This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by providing a basic background to the morphology and physiology of the biological and the foundations and advances of the artificial neural networks. The first part then continues with a survey of all current mathematical models and some of their derived properties. In the second part, a new family of models is formulated, compared with the rest, and developed analytically and numerically. Finally, important additional aspects and any limitations to deal with in the future are discussed.
翻译:这项工作展示了目前收集的与神经网络有关的数学模型,并提议建立一个具有扩展结构和动态的新体系,以选择认知能力,首先是为生物形态和生理背景以及人造神经网络的基础和进步提供一个基本背景,然后是继续对所有当前数学模型及其某些衍生特性进行调查,在第二部分,与其余模型相比,形成一个新的模型体系,并以分析和数字方式加以发展,最后,讨论了今后要处理的其他重要方面和任何限制。