<s>
Sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
(	O
SDM	O
)	O
is	O
a	O
mathematical	O
model	O
of	O
human	O
long-term	O
memory	O
introduced	O
by	O
Pentti	O
Kanerva	O
in	O
1988	O
while	O
he	O
was	O
at	O
NASA	O
Ames	O
Research	O
Center	O
.	O
</s>
<s>
Sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
is	O
used	O
for	O
storing	O
and	O
retrieving	O
large	O
amounts	O
(	O
bits	O
)	O
of	O
information	O
without	O
focusing	O
on	O
the	O
accuracy	O
but	O
on	O
similarity	O
of	O
information	O
.	O
</s>
<s>
It	O
is	O
a	O
generalized	O
random-access	B-Architecture
memory	I-Architecture
(	O
RAM	B-Architecture
)	O
for	O
long	O
(	O
e.g.	O
,	O
1,000	O
bit	O
)	O
binary	O
words	O
.	O
</s>
<s>
The	O
theory	O
of	O
the	O
memory	O
is	O
mathematically	O
complete	O
and	O
has	O
been	O
verified	O
by	O
computer	B-Application
simulation	I-Application
.	O
</s>
<s>
It	O
arose	O
from	O
the	O
observation	O
that	O
the	O
distances	O
between	O
points	O
of	O
a	O
high-dimensional	B-Algorithm
space	I-Algorithm
resemble	O
the	O
proximity	O
relations	O
between	O
concepts	O
in	O
human	O
memory	O
.	O
</s>
<s>
The	O
theory	O
is	O
also	O
practical	O
in	O
that	O
memories	O
based	O
on	O
it	O
can	O
be	O
implemented	O
with	O
conventional	O
random-access	B-Architecture
memory	I-Architecture
elements	O
.	O
</s>
<s>
Sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
is	O
a	O
mathematical	O
representation	O
of	O
human	O
memory	O
,	O
and	O
uses	O
high-dimensional	B-Algorithm
space	I-Algorithm
to	O
help	O
model	O
the	O
large	O
amounts	O
of	O
memory	O
that	O
mimics	O
that	O
of	O
the	O
human	O
neural	O
network	O
.	O
</s>
<s>
SDM	O
can	O
be	O
considered	O
a	O
realization	O
of	O
locality-sensitive	B-Algorithm
hashing	I-Algorithm
.	O
</s>
<s>
As	O
a	O
general	O
guideline	O
,	O
those	O
hard	O
locations	O
should	O
be	O
uniformly	O
distributed	O
in	O
the	O
virtual	B-Architecture
space	I-Architecture
,	O
to	O
mimic	O
the	O
existence	O
of	O
the	O
larger	O
virtual	B-Architecture
space	I-Architecture
as	O
accurately	O
as	O
possible	O
.	O
</s>
<s>
The	O
normal	O
distribution	O
F	O
with	O
mean	O
n/2	O
and	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
a	O
good	O
approximation	O
to	O
it	O
:	O
</s>
<s>
The	O
SDM	O
may	O
be	O
regarded	O
either	O
as	O
a	O
content-addressable	B-Data_Structure
extension	O
of	O
a	O
classical	O
random-access	B-Architecture
memory	I-Architecture
(	O
RAM	B-Architecture
)	O
or	O
as	O
a	O
special	O
type	O
of	O
three	O
layer	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
.	O
</s>
<s>
The	O
main	O
SDM	O
alterations	O
to	O
the	O
RAM	B-Architecture
are	O
:	O
</s>
<s>
An	O
idealized	O
description	O
of	O
neuron	O
is	O
as	O
follows	O
:	O
a	O
neuron	O
has	O
a	O
cell	O
body	O
with	O
two	O
kinds	O
of	O
branches	O
:	O
dendrites	O
and	O
an	O
axon	B-Algorithm
