Information-theoretic fitness functions are becoming increasingly popular to produce generally useful, task-independent behaviors. One such universal function, dubbed empowerment, measures the amount of control an agent exerts on its environment via its sensorimotor system. Specifically, empowerment attempts to maximize the mutual information between an agent's actions and its received sensor states at a later point in time. Traditionally, empowerment has been applied to a conventional sensorimotor apparatus, such as a robot. Here, we expand the approach to a distributed, multi-agent sensorimotor system embodied by a neural cellular automaton (NCA). We show that the addition of empowerment as a secondary objective in the evolution of NCA to perform the task of morphogenesis, growing and maintaining a pre-specified shape, results in higher fitness compared to evolving for morphogenesis alone. Results suggest there may be a synergistic relationship between morphogenesis and empowerment. That is, indirectly selecting for coordination between neighboring cells over the duration of development is beneficial to the developmental process itself. Such a finding may have applications in developmental biology by providing potential mechanisms of communication between cells during growth from a single cell to a multicellular, target morphology. Source code for the experiments in this paper can be found at: \url{https://github.com/caitlingrasso/empowered-nca}.

翻译：信息论适应度函数正日益普及，用于产生具有普遍效用且独立于具体任务的行为。其中一种被称为“赋能”的通用函数，通过智能体的感知运动系统来衡量其对环境的控制程度。具体而言，赋能旨在最大化智能体当前时刻的动作与未来某一时刻所接收感知状态之间的互信息。传统上，赋能主要应用于机器人等常规感知运动系统。本文将该方法拓展至由神经元胞自动机（NCA）实现的分布式多智能体感知运动系统。研究表明，在NCA执行形态发生（生长并维持预定形状）任务的演化过程中，将赋能作为次要目标加入，相较于仅针对形态发生进行演化，能获得更高的适应度。结果提示形态发生与赋能之间可能存在协同关系。换言之，在发育过程中间接选择相邻细胞间的协调机制，对发育过程本身具有促进作用。这一发现可能为发育生物学提供潜在应用，揭示从单细胞发育为多细胞目标形态过程中细胞间通讯的可能机制。本文实验源代码可见于：\url{https://github.com/caitlingrasso/empowered-nca}。