We present an opinion model founded upon the principles of the bounded confidence interaction among agents. Our objective is to explain the polarization effects inherent to vector-valued opinions. The evolutionary process adheres to the rule where each agent aspires to increase polarization through communication with a single friend during each discrete time step. The dynamics ensure that agents' ultimate (temporal) configuration will encompass a finite number of outlier states. We introduce deterministic and stochastic models, accompanied by a comprehensive mathematical analysis of their inherent properties. Additionally, we provide compelling illustrative examples and introduce a stochastic solver tailored for scenarios featuring an extensive set of agents. Furthermore, in the context of smaller agent populations, we scrutinize the suitability of neural networks for the rapid inference of limit configurations.

翻译：我们提出一种基于智能体间有限置信交互原则的观点模型。其目标在于解释向量值观点中固有的极化效应。演化过程遵循如下规则：在每个离散时间步中，每个智能体通过与单一好友通信来追求极化增强。该动力学机制确保智能体的最终（时间）构型将包含有限数量的离群状态。我们引入了确定性与随机性模型，并对其内在特性进行了全面的数学分析。此外，我们提供了具有说服力的示例说明，并针对大规模智能体场景设计了一种随机求解器。同时，在较小规模智能体群体背景下，我们深入探究了神经网络用于快速推断极限构型的适用性。