.	O
</s>
<s>
It	O
receives	O
input	O
signals	O
from	O
other	O
neurons	O
via	O
dendrites	O
,	O
integrates	O
(	O
sums	O
)	O
them	O
and	O
generates	O
its	O
own	O
(	O
electric	O
)	O
output	O
signal	O
which	O
is	O
sent	O
to	O
outside	O
neurons	O
via	O
axon	B-Algorithm
.	O
</s>
<s>
The	O
points	O
of	O
electric	O
contact	O
between	O
neurons	O
are	O
called	O
synapses	B-Application
.	O
</s>
<s>
The	O
relative	O
importance	O
of	O
a	O
synapse	B-Application
to	O
the	O
firing	O
of	O
neuron	O
is	O
called	O
synaptic	O
weight	O
(	O
or	O
input	O
coefficient	O
)	O
.	O
</s>
<s>
There	O
are	O
two	O
kinds	O
of	O
synapses	B-Application
:	O
excitatory	O
that	O
trigger	O
neuron	O
to	O
fire	O
and	O
inhibitory	O
that	O
hinder	O
firing	O
.	O
</s>
<s>
The	O
neuron	O
is	O
either	O
excitatory	O
or	O
inhibitory	O
according	O
to	O
the	O
kinds	O
of	O
synapses	B-Application
its	O
axon	B-Algorithm
makes	O
.	O
</s>
<s>
The	O
higher	O
the	O
threshold	O
the	O
more	O
important	O
it	O
is	O
that	O
excitatory	O
synapses	B-Application
have	O
input	O
while	O
inhibitory	O
ones	O
do	O
not	O
.	O
</s>
<s>
Kanerva	O
's	O
key	O
thesis	O
is	O
that	O
certain	O
neurons	O
could	O
have	O
their	O
input	O
coefficients	O
and	O
thresholds	O
fixed	O
over	O
the	O
entire	O
life	O
of	O
an	O
organism	O
and	O
used	O
as	O
address	O
decoders	O
where	O
n-tuple	O
of	O
input	O
coefficients	O
(	O
the	O
pattern	O
to	O
which	O
neurons	O
respond	O
most	O
readily	O
)	O
determines	O
the	O
n-bit	O
memory	B-General_Concept
address	I-General_Concept
,	O
and	O
the	O
threshold	O
controls	O
the	O
size	O
of	O
the	O
region	O
of	O
similar	O
address	O
patterns	O
to	O
which	O
the	O
neuron	O
responds	O
.	O
</s>
<s>
This	O
mechanism	O
is	O
complementary	O
to	O
adjustable	O
synapses	B-Application
or	O
adjustable	O
weights	O
in	O
a	O
neural	O
network	O
(	O
perceptron	B-Algorithm
convergence	O
learning	O
)	O
,	O
as	O
this	O
fixed	O
accessing	O
mechanism	O
would	O
be	O
a	O
permanent	O
frame	O
of	O
reference	O
which	O
allows	O
to	O
select	O
the	O
synapses	B-Application
in	O
which	O
the	O
information	O
is	O
stored	O
and	O
from	O
which	O
it	O
is	O
retrieved	O
under	O
given	O
set	O
of	O
circumstances	O
.	O
</s>
<s>
When	O
the	O
threshold	O
c	B-Language
is	O
in	O
range	O
the	O
output	O
of	O
the	O
neuron	O
is	O
0	O
for	O
some	O
addresses	O
(	O
input	O
patterns	O
)	O
and	O
1	O
for	O
others	O
.	O
</s>
<s>
When	O
the	O
threshold	O
is	O
S	O
(	O
the	O
maximum	O
for	O
the	O
weighted	O
sum	O
)	O
the	O
neuron	O
responds	O
only	O
to	O
its	O
own	O
address	O
and	O
acts	O
like	O
an	O
address	O
decoder	O
of	O
a	O
conventional	O
random-access	B-Architecture
memory	I-Architecture
.	O
</s>
<s>
Unlike	O
conventional	O
Turing	B-Architecture
machines	I-Architecture
SDM	O
is	O
taking	O
advantage	O
of	O
parallel	O
computing	O
by	O
the	O
