Like me ? - Measures of correspondence and imitation

Imitation is a powerful mechanism for efficient learning of novel behaviors that both supports and takes advantage of sociality. A fundamental problem for imitation is to create an appropriate (partial) mapping between the bo dy of the system being imitated and the imitator. By considering for each o f these two systems an associated automaton (respectively, transformation s emigroup) structure, attempts at such mapping can be considered (partial) r elational homomorphisms. This article shows how mathematical techniques can be applied to characterize how far a behavior is from a successful imitati on and how to evaluate attempts at imitation arising from a particular corr espondence between the imitator and model. For the imitator and the imitated, affordances in the agent-environment str uctural coupling are likely to be different, all the more so in the case of dissimilar embodiment. We argue that the use of what is afforded to the im itator to attain corresponding effects or, as in dance, sequences of effect s, is necessary and sufficient for successful imitation. However, the judge d degree of success or failure of an attempted behavioral match depends on some externally imposed or-in the case of autonomous agents-internally dete rmined criteria on effects of the attempted imitative behavior (including e ffects attained successively as well as final effects). These criteria corr espond to metrics-measures of difference-which can guide the evaluation of a col respondence, the learning of a correspondence, or learning how to app ly one. Metrics on states and sequences of action events in the system-envi ronment coupling allow judgment of similarity for 'observer-dependent' purp oses. This allows one to formally define successful imitation with respect to such criteria. The resulting measures can be used to compare various can didate mappings (e.g., body plan or perception-action correspondences). Add itionally, this may be applied in the automated construction and learning o f mappings to be used in imitation for artificial, hardware, and software s ystems.