Most system designers of complex artificial systems

explicitly/implicitly use a design principle, in which higher-level

functions are composed of encapsulated lower-level modules. Modularity

is seen as a necessary feature of large-scale software design.

However, in human cognitive development, it is unlikely that there

exists an executive function, analogous to a systems analyst,

at work in the modularization of cognitive function.

In this research, we address the question: ``If higher-level

cognitive functions are organized based on encapsulated lower-level

modules, how are these modules created in the course of development?''

Elman (1993) suggested that a developmental increase in

working memory capacity promotes encapsulation, and improves learning.

We claim that ``maturational biases'' such as body growth also

promotes encapsulation. To elaborate upon this hypothesis, we have been

using autonomous robots as the subject of cognitive development, and

constructing computer programs by which robots can behave analogously to

infants (Hiraki,Sashima and Phillips 1997; Hiraki,Sashima and Phillips

in press). The following summarizes the result of a simulation

focusing on the relationship between spatial development and changes

of degrees of freedom (DOF) with body growth.

Psychological experiments on children's development of spatial

knowledge suggest experience at self-locomotion with visual tracking

as important factors. Yet, the mechanism underlying development is

unknown. We have proposed a robot that learns to ``mentally track''

a target object (i.e., maintaining a representation of an object's

position when outside the field-of-view) as a model for spatial

development. Mental tracking is considered as prediction of an

object's position given the previous environmental state and motor

commands, and the current environment state resulting from

movement. Following Jordan and Rumelhart's (1992) forward modeling

architecture, the system consists of two components: an inverse model

of sensory input to desired motor commands; and a forward model of

motor commands to desired sensory input (goals).

In order to get a understanding of the relationship between

body growth and spatial development, we compared the robot under

stepwise and non-stepwise conditions. In the stepwise development

condition, we simulated three stages of a child's development of motor

skills with the robot by varying its permitted actions (DOF). In stage 1,

the robot is only permitted head rotation. In stage 2, the robot can

rotate both head and body. Finally, in stage 3, the robot is also

permitted self-locomotion, whereas in stages 1 and 2, locomotion was

performed by an external agent.

In the non-stepwise condition, the robot

commences training at stage 3 (i.e., all actions permitted).

In each condition, the robots were tested on the ``three cups''

paradigm (where children are required to select the cup containing the

hidden object under various movement conditions). The result showed

that there was a faster decrease in error under the stepwise condition

than under the non-stepwise condition in stage 3 for both forward and

inverse models. The simulation results suggested that gradual growth

of body might help spatial development by limiting degrees of freedom

that infants must control.

Elman, J. (1993).

Learning and development in neural networks: The importance

of starting small.

Cognition, 48. 71-99.

Hiraki, K., Sakima, A., Phillips, S. (1997).

Mental Tracking: A Computational Model of Spatial Development.

Proc. of International Joint Conference of Artificial Intelligence.

301-307, Morgan Kaufmann.

Hiraki, K., Sakima, A., Phillips, S. (in press).

From Egocentric to Allocentric Spatial Behavior: A Computational

Model of Spatial Development,

ADAPTIVE BEHAVIOR, MIT Press.

Jordan, M.I. and Rumelhart, D.E. (1992).

Forward Models: Supervised learning with

a distal teacher,

Cognitive Science, 16,

307--354.