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.

翻译：赋权——一种独立于领域的信息论度量——先前已被证明在作为适应度函数时，能辅助搜索具备稳态能力的神经细胞自动机（NCA）进行演化。在我们的前期研究中，我们将赋权（定义为智能体动作与未来感知之间的最大时滞互信息）成功扩展至以NCA为载体的分布式感知运动系统中。然而，动作与其对应感知之间的时间延迟是任意选取的。本文在前期工作基础上，进一步探究赋权的时间尺度如何影响其作为辅助目标加速稳态NCA发现的效能。研究表明：与仅依赖稳态的演化选择相比，较短的时间延迟能显著提升赋权效能，其效果优于较长延迟的赋权。此外，我们评估了演化所得NCA的稳定性与适应性——这两者既是生命系统的标志性特征，也是人工生命系统试图复现的核心属性。研究发现，短时赋权的NCA具有更优的稳定性，并能更好地泛化至未知的稳态挑战。综上，这些发现为在其他人工制品演化中应用赋权提供了理论依据，并揭示了如何通过赋权加速其目标行为的演化。本文实验的源代码见：https://github.com/caitlingrasso/empowered-nca-II。