address	O
decoders	O
.	O
</s>
<s>
The	O
address	O
pattern	O
is	O
used	O
to	O
select	O
hard	O
memory	B-General_Concept
locations	I-General_Concept
whose	O
hard	O
addresses	O
are	O
within	O
a	O
certain	O
cutoff	O
distance	O
from	O
the	O
address	O
pattern	O
.	O
</s>
<s>
During	O
a	O
read	O
,	O
an	O
address	O
pattern	O
is	O
used	O
to	O
select	O
a	O
certain	O
number	O
of	O
hard	O
memory	B-General_Concept
locations	I-General_Concept
(	O
just	O
like	O
during	O
a	O
write	O
)	O
.	O
</s>
<s>
All	O
of	O
the	O
items	O
are	O
linked	O
in	O
a	O
single	O
list	O
(	O
or	O
array	O
)	O
of	O
pointers	O
to	O
memory	B-General_Concept
locations	I-General_Concept
,	O
and	O
are	O
stored	O
in	O
RAM	B-Architecture
.	O
</s>
<s>
The	O
corresponding	O
critical	O
distance	O
of	O
a	O
Sparse	B-Architecture
Distributed	I-Architecture
Memory	I-Architecture
can	O
be	O
approximately	O
evaluated	O
minimizing	O
the	O
following	O
equation	O
with	O
the	O
restriction	O
and	O
.	O
</s>
<s>
Theoretical	O
work	O
on	O
SDM	O
by	O
Kanerva	O
has	O
suggested	O
that	O
sparse	O
coding	O
increases	O
the	O
capacity	O
of	O
associative	B-Data_Structure
memory	I-Data_Structure
by	O
reducing	O
overlap	O
between	O
representations	O
.	O
</s>
<s>
Experimentally	O
,	O
sparse	O
representations	O
of	O
sensory	O
information	O
have	O
been	O
observed	O
in	O
many	O
systems	O
,	O
including	O
vision	B-Application
,	O
audition	O
,	O
touch	O
,	O
and	O
olfaction	O
.	O
</s>
<s>
However	O
,	O
despite	O
the	O
accumulating	O
evidence	O
for	O
widespread	O
sparse	O
coding	O
and	O
theoretical	O
arguments	O
for	O
its	O
importance	O
,	O
a	O
demonstration	O
that	O
sparse	O
coding	O
improves	O
the	O
stimulus-specificity	O
of	O
associative	B-Data_Structure
memory	I-Data_Structure
has	O
been	O
lacking	O
until	O
recently	O
.	O
</s>
<s>
demonstrated	O
that	O
sparseness	O
is	O
controlled	O
by	O
a	O
negative	O
feedback	O
circuit	O
between	O
Kenyon	O
cells	O
and	O
the	O
GABAergic	O
anterior	O
paired	O
lateral	O
(	O
APL	B-Language
)	O
neuron	O
.	O
</s>
<s>
Systematic	O
activation	O
and	O
blockade	O
of	O
each	O
leg	O
of	O
this	O
feedback	O
circuit	O
show	O
that	O
Kenyon	O
cells	O
activate	O
APL	B-Language
and	O
APL	B-Language
inhibits	O
Kenyon	O
cells	O
.	O
</s>
<s>
Disrupting	O
the	O
Kenyon	O
cell-APL	O
feedback	O
loop	O
decreases	O
the	O
sparseness	O
of	O
Kenyon	O
cell	O
odor	O
responses	O
,	O
increases	O
inter-odor	O
correlations	O
,	O
and	O
prevents	O
flies	O
from	O
learning	O
to	O
discriminate	O
similar	O
,	O
but	O
not	O
dissimilar	O
,	O
odors	O
.	O
</s>
<s>
A	O
2017	O
publication	O
in	O
Science	O
showed	O
that	O
fly	O
olfactory	O
circuit	O
implements	O
an	O
improved	O
version	O
of	O
binary	O
locality	B-Algorithm
sensitive	I-Algorithm
hashing	I-Algorithm
via	O
sparse	O
,	O
random	O
projections	O
.	O
</s>
<s>
The	O
