Moderate deviations for the overlap parameter in the Hopfield model

DOI10.1007/S00440-004-0349-8zbMath1062.60021OpenAlexW2073504893MaRDI QIDQ1765113

Peter Eichelsbacher, Matthias Loewe

Publication date: 22 February 2005

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-004-0349-8

zbMATH Keywords

neural networkcritical temperaturelarge deviationsdisordermoderate deviations

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Large deviations (60F10) Neural nets applied to problems in time-dependent statistical mechanics (82C32)

Related Items (5)

Multiple critical behavior of probabilistic limit theorems in the neighborhood of a tricritical point ⋮ Moderate deviations for random field Curie-Weiss models ⋮ Lindeberg's method for moderate deviations and random summation ⋮ Rates of convergence in the Blume-Emery-Griffiths model ⋮ Opinion formation in a heterogeneous population --- a new approach to the Hopfield model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A central limit theorem for the overlap in the Hopfield model
• An almost sure central limit theorem for the overlap parameters in the Hopfield model
• Lower bounds on the restitution error in the Hopfield model
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Metastates in disordered mean-field models: Random field and Hopfield models
• On the storage capacity of Hopfield models with correlated patterns
• 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
• Mathematical aspects of spin classes and neural networks
• Rigorous results for the Hopfield model with many patterns
• Large deviations and concentration properties for \(\nabla_\varphi \) interface models
• Rigorous low-temperature results for the mean field \(p\)-spins interaction model
• Extreme value behavior in the Hopfield model
• The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature
• The entropy of graded algebras
• An almost sure large deviation principle for the Hopfield model
• The capacity of the Hopfield associative memory
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• On the replica symmetric equations for the Hopfield model
• Neural networks and physical systems with emergent collective computational abilities.
• On the Hopfield model at the critical temperature

This page was built for publication: Moderate deviations for the overlap parameter in the Hopfield model