Phase portrait characteristics of random neural networks

Considers statistical properties of the phase portraits of random binary networks such as the mean number of fixed points, the stability of these points, the convergence time, and the volumes of the attraction basins. The phase portrait characteristics are analyzed in terms of the vector lengths, i.e., the distances between sequential trajectory states in the Hamming metric. The trajectories are characterized by the Markovian matrix for the vector lengths. The time-reversed Markovian process enables one to explore the structure of the attraction basins. The statistical properties of network behavior are found to depend on only two key parameters of the network architecture, being insensitive to the details of network configuration. Some features of the network phase portrait are universal, due to their statistical nature. An example is the hyperbolic distribution of the largest attraction basin volumes. The theory is verified by applying it to neural networks with asymmetric diluted interconnections