Rigorous results on the thermodynamics of the dilute Hopfield model

DOI10.1007/BF01048041zbMath1096.82517OpenAlexW2088703542MaRDI QIDQ2499847

Anton Bovier, Véronique Gayrard

Publication date: 23 August 2006

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

Full work available at URL: https://doi.org/10.1007/bf01048041

zbMATH Keywords

Neural networksrandom graphsHopfield modelmean-field theory

Mathematics Subject Classification ID

Neural nets applied to problems in time-dependent statistical mechanics (82C32)

Related Items (7)

Gibbs states of the Hopfield model in the regime of perfect memory ⋮ Eigenvalue distribution of large dilute random matrices ⋮ The Hopfield model on a sparse Erdös-Renyi graph ⋮ Opinion formation in a heterogeneous population --- a new approach to the Hopfield model ⋮ Capacity of an associative memory model on random graph architectures ⋮ Unnamed Item ⋮ Gibbs states of the Hopfield model with extensively many patterns.

Cites Work

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• Some rigorous results on the Hopfield neural network model
• The eigenvalues of random symmetric matrices
• 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
• The thermodynamics of the Curie-Weiss model with random couplings
• A free energy bound for the Hopfield model
• Neural networks and physical systems with emergent collective computational abilities.

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