ON THE STABILITY OF NEURAL NETWORKS WITH ARBITRARY WEIGHTS

Dynamical properties of a general neural network are discussed. A cond ition for the neural activation dynamics being stable is derived. The stability condition does not put any symmetry restriction on the weigh ts. The transitions from stable to non-stable dynamics are analysed an d their analogy to phase transitions in statistical mechanics discusse d. In general, the network dynamics can violate the stability conditio n. To avoid that happening, a method is introduced which makes the dyn amics adaptive such that the stability condition is sustained. Relatio ns to some previous works on stability are discussed.