  The concept of attention, numerical weights that emphasize the importance of
particular data, has proven to be very relevant in artificial intelligence.
Relative entropy (RE, aka Kullback-Leibler divergence) plays a central role in
communication theory. Here we combine these concepts, attention and RE. RE
guides optimal encoding of messages in bandwidth-limited communication as well
as optimal message decoding via the maximum entropy principle (MEP). In the
coding scenario, RE can be derived from four requirements, namely being
analytical, local, proper, and calibrated. Weighted RE, used for attention
steering in communications, turns out to be improper. To see how proper
attention communication can emerge, we analyze a scenario of a message sender
who wants to ensure that the receiver of the message can perform well-informed
actions. If the receiver decodes the message using the MEP, the sender only
needs to know the receiver's utility function to inform optimally, but not the
receiver's initial knowledge state. In case only the curvature of the utility
function maxima are known, it becomes desirable to accurately communicate an
attention function, in this case a by this curvature weighted and re-normalized
probability function. Entropic attention communication is here proposed as the
desired generalization of entropic communication that permits weighting while
being proper, thereby aiding the design of optimal communication protocols in
technical applications and helping to understand human communication. For
example, our analysis shows how to derive the level of cooperation expected
under misaligned interests of otherwise honest communication partners.
