Positive and negative circuits in discrete neural networks

We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points, depending on the architecture of the network.