Dynamical Field Theory Predicts a Developmental Reversal in an ANotBLike Task

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Dynamical Field Theory Predicts a Developmental
Reversal in anA-Not-B-Like Task

• Joshua Goldberg
• Gregor Schöner
• Esther Thelen

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Overview

• A-not-B Background.
• Dynamical Field Model.
• Distractor task.
• Modeling results.
• Discussion.
• Alternate model.

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From Piaget

• OBS. 39. At 010 (3) Jacqueline looks at the
  parrot on her lap. I place my hand on the
  object she raises it and grasps the parrot. I
  take it away from her and, before her eyes, I
  move it away very slowly and put it under a rug,
  40 cm away. Meanwhile I place my hand on her lap
  again. As soon as Jacqueline ceases to see the
  parrot she looks at her lap, lifts my hand and
  hunts beneath it.
• The Construction of Reality In
  The Child, 1954.

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Piagets A-not-B Task

• Hide a toy at location A.
• Hide it at a new location B.
• Perseverative error Baby searches at A.

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Adapted (I.U.) A-not-B apparatus

• Buttons that light up. (No hidden toys.)
• Focus moves from object-permanence to
  sensory-motor processes.
• Collect more data than simply A vs. B.
• (time spent, total force, number of presses)

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A-not-B task

• Train with A-trials
• Cue at A.
• Let the baby press.
• Test with a B trial
• Cue at B.
• Delay a few seconds.
• Let the baby press after the delay.

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Video B-trial
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Real world peresveration (nytimes)
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Some Principles of Dynamical Systems Theory

• Rich dependence on multiple task parameters.
• Continuous, metric time and space.
• Behaviors must be selected stably (not read out
  at an arbitrary instant.)
• Need to account for this stability.

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Dynamical Field Model

• Model behavior using a neural field with
  nonlinear interaction dynamics.

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Dynamical Field Model of Reaching Overview

• Activation field.
• Motor memory.
• Task-related inputs.
• Activation field interaction.
• Resting level.

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Activation field

• An activation function over reaching directions.
• A peak represents a decision to reach, but only
  if it is stable.

left
right
A B
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Motor memory

• Small bias to repeat previous reaches.
• Driven by above-threshold peaks in activation
  field. (Grows slowly.)
• Drives activation field in turn.

A B

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Task-related inputs

• Persistent structure of the task environment.
• e.g., two buttons, always there.

• Time-dependent inputs.
• e.g., experimenters cue at A.

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Activation field interaction

• Interaction when peaks are above threshold.
• Locally cooperative.
• Globally competitive.
• Activation field dynamics are bistable.

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Effects of bistability

• Less rigid
• Time to build up activation before closing out
  alternatives.
• Decision, once made, is very stable.

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Resting level

• controls how much input is needed to
  self-stabilize.
• Young (10 months) low resting level.
• Old (14 months) high resting level.
• Boost the resting level when toy is presented.

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Field Model Overview
Activation field
Task-related inputs
Motor memory (slow)
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Some tested A-not-B predictions.

• More A-trials
• More perseveration.
• Longer delay in the B-trial
• More perseveration.
• Distance between targets
• Closer gives more perseveration farther gives
  less.
• Glittery sleeves
• More perseveration.
• Sandbox task (unstructured space)
• Reach location drifts gradually over delay.

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Motivation for a new task

• Better access to dynamical interplay of two
  different sorts.
• between task parameters with opposing biases.
• between competing activation field peaks.

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The Distractor task

• Train with typical A-trials
• Cue at A.
• Let the baby press.
• Test with a Distractor trial
• Cue at A.
• Delay.
• Distractor (flashy light) at B sometime during
  delay.
• Let the baby press after the delay.

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Video Distractor trial
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Task parameters Example

• Distractor delay (earlier vs. later) and duration
  (longer vs. shorter).

time 0--1--2--3--4--5--6--7--8
Early/Long ------------
Late/Short -------------------
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Task parameters

• Amount of training
• Distractor duration
• Distractor delay
• Age

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Parameter-space

• Four task dimensions
• (training x duration x delay x age)
• Determine likely reach location. (A vs. B)
• Visualize parameter space via large numbers of
  simulated experiments.

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Full parameter space (preview)
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Piece of parameter-space, new
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Full parameter space (preview)
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The reversal predictions
A
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Late/short -- young
Late/short, young
Late/short, young
B
A
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Late/short old
Late/short, old
B
A
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Early/long old
Early/long, old
B
A
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Early/long -- young
Early/long, young
B
A
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The reversal predictions again.
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• Reaches to (e.g.,) A in different conditions
  occur for qualitatively different reasons.

