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A new type of Structured Artificial Neural Networks based on the Matrix Model of Computation. Sergio Pissanetzky. The Matrix Model of Computation (MMC) consists of two sparse matrices: M = (C, Q) C = Matrix of Services Q = Matrix of Sequences. - PowerPoint PPT Presentation
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A new type of Structured Artificial Neural Networks
based on the Matrix Model of Computation
Sergio Pissanetzky
The Matrix Model of Computation (MMC) consists of two sparse matrices:
M = (C, Q)
C = Matrix of Services
Q = Matrix of Sequences
The MMC is simple, yet very rich in features
Universal Self-organizing
Mathematically formal Natural ontology
Turing – equivalent Dynamic mode
Quantum-equivalent Connectionist
Relational database Massively parallel
Computer program Data channel
Object – oriented Transformations, refactoring
Algebra, formal algorithms
Training modes
w1
w2
Σ
x1
x2
b1
w3
w4
Σx3
x4
b2
φ1v1 x5φ2v2
equation serv x1 x2 x3 x4 x5 w1 w2 w3 w4 b1 b2 v1 v2v1=w1x1+w2x2+b1 ILF1 A A A A A Cx3=φ1(v1) φ1 C Av2=w3x3+w4x4+b2 ILF2 A A A A A Cx5=φ2(v2) φ2 C A
Converting a neural network to MMC
equation serv x1 x2 x3 x4 x5 w1 w2 w3 w4 b1 b2 v1 v2entire network ntw A A A C A A A A A A
equation serv x1 x2 x3 x4 x5 w1 w2 w3 w4 b1 b2 v1 v2v1=w1x1+w2x2+b1 ILF1 A A A A A Cx3=φ1(v1) φ1 C Av2=w3x3+w4x4+b2 ILF2 A A A A A Cx5=φ2(v2) φ2 C A
MMC as new type of neural network
● MMC is equivalent to the equations● MMC supports all ANN features.● In addition, MMC supports global features such as network structure and organization, objects and ontologies.
The Scope Constriction Algorithm(SCA)
SCA organizes information into objects and reveals the natural ontology of the system.
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
tc = a * fz
tj = b * fx
tf = d * vz
tk = b * fy
tb = a * fy
te = d * vy
tl = b * fz
ta = a * fx
td = d * vx
wz = vz + tl
tg = ta + td
wx = vx + tj
sx = rx + tg
th = tb + te
wy = vy + tk
ti = tc + tf
sz = rz + ti
sy = ry + th
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz syPROGRAM DATA
a, fz
b, fx
d, vz
b, fy
a, fy
d, vy
b, fz
a, fx
d, vx
vz
vx
rx
vy
rz
ry
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
Profiletc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz sy
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
Data channel
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz sy
“Turbulent” flow
CC
CC
CC
CC
CA C
A A CA C
A CA A C
A CA A C
A CA C
Service Commutativity
tc tj tf tk tb te tl ta td wz tg wx sx th wy ti sz sy
CC
A A CA C
CA C
CC
A A CA C
CA C
CC
A A CA C
CA C
td ta tg sx tj wx te tb th sy tk wy tf tc ti sz tl wztd = d * vx
ta = a * fx
tg = ta + td
sx = rx + tg
tj = b * fx
wx = vx + tj
te = d * vy
tb = a * fy
th = tb + te
sy = ry + th
tk = b * fy
wy = vy + tk
tf = d * vz
tc = a * fz
ti = tc + tf
sz = rz + ti
tl = b * fz
wz = vz + tl
PROGRAM DATAd, vx
a, fx
rx
b,fx
vx
d, vy
a, fy
ry
b, fy
vy
d, vz
a, fz
rz
b, fz
vz
“Laminar” flowG
H
H
H
G
G
Where do objects come from?
● SCA only minimizes the scopes.● In nature, scopes are resources.● Processes compete for resources.● Scopes are naturally minimized.● Objects and inheritance arise naturally.
● New information keeps arriving.● SCA keeps forming new objects.● Larger objects grow out of smaller objects. ● Objects evolve with time. Some stabilize.● The process continues indefinitely.
DYNAMICS
Lyapunov Dynamics vs. MMC Dynamics
Lyapunov MMCstate variables X(t) row indicesstate space continuous discretedynamics dX(t)/dt = F[X(t)] SCAattractors points, orbits classes of objectsequilibrium depends stable and convergentenergy function V[X(t)] profilebiologically viable
no yes
universal no yes
CONCLUSIONS AND OUTLOOK
● Objects and inheritance arise naturally when concurrent processes compete for resources. They are the solution to the optimum resource allocation problem.
● Impact on Computer Science, Software Engineering,Refactoring, the Semantic Web, Artificial Intelligence, Biology, Neuroscience, Linguistics, Jurisprudence.
● Conjecture: Our mind uses a similar process tomake ontologies.