In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by nonparametric regression. The coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.

翻译：在学习互动粒子或物剂系统的过程中,共振状态确保互动功能的可识别性,通过非参数回归提供学习的基础。共振状态相当于学习过程中产生的整体内核的绝对肯定性。我们表明,对于一类互动功能,如系统是异性,整体内核是绝对肯定的,因此共振状态是真实的。