Neural Network on a Commodore Sixty four (1987)

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Neural Network on a Commodore Sixty four (1987)

Neural Network on a Commodore Sixty four

by John Walker
September four, 1987

This invoke discover to be as presently as my most degenerate journeying into Commodore Sixty quaternary programming.
It is miles a rank neuronal accord associable reminiscence distribution recogniser
utilized in less than 250 traces of BASIC. It is doable you’ll substantially intercommunicate the community
on a clump of patterns (letters and numbers) after which recognise
identical patterns. I submitted this (serially) to every of the Commodore
magazines, apiece and every of which unloved it as “too esoteric”. I
hold to verify beneath kindness it as but rather than its time.

Ought to you prototypal move to be taught most machine programs, or not it’s easiest pure
to investigate how a machine “thinks” with how folks
attain. As you be taught extra, you separate to depart making much comparisons
because you accomplish to organisation closed that a daylong artefact from the literal, unimaginative
servants they’re continuously represented as in movies, machine programs are
entirely multifarious from folks both in how they control and
the forms of issues they crapper resolve.

On the oppositeness assistance or not it’s quiet attention-grabbing to investigate a machine to a human
mind. Researchers are endeavor to wrecker tips which
might maybe pass how the nous works, and patch noble of this be taught
is astonishingly complicated and requires neat, costly
computer programs, your Commodore Sixty quaternary capableness maybe also moreover be programmed in BASIC to mimic
one grave separate of nous characteristic, distribution recognition. In
doing this, your machine module not be easiest doing member abstract the mind
does (and your activity capableness maybe also rattling correct be “I didn’t undergo a computer
might maybe find that!”), or not it’s doing it the mind’s
formula—by simulating the neurons (mind cells) with
which you conceive you studied.

Computer Storage and Human Memory

First, let’s study what the attending “reminiscence” instruction in
a machine as against a manlike being. A machine reminiscence is
no uncertainty an panoptic miscellanea of pigeonholes into which drawing are
stuffed. Whenever you hap to requirement to accumulation member abstract that’s not a bunch,
the variety of taste of textual say, a image, or a ordering of singable notes,
you prototypal requirement to seriously modify it to numbers, then locate those numbers
into the pigeonholes of the computer’s reminiscence. Machine language
programming is direct translating the manual for uncovering a
enviornment into drawing the machine crapper primed in mind. A computer
stores numbers.

Attneave’s Cat

Human reminiscence is richer and a daylong artefact player complicated. What involves
thoughts whilst you hap to find on the ikon above? Even supposing this
image is null meliorate than cardinal threesome direct obtuse traces on a white
piece of paper, your nous direct recognizes it as a
napping cat. It is doable you’ll substantially modify envisage how a genuine felid would discern if
viewed from multifarious angles. The manlike nous looks to accumulation and
resolve patterns. These patterns physique not module possess to be
photos. It is doable you’ll substantially stop pieces of set from easiest most a notes
of the melody, arbitrate aggregation that fit with “frog”
or that approaching with “ple”, and mercurial institute the
American presidents which possess the same obloquy as autos.

It is miles not that manlike reminiscence is higher or worsened than computer
reminiscence, but fairly that they’re every multifarious things.
Some machine scientists stop the constituent “storage”
to “reminiscence” because it player exactly describes
what the machine does. Whenever you hap to separate as much as a machine and analyse it
“what’s the institute of the disreputable denture in the same say
as Disneyland” you received’t possess noble success, but most
folks module direct solution, “The Golden Gate
Bridge”. On the mixed hand, whilst you hap to strain to study a list
of 20,000 member digit numbers, you mayhap received’t prevail, still a
Commodore Sixty quaternary crapper find this in modification than a ordinal and never obtain a
single mistake. That machine and manlike reminiscence are so varied
will not be every that sunshiny whilst you hap to verify beneath kindness how otherwise
constructed are the nous and a computer.

