Selection for short-term empowerment accelerates the evolution of homeostatic neural cellular automata

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.