dynamics of learning: a case study
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Dynamics of learning: A case study. Jay McClelland Stanford University. Piaget’s theory of stages and development. Our knowledge takes qualitatively different forms at different stages This occurs because our knowledge schemas adapt with experience - PowerPoint PPT PresentationTRANSCRIPT
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Dynamics of learning: A case study
Jay McClellandStanford University
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Piaget’s theory of stages and development
• Our knowledge takes qualitatively different forms at different stages
• This occurs because our knowledge schemas adapt with experience– ‘Equilibration: Assimilation & Accommodation’
• Questions about the theory:– What do these words mean?– How does it work?– How can incremental adjustments lead to qualitative
change?
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An example domain: The balance scale
Will the scale tip left, tip right, or balance?
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Siegler’s First Two Rules
Rule assessment procedure: 24 problems of 6 typesChildren are characterized as ‘using a rule’ if 20/24 responses are consistent with it
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Findings
• Children 5-7 generally behave in accordance with Rule 1
• Then, most children’s behavior is briefly consistent with Rule 2, before they progress to more complex patterns of responding
• Around the time of these transitions, children exhibit increasing, graded sensitivity to the distance cue– Rule 1 kids will take distance into account if the distance
difference is large enough
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Siegler’s Intervention Experiment
• Two groups of ‘Rule 1’ children– Young (about 5 yrs old)– Older (7-8 yrs old)
• All children see 16 ‘conflict’ problems
• After the experience:– Older children progress to Rule 2– Younger children show no change or start choosing
randomly
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An Alternative to Rules• Knowledge is implicit
– In the connections in a neural network
• Experience with problems shapes the connections
• The network learns to become sensitive to weight and distance gradually through the accumulation of small changes
• Like children, it shows graded sensitivity to distance
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Graded Differences in Connections Lead to Different Outcomes of Learning at Different Points in Development
• Training with conflict problems at epoch 20 leads to degradation of performance.
• Training at 40 epochs leads to progress.
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Is the Model too Continuous?
• ‘Rules’ might be seen as similar to phases of matter (solid, liquid, gas)
• This view predicts that children’s performance should exhibit ‘catastrophe flags’ that signify such transitions
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Another Interesting Question
Can the model teach itself?
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Van der Maas et al Experiment
• Pre-test• A series of distance problems• Post-test• Over 300 children tested!
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Van der Maas et al Catastrophe Flags
• Pre and post-test– ‘Inaccessible region’– Jump across gap
• Distance series– ‘Maxwell’– ‘Hysteresis’– ‘Sudden jump’
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Findings
Rule 1Rule 2
Hysteris
is
Maxwell
Jump
Unscorab
le05
101520253035
Distance Series: Proportion of Children
Showing Each Type of Pat -tern
Proportion of Children
Pretest Scores
Posttest Scores
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Simulation with Model that Teaches Itself
Rule 1Rule 2
Hysteris
is
Maxwell
Jump
Unscorab
le0
10
20
30
40
50
60ChildrenSimulation
Model Pretest Scores
Model Posttest Scores
Distance Series: Children vs. Model
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Conclusion
• We are far from a perfect understanding of transitions in learning
• But we have come a long way• Simple rule-based models miss a lot• Models with learning dynamics capture quite a
lot more:– They show gradual knowledge accumulation and
yet capture patterns of change similar to what we see in children