Hybrid CASystems: Coupling Cellular Automata with Artificial Neural Nets

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Hybrid CA-Systems Coupling Cellular Automata
with Artificial Neural Nets

• Christina Stoica
• www.cobasc.de
• Institute for Computer Science and Business
  Information Systems
• University of Duisburg-Essen
• Germany

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Hybrid Systems
The nearly universal usability of cellular
automata (CA) is well known. Models become still
more powerful by coupling CA with artificial
neural nets (NN).

• Such CA-NN-models may be called "hybrid systems"
  that contain certain characteristics of
• learning,
• adaptability and
• flexibility.

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First example
SIMULATION OF TRAFFIC FLOWS
Kohonen Feature Map
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Second Example
NEURAL CA-SYSTEM
models individual learning processes in
dependency of a certain social milieu
The cells of the CA consist of Bi-directional
Associative Memory-Nets (BAM) and a Kohonen
Feature Map (KFM).
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simulation of traffic flows - CA
The cells of the CA represent different types of
cars, i.e. different with respect to velocity and
type of driving. These artificial cars move on
different lanes of a highway. Because of the
different velocities and types of driving
accidents and other problems will occur that lead
to backups. In particular, high density of
traffic will increase the probability of
accidents.
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simulation of traffic flows - CA
Obstacle If possible overtake, else slow down
Speed limit adapt the speed
The state of the cells is defined as S
0,1,2 0 speed up 1 overtake 2 adapt
the speed
Enlarged" Moore neighborhood i.e. two additional
cells outside of the Moore neighborhood are taken
into consideration. Is the cell on the right
line, then consider only the cells at the front,
on the left and the additional two cells on the
left side.
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simulation of traffic flows - CA
If car right line then compute the state St1
If R set of all cells on the right line, then
Sir ? R If ?Sir 4, then the car speeds
up. If L set of all cells on the left line,
then apply for all Sir ? R If ?Sil 4, then
the car can overtake
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simulation of traffic flows
In order to regulate the traffic and to avoid too
many accidents the access roads to the highways
are regulated by special traffic lights. These
traffic lights stop the access if the density of
traffic is too high and/or if there are already
accidents with according backups.
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simulation of traffic flows
In the CA-model the traffic lights are regulated
by a Kohonen feature map, which belongs to the
type of non supervised learning nets. The net
is trained to certain critical values of traffic
density.
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simulation of traffic flows
Assumptions There exists a station of
measurement, e.g. 1 km before and after an access
road. The numbers of cars, the distance and the
speed is measured.
The collected data from the CA are the training
data for the KFM.
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simulation of traffic flows - KFM
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simulation of traffic flows - KFM

Learning rule Winner-take-all
X(w1,....xn), wjwi,...wnj
XInputvector Wconnection strength
The amount the units learn will be governed by a
neighbourhood kernel h, which is a decreasing
function of the distance of the units from the
winning unit on the map lattice
j-z Distance of neuron j to the kernel ?zradius
within the units will be changed
The weights will be changed according to the
formula
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simulation of traffic flows - KFM
Learning rate (for this model)
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simulation of traffic flows
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simulation of traffic flows
The practical use of such a system is the
possible optimization of the real regulating
systems that already exist on the Autobahnen in
the German Rhein-Ruhr Region.
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Second Example
The Evolution of Neural Networks in a "Social"
Context
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The Evolution of Neural Networks in a "Social"
Context
A computational model as a possibility to analyse
some important concepts of cognitive development
embedded in a social context.
The model consists of
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Theoretical descriptions of cognitive ontogenesis
have a long and famous tradition in the last
years research changed the focus of descriptions
by including the interdependency between social
context and cognitive development.
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"dependency of social context"
cognitive development of a learning system
gets information from its environment
organizes its own evolution by constructing
cognitive representations
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• The factual development of the system is
  dependent on
• its particular developmental logic,
• i.e., the cognitive dynamics that governs
  its evolutionary path.
• environment or context respectively determines
  the development by orientating the system into
  certain directions and by slowing or
  fastening the whole process.