applications	O
include	O
vision	B-Application
detecting	O
and	O
identifying	O
objects	O
in	O
a	O
scene	O
and	O
anticipating	O
subsequent	O
scenes	O
robotics	O
,	O
signal	O
detection	O
and	O
verification	O
,	O
and	O
adaptive	O
learning	O
and	O
control	O
.	O
</s>
<s>
or	O
,	O
in	O
other	O
words	O
,	O
the	O
Nearest	B-Algorithm
neighbor	I-Algorithm
search	I-Algorithm
problem	O
.	O
</s>
<s>
With	O
we	O
have	O
a	O
conventional	O
random-access	B-Architecture
memory	I-Architecture
.	O
</s>
<s>
SDM	O
can	O
be	O
applied	O
in	O
transcribing	B-Application
speech	I-Application
,	O
with	O
the	O
training	O
consisting	O
of	O
"	O
listening	O
"	O
to	O
a	O
large	O
corpus	O
of	O
spoken	O
language	O
.	O
</s>
<s>
In	O
transcribing	B-Application
speech	I-Application
,	O
these	O
branching	O
points	O
are	O
detected	O
and	O
tend	O
to	O
break	O
the	O
stream	O
into	O
segments	O
that	O
correspond	O
to	O
words	O
.	O
</s>
<s>
At	O
the	O
University	O
of	O
Memphis	O
,	O
Uma	O
Ramamurthy	O
,	O
Sidney	O
K	O
.	O
D'Mello	O
,	O
and	O
Stan	O
Franklin	O
created	O
a	O
modified	O
version	O
of	O
the	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
system	O
that	O
represents	O
"	O
realizing	O
forgetting.	O
"	O
</s>
<s>
The	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
system	O
distributes	O
each	O
pattern	O
into	O
approximately	O
one	O
hundredth	O
of	O
the	O
locations	O
,	O
so	O
interference	O
can	O
have	O
detrimental	O
results	O
.	O
</s>
<s>
Negated-translated	O
sigmoid	O
decay	O
mechanism	O
:	O
</s>
<s>
In	O
the	O
exponential	O
decay	O
function	O
,	O
it	O
approaches	O
zero	O
more	O
quickly	O
as	O
x	O
increases	O
,	O
and	O
a	O
is	O
a	O
constant	O
(	O
usually	O
between	O
3-9	O
)	O
and	O
c	B-Language
is	O
a	O
counter	O
.	O
</s>
<s>
For	O
the	O
negated-translated	O
sigmoid	B-Algorithm
function	I-Algorithm
,	O
the	O
decay	O
is	O
similar	O
to	O
the	O
exponential	O
decay	O
function	O
when	O
a	O
is	O
greater	O
than	O
4	O
.	O
</s>
<s>
Ashraf	O
Anwar	O
,	O
Stan	O
Franklin	O
,	O
and	O
Dipankar	O
Dasgupta	O
at	O
The	O
University	O
of	O
Memphis	O
;	O
proposed	O
a	O
model	O
for	O
SDM	O
initialization	O
using	O
Genetic	B-Algorithm
Algorithms	I-Algorithm
and	O
Genetic	O
Programming	O
(	O
1999	O
)	O
.	O
</s>
<s>
Genetic	B-General_Concept
memory	I-General_Concept
uses	O
genetic	B-Algorithm
algorithm	I-Algorithm
and	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
as	O
a	O
pseudo	O
artificial	O
neural	O
network	O
.	O
</s>
<s>
breaks	O
down	O
,	O
the	O
processing	O
performed	O
by	O
the	O
model	O
can	O
be	O
interpreted	O
as	O
that	O
of	O
a	O
statistical	O
predictor	O
and	O
each	O
data	O
counter	O
in	O
an	O
SDM	O
can	O
be	O
viewed	O
as	O
an	O
independent	O
estimate	O
of	O
the	O
conditional	O
probability	O
of	O
a	O
binary	O
function	O
f	O
being	O
equal	O
to	O
the	O
activation	O
