Statistical properties of random asymmetrical neural networks

A fully connected set of formal neurons that has not been subject to any training algorithm is studied. The thresholds and couplings are random variables chosen from Gaussian distributions. The dynamics of the model can be studied within a mean field approximation. Our results show a change of behaviour from a monostable to a bistable regime as the parameters are modified. A nonequilibrium potential is introduced to describe the model, and an analogy with a usual phase transition can be drawn. This analogy suggests using a thermodynamical approach to study the problem. Both the dynamical and the thermodynamical approaches give the same phase diagram for the model. The mean value of the threshold controls the order of the phase transition between the monostable and bistable regimes.