  The evolution of symbolic communication is a longstanding open research
question in biology. While some theories suggest that it originated from
sub-symbolic communication (i.e., iconic or indexical), little experimental
evidence exists on how organisms can actually evolve to define a shared set of
symbols with unique interpretable meaning, thus being capable of encoding and
decoding discrete information. Here, we use a simple synthetic model composed
of sender and receiver agents controlled by Continuous-Time Recurrent Neural
Networks, which are optimized by means of neuro-evolution. We characterize
signal decoding as either regression or classification, with limited and
unlimited signal amplitude. First, we show how this choice affects the
complexity of the evolutionary search, and leads to different levels of
generalization. We then assess the effect of noise, and test the evolved
signaling system in a referential game. In various settings, we observe agents
evolving to share a dictionary of symbols, with each symbol spontaneously
associated to a 1-D unique signal. Finally, we analyze the constellation of
signals associated to the evolved signaling systems and note that in most cases
these resemble a Pulse Amplitude Modulation system.
