Storage Capacity of Generalized Palimpsests

D. Bonnaz

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 Aopt 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 T∝A2 and Aopt∝Np-12.

Domaines: Articles anciens

D. Bonnaz. Storage Capacity of Generalized Palimpsests. Journal de Physique I, 1997, 7 (12), pp.1709-1721. ⟨10.1051/jp1:1997165⟩. ⟨jpa-00247482⟩