The Hopfield Network for p/N → o

  • Berndt Müller
  • Joachim Reinhardt
Part of the Physics of Neural Networks book series (NEURAL NETWORKS)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Berndt Müller
    • 1
  • Joachim Reinhardt
    • 2
  1. 1.Department of PhysicsDuke UniversityDurhamUSA
  2. 2.Institut für Theoretische PhysikJ.-W.-Goethe-UniversitätFrankfurt 1Fed. Rep. of Germany

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