Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica ...
-
Upload
alexander-smith -
Category
Documents
-
view
217 -
download
2
Transcript of Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica ...
![Page 1: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/1.jpg)
Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets
Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets
Christina Stoicawww.cobasc.de
Institute for Computer Science and Business Information Systems
University of Duisburg-Essen
Germany
![Page 2: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/2.jpg)
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.
![Page 3: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/3.jpg)
First example
SIMULATION OF TRAFFIC FLOWS
Kohonen Feature Map
The cells of the CA represent different types of cars
regulates the special traffic lights
![Page 4: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/4.jpg)
Second Example
NEURAL CA-SYSTEM
The cells of the CA consist of Bi-directional Associative Memory-Nets (BAM) and a Kohonen Feature Map (KFM).
models individual learning processes in dependency of a certain social milieu
![Page 5: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/5.jpg)
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.
![Page 6: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/6.jpg)
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.
![Page 7: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/7.jpg)
If car = right line then compute the state St+1:
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
sir t 1
0,if skr t 4k,r R ir
1,if skr t 4 sk,l t 4k,l
k,r R ir
2,if sir t 4 sk,l t 4k,l
k,r R ir
simulation of traffic flows - CA
![Page 8: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/8.jpg)
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.
![Page 9: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/9.jpg)
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.
![Page 10: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/10.jpg)
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.
![Page 11: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/11.jpg)
simulation of traffic flows - KFM
Traffic light offNormalphase of
traffic light
Trafficlight
flashes x 45 X - -
45 x 25 - X -Distance
(in m) x 25 - - X x 90 X - -
90 x 50 - X -Speed
(in km/h)x50 - - Xx 20 X - -
20 x 33 - X -Number of carsx 33 - - X
![Page 12: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/12.jpg)
simulation of traffic flows - KFM Learning rule: Winner-take-all:
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
wij
t 1 wij
t oi w
jt
x wz min
ix w
jX=(w1,....xn), wj={wi,...wnj}
X=InputvectorW=connection strength x w
ij x
i w
ij 2
i
1
2
hiz exp j z 2 / 2 z2
wij t 1 wij t hiz x t w ij t , j The weights will be changed according to the formula:
j-z= Distance of neuron j to the kernel
z=radius within the units will be changed
![Page 13: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/13.jpg)
simulation of traffic flows - KFM
(t1) max* ( min/ max)t / t max
Radius:max
maxminmax/)/(*)1( tttz
t : actual iteration step max1 tt maxt : number of iteration steps
max : size of the radius at the beginning (in this case 40)min : limit of the radius (in this case 2)
For )(tz is valid: maxmin )( t
Learning rate (for this model):
t : actual iteration step max1 tt maxt : number of iteration stepsmax : learning rate at the beginning (in this case 1)min : minimum of the learning rate (in this case 0,001)
For )(t is valid: maxmin )( t
![Page 14: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/14.jpg)
simulation of traffic flows
![Page 15: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/15.jpg)
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.
![Page 16: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/16.jpg)
Second Example:
The Evolution of Neural Networks in a "Social" Context
![Page 17: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/17.jpg)
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
Neural Networks (BAM / SOM)
individual level
Cellular Automaton Boolean Network social level
![Page 18: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/18.jpg)
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.
![Page 19: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/19.jpg)
"dependency of social context"
cognitive developmentof a learning system
gets inform
ation from
its enviro
nment
organizes its own evolution by constructing cognitive representations
![Page 20: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/20.jpg)
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.
![Page 21: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/21.jpg)
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.
![Page 22: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/22.jpg)
Concept Building Analogy
Conceptual learning (supervised vs. unsupervised learning)
Social learning
![Page 23: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/23.jpg)
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
![Page 24: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/24.jpg)
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
![Page 25: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/25.jpg)
„Learning rule“:
The weight matrix is computed by the following algorithm:
BAM
![Page 26: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/26.jpg)
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.
Creating new concepts
![Page 27: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/27.jpg)
Creating new concepts -> Analogy
If (X,-) is a new vector with no according Y-part, then Y is calculated:
XW = Y withX‘W = 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‘.
![Page 28: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/28.jpg)
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:
![Page 29: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/29.jpg)
Kohonen Feature Map (KFM)
Self-Organising Map (SOM)
Learning rule: Winner-take-all:
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
wij
t 1 wij
t oi w
jt
x wz min
ix w
jX=(w1,....xn), wj={wi,...wnj}
X=InputvectorW=connection strength x w
ij x
i w
ij 2
i
1
2
hiz exp j z 2 / 2 z2
wij t 1 wij t hiz x t w ij t , j The weights will be changed according to the formula:
j-z= Distance of neuron j to the kernel
z=radius within the units will be changed
![Page 30: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/30.jpg)
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).
![Page 31: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/31.jpg)
![Page 32: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/32.jpg)
![Page 33: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/33.jpg)
![Page 34: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/34.jpg)
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 CB
with
CB | | CD for all D N(A) and
If ck CB and ck CA andIf (Xk) is presented to A, then
CA ={c1,....,cn,ck} in the next time step
Learning in a social milieu
![Page 35: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/35.jpg)
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.
![Page 36: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/36.jpg)
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)
Transformation
![Page 37: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/37.jpg)
The Program
![Page 38: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/38.jpg)
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.
![Page 39: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/39.jpg)
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.
![Page 40: Hybrid CA-Systems: Coupling Cellular Automata with Artificial Neural Nets Christina Stoica Institute for Computer Science and Business Information.](https://reader035.fdocuments.net/reader035/viewer/2022070305/551470775503462d4e8b6016/html5/thumbnails/40.jpg)
Thank You