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Referring to cognitive ontogenesis, the fact must
be taken into consideration that intelligent
actors "construct" actively the concepts and
cognitive categories they use for world
representation.
Even learning processes by which people take over
concepts from other people are no simple
imitation processes but rather complex
constructive ones whose results are dependent on
the individual learning biography of the learners
and the social context in which they take over
the new concepts.
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Conceptual learning ? (supervised vs.
unsupervised learning)
Concept Building ? Analogy
Social learning
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Supervised vs. unsupervised learning
Supervised learning means that the learner gets
an immediate response (valuation) after solving a
problem.
Non supervised learning means that the cognitive
task has to be fulfilled by applying particular
schemas that the learner has learned
before. Usually theses processes are done without
immediate responses or valuation respectively by
the environment
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Bi-directional Associative Memory
(BAM) Hetero-associative network The network
gets pairs of vectors e.g. X1
(x11,x12,....,x1n)T Y1 (y11,y12,.....,y1m)T X2
(x21,x22,....,x2n)T Y2 (y21,y22,.....,y2m)T X3
(x31,x32,....,x3n)T Y3 (y31,y32,.....,y3m)T (
Contains the features) (contains the concepts
for the features) (x,y)??1,-1?
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BAM
Learning rule
The weight matrix is computed by the following
algorithm
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Creating new concepts
Each cognitive system has often the task to
create concepts by its own. This creative
operation is not done arbitrarily but mainly by
formation of analogy If a learner has to create
new concepts by himself - without supervising -
(s)he will rather often (perhaps not always) do
so by applying the logic (s)he has learned before.
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Creating new concepts - Analogy

If (X,-) is a new vector with no according
Y-part, then Y is calculated XW Y with XW
Y W is the weight matrix of X and Y,
with H(X,X) min for all X. H(X,X) is the
Hamming distance of X and X.
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Building semantical networks

The second type that is used to model the
generation of semantic networks is a "Kohonen
Feature Map" (KFM), which is able to learn in an
unsupervised way.
KFM is the best known example of unsupervised
learning. Its task is the collecting and
ordering of singular concepts, that is the
forming of concept clusters. Learning occurs in
this type conforming to the following learning
rule
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Kohonen Feature Map (KFM) Self-Organising Map
(SOM)

Learning rule Winner-take-all
X(w1,....xn), wjwi,...wnj
XInputvector Wconnection strength
The amount the units learn will be governed by a
neighbourhood kernel h, which is a decreasing
function of the distance of the units from the
winning unit on the map lattice
j-z Distance of neuron j to the kernel ?zradius
within the units will be changed
The weights will be changed according to the
formula
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Building semantical networks

The resulting ensemble of clusters is a formal
representation of a semantic network. The KFM
gets the information directly from the different
BAM networks. The Y-vectors represent the
concepts that shall be clustered according to the
X-vectors, which consist of the respective
features of perceptions.
The KFM clusters only the concepts and not the
features, so it is not always evident why the
clusters are generated this way (this fact can be
observed in human interactions as well).
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Learning in a social milieu
Each learner A (a cell in the CA) can be
represented as theaccording set of concepts
CA c1,....,cn with ci (Xi,Yi). If B ?
N(A) (the Moore neighbourhood of A) has a set
CBwith CB ? CD for all D ? N(A) and If ck
? CB and ck ? CA and If (Xk) is presented to A,
then CA c1,....,cn,ck in the next time step
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Reproduction
Two actors who are placed together on the grid
and who have reached a sufficient age can get a
child, i.e., a new actor is generated with an age
of 0. The relations between the parents and
the child become asymmetrical, that is
one-directional from the parents to the child.
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Transformation
Basically the actors (learners) are placed on the
grid according to the topology of a cellular
automaton (CA). This means that the relations
between the actors are symmetrical R(a,b)
R(b,a)

If two artificial actors became parents, then the
CA is transformed into a Boolean net (BN) with
asymmetrical or anti-symmetrical
relations. R(a,b) ??R(b,a) ? R(a,b) ? R(b,a)
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The Program
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Conclusions
The differences of individual developments are
often (although not always) due to the temporal
order in which learners get acquainted with new
concepts.
Therefore it is not enough to analyse the
difference of learning milieus in terms of the
number of concepts they offer to the learners but
it is nearly as important to observe the temporal
order of informational processes.
In this sense culture as ordered sets of concepts
must be taken into regard when analysing learning
processes.
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Conclusions
A social milieu that forces the learner to learn
everything the social environment offers can be
counterproductive for the learner he has to
spend all his time to take over knowledge already
known and can not unfold his own innovative
capability.
Therefore a cognitive development that allows the
learner to unfold his creativity must rely upon
an environment that allows "social forgetting",
i.e., ignoring some knowledge that has been
achieved by elders.
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Thank You