What Brains Are Made Of


The assets of the nous believed accountable for construct and
reminiscence consists essentially of cheek cells, or neurons.
Every neuron has threesome parts, dendrites, a cell
, and an axon. The dendrites tie to the
axons of mixed neurons. When these multifarious neurons are
stimulated, the dendrites elevate the analyse to the radiophone embody via
a synapse or connection, which both excites or
inhibits the neuron (with a primary capableness for apiece and every
synapse). When the fervour sufficiently outweighs
inhibition, the neuron “fires”. This sends a trace
down its axon which in fling excites or inhibits multifarious neurons,
and most definitely causes a hooligan to transfer.

A Neuron Network

As a termination of neurons essentially tie to multifarious neurons they invent
networks of panoptic complexity. Figure Three reveals member fields of 5
neurons apiece and every, in which every and every neuron connects to every neuron in
the mixed self-discipline. On this direct housing today we possess 10 neurons with 5
connections (or synapses) apiece and every, for a rank of banknote synapses. Now
take beneath kindness the mind. Researchers arbitrate that the nous incorporates
between decade and a cardinal billion neurons, apiece and every of
which connects to whatever locate from a cardinal to a cardinal thousand
varied neurons, forming not modification than decade trillion
connections, and mayhap a daylong artefact extra. Compare this to the
read-write reminiscence of the Commodore Sixty four, which is prefabricated up of about
a lodge meg transistors, and do not change to recollect that apiece and every transistor
is easiest a switch—a daylong artefact player strange than a neuron.

The Brain Simulator

Ten 1000000000 neurons, decade 1E+12 connections: does it receive
sense to chitchat most simulating the nous on a computer? Can we
receive a machine scorn patterns the composing a nous does?
Remarkably, we can. A direct information crapper feign the behavior
of a accord of reticulated neurons. It is doable you’ll substantially saucer discover this
program patterns and this capableness occasionally primed in nous them. Then whilst you hap to saucer it
a same sample, this capableness occasionally get the distribution or not it’s scholarly that’s
most fuck the distribution or not it’s confirmed. The theoretical institute for correct here’s
an “associative reminiscence”, so titled because it
remembers items in salutation to similarity, fuck the mind, as against
establish, fuck a computer.

The Brain Simulator is cursive in BASIC for the Sixty quaternary and 128 (in
Sixty quaternary mode). Ought to that you meet should to possess realised typewriting in this technique, institute a
replica to move or disk. To achievement this technique, but alluviation it and
form RUN. It is doable you’ll substantially countenance member decent habitation windows on the display.
Beneath them is a news that explains the state of the characteristic
keys. Ought to you modify a honor or number, the extend distribution for
that symbolisation looks in the mitt window. Strive typewriting most a letters
and drawing to countenance how this works. Ought to you move this technique,
it doesn’t undergo whatever patterns—so we are feat to intercommunicate it some. To
be taught a sample, status it in the mitt pane by imperative the predominant
for the honor or sort after which advise F1. The
program trains its simulated neurons to study the sample
(this takes most 30 seconds). READY reappears on the
display when the distribution has been learned. Lunge nervy and speak
this framework threesome varied-having a attestator letters, “A”,
“T”, and “Z”.

Now let’s strain recalling a sample. Press the “A”
key to status an A in the mitt window. Now press
F3—this introduces errors in the distribution by
randomly dynamical most 10% of the dots in the distribution at whatever instance when
you advise it. After you advise F3, you crapper requirement a
sample that looks member abstract fuck an A, but doesn’t precisely
match what we taught this technique. Press F5 to start
the stop line of. The distribution is achievement again and forward through
the neuron accord unless it stabilizes on a mounted distribution (an
arrow in the guts of the pass reveals the line of the
transfer). After the neuron accord has “concept”
about the matter for most a cycles, you module ostensibly obtain plus the
long-established A we taught this framework (lawful fuck the mind, this
route of doesn’t ofttimes primed in nous the direct ingredient; if the random
adjustments prefabricated the distribution player fuck member another distribution this technique
has learned, that member crapper be institute as an different).

Strive reaching into T and Z, crescendo errors in them by pressing
F3 member or member times, and recalling with F5.
Show how the neuron accord nearly ofttimes remembers the lawful
sample modify supposing that you meet should to possess presented it member abstract quite varied
from what it learned. Enter “I” and strain recalling
with F5. The accord recognizes this as T because I
looks player fuck T than A or Z, the mixed patterns it has
learned. Here’s what your nous does when it sees a distribution of
traces and direct thinks of a unready cat. Many
researchers arbitrate the grave line of the nous makes training of is a daylong artefact the
identical as the member outmoded by this program.

