Some rigorous results on the Hopfield neural network model

DOI10.1007/BF01041071zbMath0716.92003OpenAlexW2061757155MaRDI QIDQ753700

Hans Koch, Jacques Piasko

Publication date: 1989

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01041071

zbMATH Keywords

thermodynamic limitsymmetric solutionscritical pointsHopfield modelfree energy densitymean field equationsrandom interactionmean field variablesthermal equilibrium distribution

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Neural nets applied to problems in time-dependent statistical mechanics (82C32)

Related Items (12)

Gibbs states of the Hopfield model in the regime of perfect memory ⋮ Rigorous bounds on the storage capacity of the dilute Hopfield model ⋮ Thermodynamic limit of the \(q\)-state Potts-Hopfield model with infinitely many patterns ⋮ Local energy statistics in spin glasses ⋮ Rigorous results for the free energy in the Hopfield model ⋮ Rigorous results on the thermodynamics of the dilute Hopfield model ⋮ The free energy of a class of Hopfield models ⋮ The thermodynamics of the Curie-Weiss model with random couplings ⋮ The swapping algorithm for the Hopfield model with two patterns ⋮ Large deviation principles for the Hopfield model and the Kac-Hopfield model ⋮ On the free energy of the Hopfield model ⋮ Unnamed Item

Cites Work

• Nonlinear neural networks. I: General theory.
• The existence of persistent states in the brain
• The capacity of the Hopfield associative memory
• Neural networks and physical systems with emergent collective computational abilities.

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