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May 14, 2023
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.
