  We consider the problem of communicating a sequence of concepts, i.e.,
unknown and potentially stochastic maps, which can be observed only through
examples, i.e., the mapping rules are unknown. The transmitter applies a
learning algorithm to the available examples, and extracts knowledge from the
data by optimizing a probability distribution over a set of models, i.e., known
functions, which can better describe the observed data, and so potentially the
underlying concepts. The transmitter then needs to communicate the learned
models to a remote receiver through a rate-limited channel, to allow the
receiver to decode the models that can describe the underlying sampled concepts
as accurately as possible in their semantic space. After motivating our
analysis, we propose the formal problem of communicating concepts, and provide
its rate-distortion characterization, pointing out its connection with the
concepts of empirical and strong coordination in a network. We also provide a
bound for the distortion-rate function.