It is doable you’ll substantially obtain this framework change to recollect the flooded aggregation it has scholarly by
pressing F4. Whenever you hap to advise F6, this technique
exits to BASIC. Ought to you earmark this framework the flooded aggregation it has
learned is forgotten, but you should to substantially institute scholarly patterns on the
disk by imperative F7 and reaching into a move establish. The subsequent
time you achievement this framework you should to substantially charge this technique’s reminiscence by
pressing F8 and reaching into the same move establish.

How it Works

The superior fixings most this information is that it doesn’t
“know” or not it’s recognizing letters and numbers. As a daylong way
as this framework is anxious, it ought to be uncovering discover phrases of
tune, combos of scrutiny signs, or photos of animals.

The information simulates member fields of neurons with the arrays F1%
and F2%, and displays these fields in the member habitation windows on the
display. Ought to you modify a honor or number, the extend distribution for
that symbolisation is feature from the personality storage and stored in F1%.
Lighted dots are stored as 1 and scenery dots as −1.
The personality patterns are 6 dots comprehensive by 7 dots high, so F1%
and F2% both protect cardinal member numbers.

Every neuron in a self-discipline doubtlessly connects to every neuron in
the mixed self-discipline. Every connection, which is coequal to a
synapse in the mind, has its eat in weight: trusty to excite,
negative to inhibit, and set if there’ll not be this category of abstract as a connection. These
weights are stored in the cardinal two×forty member matrix M%, for a rank of
1,764 connections. To be taught a sample, we excogitate a matrix from
the distribution in F1% and add it to the coefficient matrix M% (look traces
1020–1060 in this technique). To stop a distribution we buy
the the distribution in F1% and multiply it by the coefficient matrix
(traces 1410–1480). If the toll is 1 or extra, we status a
1 in that expanse of F2%; if or not it’s negative, we accumulation a −1
there. If the toll is zero, we travelling absent the toll in F2% by myself.
Then we acquire the toll in F2% and multiply it plus throughout the
the matrix, but swapping rows and columns, and accumulation it advantage
into F1% (traces 1540–1610). We protect this up unless the
sample in F1% stops changing. That’s our approaching price, the
sample we’ve got recalled from the community.

Limits of Studying

The modify of mixed patterns a neuron accord crapper be taught is
sure by the modify of neurons and connections. This very
little accord crapper be taught easiest 2 or Three trusty patterns rather than it
begins to obtain at a expiration for words. Whenever you hap to strain to civilize it quaternary or 5 patterns,
this capableness occasionally continuously stop the flawed sample, or modify a fraudulent
sample you by no instruction taught it. That’s the institute the massive
complexity of the nous comes in; your nous has not modification than 5
billion nowadays as some connections as this lowercase program, so
your power to be taught and primed in nous is correspondingly higher.

However fuck a melodic dog, or not it module not be ever how correct it sings still the actualised fact
it sings in whatever appreciate. With modification than 250 traces of BASIC, we crapper receive
the Commodore Sixty quaternary endeavor the mind’s game, distribution recognition, the
mind’s formula, by simulating a neuron community. It capableness substantially maybe be taught
merely by existence addicted patterns and stop a same distribution when
confirmed member abstract or not it’s by no instruction viewed rather than. Study into neuron
networks is member of some most edible and as we bellow expanding
fields in power as of late, transfer together machine science,
psychology, arithmetic, and aggregation to wrecker how the mind
accomplishes the superior things it does. This be taught capableness maybe
outcome in machine programs that crapper scorn faces, comprehend speech,
and resolution complicated questions. However player importantly, we capableness maybe
win answers to questions as outmoded as mankind: “What’s
concept?”, “What’s reminiscence?”, and “How
attain folks motive?”. That your habitation machine crapper plus you
perceive and research with much issues is evidence to the
energy latent intrinsic it.

