The Hopfield Network for p/N → o

Abstract

In this section we will analyze the statistical properties of a Hopfield network which has been trained with p patterns σ ^μ _i using Hebb’s learning rule. The analysis will be valid in the thermodynamic limit of a system of infinite size, N → ∞. However, the number of patterns p at first will be kept fixed so that the number of stored patterns per neuron, α = p/N, becomes vanishingly small. The more complicated case of finite pattern loading, α =constant, will be treated in Chapt. 17.