Algebraic decay of correlations in neural networks.

Abstract

Dynamic behavior of neural networks is studied via the dynamic mean-field theory for the Little-Hopfield model and for the dynamic model. In both models, the existence of the generalized Almeida-Thouless lines and associated dynamic instabilities are revealed. On these lines, autocorrelation functions are found to decay algebraically with exponent 1/2, while they decay exponentially above the lines