THE SLLN FOR THE FREE-ENERGY OF A CLASS OF NEURAL NETWORKS

We first show the self-averaging property in the sense of almost sure convergence for the free energy of the spin glass model and of the Hop field model with an infinite number of patterns. Then we prove the str ong law of large number(SLLN) of the free energy in the Hopfield type model with finite number of patterns. Here the Hopfield type model imp lies that the interaction among neurons is higher order, the patterns embedded in the neural network are assumed to be independent random va riables rather than only taking value +1 and -1 and i.i.d. The model w ith weighted patterns is certainly included in. The SLLN of the free e nergy in the Little model is proved. The convergence rate for above tw o cases is also estimated.