A synthesis procedure for brain-state-in-a-box neural networks

In this paper, some new qualitative properties of discrete-time neural networks based on the "brain-state-in-a-box" model are presented. These properties concern both the characterization of equilibrium points and the global dynamical behavior. Next, the analysis results are used as guidelines in developing an efficient synthesis procedure for networks that function as associative memories. A constrained design algorithm is presented that gives completely stable dynamical neural networks sharing some interesting features. It is guaranteed the absence of nonbinary stable equilibria, that is stable states with nonsaturated components. It is guaranteed that in close proximity (Hamming distance one) of the stored patterns there is no other binary equilibrium point. Moreover, the presented method allows one to optimize a design parameter that controls the size of the attraction basins of the stored vectors and the accuracy needed in a digital realization of the network.