set	O
defined	O
by	O
the	O
counter	O
's	O
memory	B-General_Concept
location	I-General_Concept
.	O
</s>
<s>
LIDA	B-Architecture
uses	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
to	O
help	O
model	O
cognition	O
in	O
biological	O
systems	O
.	O
</s>
<s>
The	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
places	O
space	O
is	O
recalling	O
or	O
recognizing	O
the	O
object	O
that	O
it	O
has	O
in	O
relation	O
to	O
other	O
objects	O
.	O
</s>
<s>
It	O
was	O
developed	O
by	O
Stan	O
Franklin	O
,	O
the	O
creator	O
of	O
the	O
"	O
realizing	O
forgetting	O
"	O
modified	O
sparse	B-Architecture
distributed	I-Architecture
memory	I-Architecture
system	O
.	O
</s>
<s>
Transient	O
episodic	O
and	O
declarative	O
memories	O
have	O
distributed	O
representations	O
in	O
LIDA	B-Architecture
(	O
based	O
on	O
modified	O
version	O
of	O
SDM	O
)	O
,	O
there	O
is	O
evidence	O
that	O
this	O
is	O
also	O
the	O
case	O
in	O
the	O
nervous	O
system	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
SDM	O
augmented	O
with	O
the	O
use	O
of	O
genetic	B-Algorithm
algorithms	I-Algorithm
as	O
an	O
associative	B-Data_Structure
memory	I-Data_Structure
.	O
</s>
<s>
Hierarchical	B-Algorithm
temporal	I-Algorithm
memory	I-Algorithm
utilizes	O
SDM	O
for	O
storing	O
sparse	O
distributed	O
representations	O
of	O
the	O
data	O
.	O
</s>
<s>
SDMs	O
provide	O
a	O
linear	O
,	O
local	O
function	O
approximation	O
scheme	O
,	O
designed	O
to	O
work	O
when	O
a	O
very	O
large/high	O
-dimensional	O
input	O
(	O
address	O
)	O
space	O
has	O
to	O
be	O
mapped	O
into	O
a	O
much	O
smaller	O
physical	B-General_Concept
memory	I-General_Concept
.	O
</s>
<s>
In	O
general	O
,	O
local	O
architectures	O
,	O
SDMs	O
included	O
,	O
can	O
be	O
subject	O
to	O
the	O
curse	B-Algorithm
of	I-Algorithm
dimensionality	I-Algorithm
,	O
as	O
some	O
target	O
functions	O
may	O
require	O
,	O
in	O
the	O
worst	O
case	O
,	O
an	O
exponential	O
number	O
of	O
local	O
units	O
to	O
be	O
approximated	O
accurately	O
across	O
the	O
entire	O
input	O
space	O
.	O
</s>
<s>
However	O
,	O
it	O
is	O
widely	O
believed	O
that	O
most	O
decision-making	B-Application
systems	I-Application
need	O
high	O
accuracy	O
only	O
around	O
low-dimensional	O
manifolds	B-Architecture
of	O
the	O
state	O
space	O
,	O
or	O
important	O
state	O
"	O
highways	O
"	O
.	O
</s>
<s>
combined	O
the	O
SDM	O
memory	O
model	O
with	O
the	O
ideas	O
from	O
memory-based	B-General_Concept
learning	I-General_Concept
,	O
which	O
provides	O
an	O
approximator	O
that	O
can	O
dynamically	O
adapt	O
its	O
structure	O
and	O
resolution	O
in	O
order	O
to	O
locate	O
regions	O
of	O
the	O
state	O
space	O
that	O
are	O
"	O
more	O
interesting	O
"	O
and	O
allocate	O
proportionally	O
more	O
memory	O
resources	O
to	O
model	O
them	O
accurately	O
.	O
</s>
<s>
Dana	O
H	O
.	O
Ballard	O
