  The fundamental limit of Semantic Communications (joint source-channel
coding) is established when the transmission needs to be kept covert from an
external warden. We derive information-theoretic achievability and matching
converse results and we show that source and channel coding separation holds
for this setup. Furthermore, we show through an experimental setup that one can
train a deep neural network to achieve covert semantic communication for the
classification task. Our numerical experiments confirm our theoretical
findings, which indicate that for reliable joint source-channel coding the
number of transmitted source symbols can only scale as the square-root of the
number of channel uses.
