Development of hierarchical structures for actions and motor imagery: a constructivist view from synthetic neuro-robotics study

Abstract

The current paper shows a neuro-robotics experiment on developmental learning of goal-directed actions. The robot was trained to predict visuo-proprioceptive flow of achieving a set of goal-directed behaviors through iterative tutor training processes. The learning was conducted by employing a dynamic neural network model which is characterized by their multiple time-scale dynamics. The experimental results showed that functional hierarchical structures emerge through stages of developments where behavior primitives are generated in earlier stages and their sequences of achieving goals appear in later stages. It was also observed that motor imagery is generated in earlier stages compared to actual behaviors. Our claim that manipulatable inner representation should emerge through the sensory–motor interactions is corresponded to Piaget’s constructivist view.

Appendix: Topology preserving map

The weight of TPM is updated by using the following equation with the neighboring function h.

$$ w_{i}(t+1) = w_{i}(t) + h_{i}(t)[x(t) - m_{i}(t)] $$

(2)

$$ h_{i} = \alpha(t) {\hbox{exp}}\left(-\frac{||r_{c} - r_{i}||^2}{\sigma(t)}\right)$$

(3)

Where x(t) and m _i (t) denote the input vector and the reference vector, respectively. In the neighborhood function the learning rate α(t) and the distribution σ(t) are annealed with time in the following time schedule.

$$ \sigma(t) = \sigma^{I}\left(\frac{\sigma^F}{\sigma^I}\right)^{\frac{t}{\rm max step}} $$

(4)

$$ \alpha(t) = \alpha^{I}\left(\frac{\alpha^F}{\alpha^I}\right)^{\frac{t}{\rm max step}} $$

(5)

Where σ^I represents the initial value of σ and σ^F represents the final value of σ. α^I is the initial learning rate. α^F is the final learning rate.