  Empowerment -- a domain independent, information-theoretic metric -- has
previously been shown to assist in the evolutionary search for neural cellular
automata (NCA) capable of homeostasis when employed as a fitness function. In
our previous study, we successfully extended empowerment, defined as maximum
time-lagged mutual information between agents' actions and future sensations,
to a distributed sensorimotor system embodied as an NCA. However, the
time-delay between actions and their corresponding sensations was arbitrarily
chosen. Here, we expand upon previous work by exploring how the time scale at
which empowerment operates impacts its efficacy as an auxiliary objective to
accelerate the discovery of homeostatic NCAs. We show that shorter time delays
result in marked improvements over empowerment with longer delays, when
compared to evolutionary selection only for homeostasis. Moreover, we evaluate
stability and adaptability of evolved NCAs, both hallmarks of living systems
that are of interest to replicate in artificial ones. We find that short-term
empowered NCA are more stable and are capable of generalizing better to unseen
homeostatic challenges. Taken together, these findings motivate the use of
empowerment during the evolution of other artifacts, and suggest how it should
be incorporated to accelerate evolution of desired behaviors for them. Source
code for the experiments in this paper can be found at:
https://github.com/caitlingrasso/empowered-nca-II.
