Modeling developmental transitions on the balance scale task

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Modeling developmental transitions on the balance
scale task

• H. van Rijn, M. van Someren, H van der Maas

Speaker Maurits Fassaert
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Contents

• Problem definition
• Model
• Results
• Questions / discussion

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Cognitive Science

• Studies the mind
• Computational models simulate cognitive processes
• Empirical data is compared to model results for
  qualitative similarities
• Modeling paradigms like ACT-R

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Balance scale task
-1
-2
-3
-4
-5
1
2
3
4
5
lt0 left
S
Dx Wx
0 balance
gt0 right
x?pins
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Criteria

• Stable behaviour and transitions
• Rule sets
• 0 Guess
• I Weight
• II Distance
• IIIConflict
• IVa Addition
• IVbTorque

Weight equal?
Guess?
no
yes
Balance
Greater weight down
Distance equal?
Distance equal?
yes
no
yes
no
Balance
Greater distance down
Greater weight down
Guess
Greater weightdistance down
Greater torque down
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Criteria

• Stable behaviour and transitions
• Rule sets
• Transitional effects without feedback

Maxwell convention
Delay convention
Sudden jump
Rule 2
Rule 1
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
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Criteria

• Stable behaviour and transitions
• Rule sets
• Transitional effects without feedback
• Torque difference effect

Rule I Balance
Rule II Left down
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Model
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Data set
Balance
Conflict Balance
Weight
Conflict Weight
Distance
Conflict distance
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ACT-R

• Cognitive architecture
• Programming language like framework
• Quantitative measurement
• Error
• Reaction time
• Neurological data
• Hybrid system
• Symbolic production rules
• Subsymbolic cost and utility functions

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ACT-R Modules
Environment
Visual module
Motor module
ACT-R buffers
Rule Composer
Procedural memory
Declarative memory
Pattern matching
Production execution
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ACT-R Memory
Declarative memory
Procedural memory
A-gtB
A
Activation
n
B ln ( S Tj-d)
U P G - C s
j1
U Utility P Successful applications G
Constant (20) C Cost s noise PC apply to
this rule and rules that follow
B Activation n number of retrievals Tj Time
since retrieval j d decay rate (0.5)
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Balance scale task in ACT-R

• Rules that compare differences left and right
• Weight introduced first at phase I
• Multi dimensionality introduced at phase II and
  III
• Multiplication introduced at phase IV
• ACT-R combines rules

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Results
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Criteria Rules Rule sets

• Combined rules resemble rule I to IV
• Rule sets emerge in the procedural memory and
  stabilize at their maximum capacity
• Introduction of new knowledge destabilizes the
  system
• Addition rule makes it hard for the system to
  learn the benefit of multiplication
• Rule IV is 100 accurate

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Phase 0
Rule that answers a guess is initially highly
activated, but slides down due to 66 error.
A(g) Answer guess
A(g)
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Phase I
Weight retrieval and uni-dimensional weight
production rules replace guessing by answering
balance, weight and conflict weight examples
correctly.
?W retrieve weight ?W A(W) if unequal weight,
answer based on weight W A(b) if equal
weight answer balance
New weight
?W A(W)
W A(b)
?W
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Phase II
Distance retrieval for examples with equal
weights refine the rule set to near the maximum
abilities of a uni-dimensional system.
W?D If equal weight then retrieve distance W,
?D A(D) if equal weight, but unequal distance
then answer based on distance W,D A(b) if
equal weight and distance then answer balance
New distance
W?D
W?D A(D)
WD A(b)
W A(b)
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Phase III
Injection of a rule that retrieves distance even
when weights are not equal signifies
multi-dimensional thinking.
? W?D If unequal weight then retrieve
distance ?W,D A(w) if unequal weight, but
equal distance then answer based on weight ? W,
?D A(g) if unequal weight and distance, answer
a guess
New multidemsional
?WD A(W)
?W?D
?W? D A(g)
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Phase IV
Injection of a multiplication production rule
finally phases out guessing and strengthens the
use of multi-dimensional thinking.
? W, ?D M If unequal weight and distance, use
multiplication
?W? D M
New Multiplication
?W?D
?W? D A(g)
?W A(W)
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Criteria Transitional and Torque-difference
effects

• Feedback is no longer provided
• Chunk activation is modified AB ?d/c

Rule I Rule II Rule I
Activation
Maxwell transition
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Criteria Transitional and Torque-difference
effects

• Feedback is no longer provided
• Chunk activation is modified AB ?d/c
• The balance between activation and saliency
  explains the different effects

Delayed
Sudden jump
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Criteria Transitional and Torque-difference
effects

• Feedback is no longer provided
• Chunk activation is modified AB ?d/c
• The balance between activation and saliency
  explains the different effects
• Torque difference is also based on distance
  difference

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Conclusion

• The model is able to reproduce all the empirical
  findings
• Future work reaction time
• Questions?
• Discussion!