Toward Computational Theory of Imitation: An Account for the Mechanism of Imitation Based on Dynamical Invariants

Abstract

Children can imitate adults’ actions with ease. An imitator who observed demonstrator’s action can produce a bodily movement which is supposed to be similar with it. Any theory and hypothesis of imitation is required to describe how the imitator recognizes the similarity or identity of actions, i.e., in what sense from the imitator’s point-of-view the produced and the observed action can be similar or identified. In this paper, we review four existing hypotheses on the mechanism of imitation. One of our criteria for the hypotheses in this review is the possibility of implementation and validation of the hypotheses in computer simulations or physical robots. A straightforward implementation without any additional ad-hoc assumption would be difficult, if the hypothesis to be implemented is flawed. Thus, the computer-based and/or physical implementation tests if a hypothesis accounts for the imitation mechanism sufficiently. This motivates us to critically review and clarify the existing literature on imitation in the sense of technical and theoretical plausibility of the existing hypotheses. We review the four existing hypotheses on imitation with some of them had been implemented in a form of computer simulations and/or robots. By pointing out the additional assumptions for the implementation, this review will reveal the latent requirements for an account for the imitation, that has not been addressed well. Lastly, we briefly propose our own account for imitation, in which bodily movements are characterized and identified on the basis of dynamical invariants under smooth transformations.