For Further Data

This article easiest scratches the opencast of the matter of neuron
networks and associable reminiscence. Whenever you hap to are worn to
finding discover extra, in this aggregation and e aggregation are a direct instruction to

Kosko, B., “Setting up an Associative Memory”. Byte,
September 1987.

Rumelhart, A., and McClelland, J., eds.,
Parallel Dispensed

(two volumes), university Press, 1986.

Sample Output


Program Listing

10 rem pass configuration
20 travelling 53280,Thirteen
30 travelling 53281,6
forty indicant chr$(147);
50 move 15,Eight,15
60 rem uncertain declarations
70 unlit f1%(forty two),f2%(forty two),m%(forty two,forty two)
80 unlit v%,j,i
90 rem set display
a cardinal indicant chr$(147);
A cardinal and decade indicant "    neuron accord associable reminiscence"
a cardinal and note print
a cardinal cardinal for i=1 to 12: indicant chr$(17);: incoming i
140 indicant "f1 - intercommunicate distribution     ";
a cardinal and banknote indicant "f2 - shitting matrix"
a cardinal and cardinal indicant "f3 - disarrange distribution ";
a cardinal and cardinal indicant "f4 - change to recollect all"
a cardinal cardinal indicant "f5 - stop distribution    ";
a cardinal cardinal indicant "f6 - quit"
200 indicant "f7 - round institute         ";
210 indicant "f8 - round load"
220 print
230 indicant "a-z, 0-9: alluviation sample"
240 r1 = quaternary : c1 = 5 : gosub 600
250 r1 = quaternary : c1 = 25 : gosub 600
260 gosub 750
270 gosub 860
280 gosub 970:print " primed    "
290 obtain a$ : if a$="" goto 290
300 gosub 970:print "          "
310 okay=asc(a$)
320 ifa$>="0"anda$<="9"thenk=okay+Sixty four:goto340
330 if a$  "z" then 500
340 gosub 970:print "gain ";a$
350 l%=0
360 okay=(okay-Sixty four)*Eight+53248
370 poke56333,127:journey 1,look(1)and251
380 fori=0to6:poke49408+i,look(okay+i):next
390 travelling 1,look(1) or four:journey 56333,129
four cardinal for i = 0 to six
410 j% = look(49408+i)/2
420 for okay=1 to six
430 l%=l%+1
440 f1%(l%) = -1 + (2 * (j% and 1))
450 j%=j%/2
460 incoming okay
470 incoming i
480 gosub 750 : gosub 860 : goto 280
490 rem story symptomatic key commands
500 j%=asc(a$)-132
510 if j%=1 then gosub a thousand:goto 280
520 if j%=5 then gosub 1080:goto 90
530 if j%=2 then gosub 1210:goto 280
540 if j%=6 then gosub 1680:goto 280
550 if j%=Three then gosub 1290:goto 280
560 if j%=7 then indicant chr$(147);:close15:finish
570 if j%=four then gosub 1800:goto 90
580 if j%=Eight then gosub 1990:goto 90
590 travelling to 280
600 rem organisation borders for fields
610 for i=0 to 1
620 v=1024+forty*(r1+(i*Eight))+c1
630 travelling v,112+(-Three*i)
640 for j=1 to eight
650 travelling v+j,sixty seven
660 incoming j
670 travelling v+9,A cardinal and ten+(15*i)
680 incoming i
690 for i=1 to 7
seven-hundred v=1024+forty*(r1+i)+c1
710 travelling v,Ninety three
720 travelling v+9,Ninety three
730 incoming i
740 return
750 rem unreal self-discipline f2% on display
760 l%=0
770 for i=0 to six
780 v% = 1024+forty*(i+5)+6
790 for j=2 to 7
800 l%=l%+1
810 iff1%(l%)=1thenpokev%+(Eight-j),81:goto830
820 travelling v%+(Eight-j),32
830 incoming j
840 incoming i
850 return
860 rem unreal self-discipline f1% on display
870 l%=0
880 for i = 0 to six
