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Ｈｏｐｆｉｅｌｄ人工神经网络和多层网络模型中有许多基本的数学问题，其中，最重要的是存储容量的问题，即吸引子的个数，在以往的文章中，大多数都以概率模型为背景，本文从组合论的角度提出了几个问题。我们把Ｈｏｐｆｉｅｌｄ网络中的状态按连接矩阵所构成的变换分类，网络的容量就是类的个数。我们得出了一些基本结果，还有一些有意义的问题，如多层网络中的结构是否可交换等问题，还有待进一步研究。
Hopfield artificial neural network and multi-layer network model has many basic mathematical problems, of which the most important is the storage capacity, that is, the number of attractors, in the past articles, most of them are based on the probability model, This article put forward several questions from the perspective of portfolio theory. We classify the states in the Hopfield network by transformations formed by the connection matrix. The capacity of the network is the number of classes. We have come to some basic results and some interesting questions, such as whether the structure of multi-layer networks can be exchanged or not, remains to be further studied.