Learning motor dependent Crutchfield's information distance to anticipate changes in the topology of sensory body maps

What can a robot learn about the structure of its own body when he does not already know the semantics, the type and the position of its sensors and motors? Previous work has shown that an information theoretic approach, based on pairwise Crutchfield's information distance on sensorimotor channels, could allow to measure the informational topology of the set of sensors, i.e. reconstruct approximately the topology of the sensory body map. In this paper, we argue that the informational sensors topology changes with motor configurations in many robotic bodies, but yet, because measuring Crutchfield's distance is very time consuming, it is impossible to remeasure the body's topology for each novel motor configuration. Rather, a model should be learnt that allows the robot to predict Crutchfield's informational distances, and thus anticipate informational body maps, for novel motor configurations. We present experiments showing that learning motor dependent Crutchfield distances can indeed be achieved.