Modelling Working Memory: Implementation of the TBRS

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Modelling Working Memory Implementation of the
TBRS

• Klaus Oberauer, University of Bristol
• Stephan Lewandowsky, University of Western
  Australia
• Simon Farrell, University of Bristol

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The Time-Based Resource-Sharing Model (TBRS)

• Cognitive Load operation duration / total time
• Predictions of TBRS
• Span (linear) function of Cognitive Load
• Span is independent of number of operations

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(No Transcript)
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Barrouillet et al., 2007, Exp. 3
Span 7.8 7.6 CL
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A dilemma for a decay model

• Relative to simple span (no processing), a
  single operation leads to substantial forgetting
• Further operations lead to hardly any additional
  forgetting

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For illustration(Oberauer Lewandowsky, 2008)
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A dilemma for a decay model

• Relative to simple span (no processing), a
  single operation leads to substantial forgetting
• ? steep decay function, weak refreshing
• Further operations lead to hardly any additional
  forgetting
• ? shallow decay function, strong refreshing

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A potential solution Equilibrium of decay and
refreshing

• Exponential decay and refreshing functions
• Loss constant proportion of current activation
• Gain constant proportion of distance to
  asymptote

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Toy Simulation Number of operations to reach
equilibrium
Process Duration 0.5 Refreshing Time 0.3
1

Decay 0.5 Refr 1
0.95
Decay 1 Refr 1.6
Decay 2 Refr 2.2
0.9
Decay 4 Refr 2.8
0.85
0.8
0.75
Proportion Correct
0.7
0.65
0.6
0.55
0.5

0
1
2
3
4
5
6
7
8
Number of Operations
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Interim Conclusion

• TBRS needs strong decay and strong refreshing

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Implementation The Architecture
aLTM
WM
Position
Position markers distributed, overlap declines
exponentially with distance WM items localist
representations activated LTM items localist
representations
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Assumptions

• Encoding
• Hebbian association between position marker and
  item (rate 6)
• Activation of item in LTM (rate 0.35)
• Both Exponential growth to asymptote 1

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Implementation Encoding
aLTM
WM
Position
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Implementation Encoding
aLTM
WM
Position
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Implementation Encoding
aLTM
WM
Position
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Implementation Encoding
aLTM
WM
Position
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Assumptions

• Recall
• Activate position markers in forward order
• ? reproduce item in WM layer
• Forward activation in aLTM to WM layer
• Add noise, pick the winner in WM layer
• Response suppression remove recalled items
  association from weight matrix

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Implementation Retrieval
aLTM
WM
Position
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Implementation Retrieval
aLTM
three
WM
Position
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Implementation Retrieval
aLTM
WM
Position
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Assumptions

• In between
• Exponential decay of weight matrix (rate 0.5)
• No decay of activation in LTM
• Refreshing in free time
• Retrieval Re-encoding
• Cumulative, starting at position 1 after each new
  item
• Rapid 80 ms per item

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Complex Span Experiment

• Number of operations after each item
• 0, 1, 4, 8
• Operation durations 0.3, 0.5, 0.7 s
• Free times 0.1, 0.6, 1.2 s
• Presentation time 1.5 s per item (0.5 s spent on
  encoding, rest on refreshing)

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Span over Load
op-duration 0.3 0.5 0.3 0.7 0.5 0.7
0.3 0.5 0.7 free time 1.2
1.2 0.6 1.2 0.6 0.6 0.1
0.1 0.1
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Proportion Correct over Load
op-duration 0.3 0.5 0.3 0.7 0.5 0.7
0.3 0.5 0.7 free time 1.2
1.2 0.6 1.2 0.6 0.6 0.1 0.1
0.1
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Serial Position Curve by N of Operations
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Serial Position Curve by Operation Duration
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Serial Position Curve by Free Time
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Trace of item strength over time6 items, 1
operation (0.3s), free time 0.6s
Strength activation of item through weight
matrix if corresponding position were reinstated
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Conclusion

• There is at least one implementation of the TBRS
  that works
• meaning
• it generates the declining span-over-load
  function
• it predicts a large effect of 0 vs. 1 operations,
  and a much smaller effect of 1 vs. more
  operations
• it generates realistic serial position curves
• But problems remain
• it predicts worse performance with 4 than 1
  operation
• most decay happens during recall