's	O
lab	O
demonstrated	O
a	O
general-purpose	O
object	O
indexing	O
technique	O
for	O
computer	B-Application
vision	I-Application
that	O
combines	O
the	O
virtues	O
of	O
principal	B-Application
component	I-Application
analysis	I-Application
with	O
the	O
favorable	O
matching	O
properties	O
of	O
high-dimensional	O
spaces	O
to	O
achieve	O
high	O
precision	O
recognition	O
.	O
</s>
<s>
The	O
indexing	O
algorithm	O
uses	O
an	O
active	B-General_Concept
vision	I-General_Concept
system	O
in	O
conjunction	O
with	O
a	O
modified	O
form	O
of	O
SDM	O
and	O
provides	O
a	O
platform	O
for	O
learning	O
the	O
association	O
between	O
an	O
object	O
's	O
appearance	O
and	O
its	O
identity	O
.	O
</s>
<s>
Ternary	O
memory	O
space	O
:	O
This	O
enables	O
the	O
memory	O
to	O
be	O
used	O
as	O
a	O
Transient	O
Episodic	O
Memory	O
(	O
TEM	O
)	O
in	O
cognitive	B-Architecture
software	I-Architecture
agents	I-Architecture
.	O
</s>
<s>
This	O
work	O
has	O
been	O
incorporated	O
into	O
SpiNNaker	B-General_Concept
(	O
Spiking	O
Neural	O
Network	O
Architecture	O
)	O
which	O
is	O
being	O
used	O
as	O
the	O
Neuromorphic	O
Computing	O
Platform	O
for	O
the	O
Human	O
Brain	O
Project	O
.	O
</s>
<s>
Non-random	O
distribution	O
of	O
locations	O
:	O
Although	O
the	O
storage	O
locations	O
are	O
initially	O
distributed	O
randomly	O
in	O
the	O
binary	O
N	O
address	O
space	O
,	O
the	O
final	O
distribution	O
of	O
locations	O
depends	O
upon	O
the	O
input	O
patterns	O
presented	O
,	O
and	O
may	O
be	O
non-random	O
thus	O
allowing	O
better	O
flexibility	O
and	O
generalization	B-Algorithm
.	O
</s>
<s>
SDMSCue	O
(	O
Sparse	B-Architecture
Distributed	I-Architecture
Memory	I-Architecture
for	O
Small	O
Cues	O
)	O
:	O
Ashraf	O
Anwar	O
&	O
Stan	O
Franklin	O
at	O
The	O
University	O
of	O
Memphis	O
,	O
introduced	O
a	O
variant	O
of	O
SDM	O
capable	O
of	O
Handling	O
Small	O
Cues	O
;	O
namely	O
SDMSCue	O
in	O
2002	O
.	O
</s>
<s>
C	B-Language
Binary	O
Vector	O
Symbols	O
(	O
CBVS	O
)	O
:	O
includes	O
SDM	O
implementation	O
in	O
C	B-Language
as	O
a	O
part	O
of	O
vector	O
symbolic	O
architecture	O
developed	O
by	O
EISLAB	O
at	O
Luleå	O
University	O
of	O
Technology	O
:	O
</s>
<s>
CommonSense	O
ToolKit	O
(	O
CSTK	O
)	O
for	O
realtime	O
sensor	O
data	O
processing	O
developed	O
at	O
the	O
Lancaster	O
University	O
includes	O
implementation	O
of	O
SDM	O
in	O
C++	B-Language
:	O
</s>
<s>
Julia	B-Application
implementation	O
by	O
Brian	O
Hayes	O
:	O
</s>
<s>
Learning	O
Intelligent	O
Distribution	O
Agent	O
(	O
LIDA	B-Architecture
)	O
developed	O
by	O
Stan	O
Franklin	O
's	O
lab	O
at	O
the	O
University	O
of	O
Memphis	O
includes	O
implementation	O
of	O
SDM	O
in	O
Java	B-Language
:	O
</s>
<s>
Python	B-Language
implementation	O
:	O
</s>
<s>
Python	B-Language
and	O
OpenCL	B-Application
implementation	O
:	O
</s>
