On the storage capacity of Hopfield models with correlated patterns

DOI10.1214/aoap/1028903378zbMath0941.60090OpenAlexW1965496542MaRDI QIDQ1296722

Matthias Loewe

Publication date: 29 November 1999

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1028903378

zbMATH Keywords

neural networksstorage capacityHopfield modelcorrelated patterns

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Neural nets applied to problems in time-dependent statistical mechanics (82C32)

Related Items (14)

A comparative study of sparse associative memories ⋮ On a model of associative memory with huge storage capacity ⋮ Hopfield model with planted patterns: a teacher-student self-supervised learning model ⋮ Effect of spatial correlations on Hopfield neural network and dense associative memories ⋮ On the capacity of an associative memory model based on neural cliques ⋮ Storing, learning and retrieving biased patterns ⋮ The Hopfield model on a sparse Erdös-Renyi graph ⋮ Fluctuations of the free energy in the high temperature Hopfield model ⋮ Moderate deviations for the overlap parameter in the Hopfield model ⋮ The storage capacity of the Hopfield model and moderate deviations ⋮ Opinion formation in a heterogeneous population --- a new approach to the Hopfield model ⋮ The swapping algorithm for the Hopfield model with two patterns ⋮ Capacity of an associative memory model on random graph architectures ⋮ Capacity bounds for the CDMA system and a neural network: a moderate deviations approach

Cites Work

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• Lower bounds on the restitution error in the Hopfield model
• Gibbs measures and phase transitions
• Gibbs states of the Hopfield model in the regime of perfect memory
• The retrieval phase of the Hopfield model: A rigorous analysis of the overlap distribution
• Rigorous bounds on the storage capacity of the dilute Hopfield model
• Rigorous results for the Hopfield model with many patterns
• Gibbs states of the Hopfield model with extensively many patterns.
• Large deviation principles for the Hopfield model and the Kac-Hopfield model
• An almost sure large deviation principle for the Hopfield model
• Neural Network Design for Efficient Information Retrieval
• The capacity of the Hopfield associative memory
• Properties of neural networks storing spatially correlated patterns
• Storage of sets of correlated data in neural network memories
• Neural networks and physical systems with emergent collective computational abilities.

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