I France, Vol. A simple analytical study of a short term memory model is performed. This model consists of a symmetric p-neuron interaction between N neurons. Learning is achieved by a generalized Hebb rule.
Saturation is prevented by the introduction of a bound A to the couplings.
At each time step, an input pattern is drawn at random, independently of the previous ones. The determination of the life time T of a memorized pattern viewed as a function of A and N is accomplished by a statistical study of the dynamic of the learning process which has been made possible under the assumption that the couplings evolve independently. This simplification reduces the determination of T to a one-dimensional problem, by considering energies rather than couplings. The choice of the optimal value of A is a compromise between the success of the learning process and the maximization of T . The essential results are expressed by the formulae and .