Presenting A Dynamic Field Model of

The A-not-B Error

What is the A-not-B error?• A-not-B involves infants reaching for a hidden toy

at the incorrect location when presented with two possible locations.

• The toy is repeatedly hidden at location A. After a short delay, infants are then allowed to reach for and retrieve the toy.

• After a few trials the toy is then clearly hidden in location B. After a short delay, they are then allowed to reach for the toy. Infants 8 to 10 months of age consistently reach to location A despite clearly seeing the toy hidden at location B.

WHY?

A Dynamic Systems Explanation• Goal: Avoid explanations based on “knowledge”,

focusing instead on what infants are doing. The dynamic processes guiding infant reaching are age-independent, general, and intricately woven with the real-time demands of the task.

• Before any model can be designed, a detailed examination of the task is necessary. This task analysis describes the central dynamics of the task in order to facilitate the creation of accurate model parameters.

• The model must account for the infant’s perseverative reaching using general and content independent processes in order to be consistent with a dynamic systems interpretation of the task.

A Task Analysis

• Task Input – The box and two identical lids• Specific Input – The interesting toy• Attention – Infants attend to the input• Memory – Infants must remember the toy location• Look – Infants must look at the input to determine location• Plan – Infants must plan their movement• Delay – Delay period of 3 to 5 seconds before allowing reach• Reach – Infants must reach for the toy• Repetition – The same reach must be repeated across trials

Look

Task

Specific

Look

Task

Specific

Plan

Look

Task

Specific

Plan

Reach

Look

Task

Specific

Plan

Reach

Remember

How are the task dynamics translated for the model?

• Two main model components: The movement planning field and the inputs to the field

• The movement planning field represents the integration of visual input and motor memory which create the decision to reach to A or B.

• The field inputs shape the change of the action decision over time.

TIME

A B

Model of A-not-B error

The mathematical form of the model:

where

is a nonlinear sigmoidal threshold function.

Field Properties

• Activation level – The level of excitation at each point in the field

• Reach threshold – When activation at a certain location crosses this threshold, a reach can be initiated in that direction.

• Time – Because the field is dynamic, it changes gradually over time. The time scale allows activation to build up or decay gradually over a continuous period.

Movement parameter

Act

ivat

ion

A B

Movement parameter

Act

ivat

ion

A B

Movement parameter

Act

ivat

ion

A B

Decision evolves in movement parameter space.

Excitation and Inhibition

• Sites in the field are coupled and cooperative in that each has the ability to both excite and inhibit the activation levels of its neighbors.

• Only sites which are activated will excite their neighbors. This excitation has a graded range such that close sites get more activation and far sites become inhibited.

• h – The initial resting state of activation is set at a certain level in the field.

• Noise – The field has a scalable noise level.

Field Inputs

• Task input – A constant input level related to the initial properties of the task environment.

• Specific input – The temporary visual or auditory cue provided by the experimenter’s interaction with parts of the task input.

• Memory input – Retains the movement planning fields previous activation levels. This storing of the previous activation levels also allows an indirect storage of previous levels of specific and task input. Memory input is critical for gradual change over time.

A BA B

A B A B

Task input: properties of the tonic task input.

A B

A B

A B

Specific input: the immediate, transient cue.

TIME

A B

Task input Specific input

Generate

reach plan

Memory is carried over to the next trial.

At the second reach to “A”

Memory input Task input

Specific input Generatereach plan

After many reaches to “A

Task input

Specific input Generatereach plan

Memory input