibition	O
between	O
minicolumns	O
in	O
the	O
same	O
hypercolumn	B-General_Concept
via	O
model	O
basket	O
cells	O
.	O
</s>
<s>
Long-range	O
connectivity	O
between	O
hypercolumns	B-General_Concept
is	O
sparse	O
and	O
excitatory	O
and	O
is	O
typically	O
set	O
up	O
to	O
form	O
number	O
of	O
distributed	O
cell	O
assemblies	O
representing	O
earlier	O
encoded	O
memories	O
.	O
</s>
<s>
Notably	O
,	O
a	O
few	O
cycles	O
of	O
gamma	B-Algorithm
oscillations	I-Algorithm
are	O
generated	O
during	O
such	O
a	O
brief	O
memory	O
recall	O
.	O
</s>
<s>
A	O
similar	O
approach	O
was	O
applied	O
to	O
model	O
reward	O
learning	O
and	O
behavior	B-Algorithm
selection	I-Algorithm
in	O
a	O
Go-NoGo	O
connected	O
non-spiking	O
and	O
spiking	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
models	O
of	O
the	O
Basal	O
ganglia	O
.	O
</s>
<s>
The	O
point-wise	B-General_Concept
mutual	I-General_Concept
information	I-General_Concept
weights	O
of	O
BCPNN	B-Algorithm
is	O
since	O
long	O
one	O
of	O
the	O
standard	O
methods	O
for	O
detection	O
of	O
drug	O
adverse	O
reactions	O
.	O
</s>
<s>
BCPNN	B-Algorithm
has	O
recently	O
been	O
successfully	O
applied	O
to	O
Machine	O
Learning	O
classification	O
benchmarks	O
,	O
most	O
notably	O
the	O
hand	O
written	O
digits	O
of	O
the	O
MNIST	B-General_Concept
database	I-General_Concept
.	O
</s>
<s>
The	O
BCPNN	B-Algorithm
approach	O
uses	O
biologically	O
plausible	O
learning	O
and	O
structural	O
plasticity	O
for	O
unsupervised	O
generation	O
of	O
a	O
sparse	O
hidden	O
representation	O
,	O
followed	O
by	O
a	O
one-layer	O
classifier	O
that	O
associates	O
this	O
representation	O
to	O
the	O
output	O
layer	O
.	O
</s>
<s>
It	O
achieves	O
a	O
classification	O
performance	O
on	O
the	O
full	O
MNIST	B-General_Concept
test	O
set	O
around	O
98%	O
,	O
comparable	O
to	O
other	O
methods	O
based	O
on	O
unsupervised	O
representation	O
learning	O
.	O
</s>
<s>
The	O
BCPNN	B-Algorithm
method	O
is	O
also	O
quite	O
well	O
suited	O
for	O
semi-supervised	O
learning	O
.	O
</s>
<s>
The	O
structure	O
of	O
BCPNN	B-Algorithm
with	O
its	O
cortex-like	O
modular	O
architecture	O
and	O
massively	O
parallel	O
correlation	O
based	O
Hebbian	O
learning	O
makes	O
it	O
quite	O
hardware	O
friendly	O
.	O
</s>
<s>
BCPNN	B-Algorithm
has	O
further	O
been	O
the	O
target	O
for	O
parallel	O
simulators	O
on	O
cluster	O
computers	O
and	O
GPU:s	O
.	O
It	O
was	O
recently	O
implemented	O
on	O
the	O
SpiNNaker	B-General_Concept
compute	O
platform	O
as	O
well	O
as	O
in	O
a	O
series	O
of	O
dedicated	O
neuromorphic	O
VLSI	O
designs	O
.	O
</s>
<s>
From	O
these	O
it	O
has	O
been	O
estimated	O
that	O
a	O
human	O
cortex	O
sized	O
BCPNN	B-Algorithm
with	O
continuous	O
learning	O
could	O
be	O
executed	O
in	O
real	O
time	O
with	O
a	O
power	O
dissipation	O
on	O
the	O
order	O
of	O
few	O
kW	O
.	O
</s>