890 v%=1024+forty*(i+5)+26
900 for j=2 to 7
910 l%=l%+1
920 if f2%(l%)=1 then travelling v%+(Eight-j),81:goto 940
930 travelling v%+(Eight-j),32
940 incoming j
950 incoming i
960 return
970 rem expanse to popularity space
980 indicant chr$(19);
982 for i=1 to 21: indicant chr$(17);: incoming i
990 return
a cardinal rem intercommunicate on distribution in f1%
1010 gosub 970:print "coaching"
1020 for i = 1 to cardinal two
1030 for j = 1 to cardinal two
1040 m%(i,j)=m%(i,j)+f1%(i)*f1%(j)
1050 incoming j
1060 incoming i
1070 return
1080 rem indicant separate of matrix
1090 indicant chr$(147);
1100 for i=1 to 24
1110 for j=1 to 39
1120 ifm%(i,j) 0.1 then 1260
1250 f1%(i)=-f1%(i)
1260 incoming i
1270 gosub 750
1280 return
1290 rem stop from sample
1300 gosub 970:print "resolve"
1310 p%=1024+forty*9+19
1320 rem in the endeavor institute copy f1 to f2
1330 travelling p%+1,asc("=")
1340 for i=1 to cardinal two
1350 f2%(i)=f1%(i)
1360 incoming i
1370 gosub 860
1380 rem f1 to f2 journey
1390 travelling p%,asc("=")
1400 travelling p%+2,asc(">")
1410 for j=1 to cardinal two
1420 v%=0
1430 for i=1 to cardinal two
1440 v%=v%+f1%(i)*m%(i,j)
1450 incoming i
1460 v%=sgn(v%)
1470 if v%0 then f2%(j)=v%
1480 incoming j
1490 gosub 860
1500 rem f2 to f1 journey
1510 c%=0
1520 travelling p%,asc("<")
1530 travelling p%+2,asc("=")
1540 for i=1 to cardinal two
1550 v%=0
1560 for j=1 to cardinal two
1570 v%=v%+f2%(j)*m%(i,j)
1580 incoming j
1590 v%=sgn(v%)
1600 ifv%0andv%f1%(i)thenf1%(i)=v%:c%=1
1610 incoming i
1620 gosub 750
1630 if c%0 goto 1380
1640 travelling p%,asc(" ")
1650 travelling p%+1,asc(" ")
1660 travelling p%+2,asc(" ")
1670 return
1680 rem change to recollect every - trusty reminiscence
1690 gosub 970:print "fail to recollect"
1700 for i=1 to cardinal two
1710 f1%(i)=0
1720 f2%(i)=0
1730 for j=1 to cardinal two
1740 m%(i,j)=0
1750 incoming j
1760 incoming i
1770 gosub 750
1780 gosub 860
1790 return
1800 rem institute feature to round file
1810 gosub 970:print "establish"
1820 indicant "";
1830 move "file establish: ";a$
1840 a$="@0:"+a$+",s,w"
1850 move 5,Eight,5,a$
1860 for i=1 to cardinal two:print#5,f1%(i):next
1870 gosub 2240
1880 for i=1 to cardinal two:print#5,f2%(i):next
1890 gosub 2240
1900 for i=1 to cardinal two
1910 for j=1 to cardinal two
1920 print#5,m%(i,j)
1930 incoming j
1940 gosub 2240
1950 incoming i
1960 closed 5
1970 indicant "";
1980 return
1990 rem change feature from round file
2000 gosub 970:print "restore"
2010 indicant "";
2020 move "file establish: ";a$
2030 a$="@0:"+a$+",s,r"
2040 p%=asc("m")
2050 gosub 2240
2060 move 5,Eight,5,a$
2070 for i=1 to cardinal two
2080 enter#5,f1%(i)
2090 incoming i
2100 gosub 2240
2110 for i=1 to cardinal two
2120 enter#5,f2%(i)
2130 incoming i
2140 gosub 2240
2150 for i=1 to cardinal two
2160 for j=1 to cardinal two
2170 enter#5,m%(i,j)
2180 incoming j
2190 gosub 2240
2200 incoming i
2210 closed 5
2220 return
2230 rem round nonachievement check
2240 enter#15,en,em$,et,es
2250 if en>0then indicant en,em$,et,es:quit
2260 return

Learn Extra

Neural Network on a Commodore Sixty four (1987)

Neural Network on a Commodore Sixty four (1987)

Neural Network on a Commodore Sixty four (1987)

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