EmergentCommunication

Recall that ˆmc(u) is exactly the listener's decoder in the IB framework (see Section 3.1.1). Therefore, anyother decoder would lend an upper bound on the informativeness loss term. Notice that under our assumptions,ˆmc is a Gaussian mixture, whereas the speaker's beliefs are simply Gaussian. All the systems with the samek form an equivalence class and the canonical system within each class is the one with minimalk. These canonical systems are the natural one to prefer, because they can attain the optimum for a given complexity with aminimal codebook.