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What the model tells us.

• Enumerates the possible dynamical stories.
• Relates qualitative regions of parameter-space by
  metric parameter shifts.

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Another measure looking

• Time-course of looking.
• Lookings relationship to reaching.

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Status of the Distractor study

• Testing in progress
• Distractor strength may be an issue.

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Munakatas A-not-B model

• A recurrent neural network model.

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Architecture
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Details

• Built-in spatially coherent connections from
  perceiving to looking and reaching.
• Memory needs to develop.
• Self-recurrent connections increase with age.
• Similar dynamics to ours, in part
• Competition crystallizes decisions.
• Older infants stabilize decisions better.

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How the model perseverates

• A-trials Hebbian learning from cover-type
  (what) to reach-to-A (where).
• B-trials During delay, decaying B-reach races
  with learned A-reach build-up.
• Interpretation normalized activations are read
  as probabilities.

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Revisiting A-not-B predictions.
Munakatas model

• More A-trials
• More perseveration.
• Longer delay in the B-trial
• More perseveration.
• Distance between targets
• Closer gives more perseveration farther gives
  less.
• Glittery sleeves
• More perseveration.
• Sandbox task (unstructured space)
• Reach location drifts gradually over delay.

• Yes
• Yes
• No
• Yes
• No

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The Distractor task?

• Distractor task in form described probably does
  not differentiate these two models.
• Difference is bistability.
• Transition from input-driven to self-stabilizing
  (developmentally or in parameter-space).
• Phase-shift (modulo task parameters) vs.
  parametric change.
• Testing seems a challenge!

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Conclusions

• Wide sampling of the parameter-spaces of
  dynamical models can yield illuminating,
  unforeseen predictions.
• We can enumerate the dynamical stories that are
  possible for a given task.
• It may take some care to demonstrate that weve
  experimentally captured the region of interest.
  
• (Looking may help.)

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• Thanks!

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abstract

• Dynamical Field Theory has led to a number of
  successful studies validating predictions that go
  well beyond where conceptual models of Piaget's
  A-not-B task would lead. I will start by
  explaining how the Field Model works. Then I
  will discuss a new variant on the A-not-B task.
  This new task pits against each other a cue and a
  distractor, occurring at different times. This
  lets us observe time-courses of competitive
  dynamics predicted by the field model that are
  not present in the basic A-not-B task.
• Large numbers of simulations across a matrix of
  experimental conditions show regions of
  parameter space that have qualitatively
  different dynamics. Focusing on two small pieces
  of parameter space, we find an interesting
  prediction of an developmental reversal of the
  effectiveness of a distractor. (One type of
  distractor that works for young infants no longer
  works when they're old another that does not
  affect young infants' reaches does work for the
  old ones.)

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Activation field interactivity

• Cooperative and competitive interaction.
• w(x-x) -wi weexp-(x-x)2/2sw2
• wi inhibitory strength
• we excitatory strength
• sw size of excitatory region
• Interaction is thresholded.
• Interactivity is dependent on resting-level.
• Bi-stable.

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Old stuff
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Another interesting place to look
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Piaget Perseveration

• OBS. 51. At 13 (9) Lucienne is in the garden
  with her mother. Then I arrive she sees me
  come, smiles at me, therefore obviously
  recognizes me... Her mother then asks her
  Where is papa? Curiously enough, Lucienne
  immediately turns toward the window of my office
  where she is accustomed to seeing me and points
  in that direction...
• The Construction of Reality In
  The Child, 1954.

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Piaget Perseveration

• OBS. 43. At 09 (16) Laurent swings in his
  hammock. In the cords above him I attach a chain
  which makes a noise at each swinging. Laurent
  looks at it constantly, with great interest. I
  then take the chain and bring it very slowly
  behind my back. Laurent watches this displacement
  of the object. As soon as the chain is hidden I
  shake it and it makes a noise Laurent then stops
  looking at me and searches for it in the air for
  a while, disregarding the direction from which
  the sound emanates.
• The Construction of Reality In
  The Child, 1954.

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A brief digression elsewhere in parameter-space.

• Old and young gt different effects of stretching
  the delay.

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What does the model really say?

• Considerations
• We do not go to the lab with known actual
  parameter ranges to test (although we do have
  intuitions).
• It may be difficult to falsify this set of
  predictions.

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A
B
Model of A-not-B error
TIME
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Activation field

• An activation function over reaching directions.
• A peak represents a decision to reach, but only
  if it is stable.

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Activation field (working on anim)

• An activation function over reaching directions.
• A peak represents a decision to reach
• but only if it is stable.