The Hopfield Network for p/N → o
In this section we will analyze the statistical properties of a Hopfield network which has been trained with p patterns σ i μ 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.
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