# Dynamic Field Model of A-not-B Reaching

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 infants 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 Specific Task Look

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. A Model of A-not-B error TI M E

B 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. Activation

Activation Decision evolves in movement parameter space. A A B

Movement parameter Activation Movement parameter A B

B Movement parameter 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 experimenters 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.

Task input: properties of the tonic task input. A A B B

A A B B Specific input: the immediate, transient

cue. B B A A A B

Task input A Specific input B Generate

TI M reach plan E Memory is carried over to the next trial. At the second reach to A

Memory input Specific input Task input Generate reach plan

After many reaches to A Memory input Specific input Task input Generate reach plan

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