Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model.

DOI10.1214/aop/1019160495zbMath1043.82036OpenAlexW1557639379MaRDI QIDQ1872156

Michel Talagrand

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1019160495

zbMATH Keywords

replica-symmetric solutionHopfield modelspin glass

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) Stochastic processes (60G99)

Related Items (14)

Neural networks retrieving Boolean patterns in a sea of Gaussian ones ⋮ A new mechanical approach to handle generalized Hopfield neural networks ⋮ The relativistic Hopfield network: Rigorous results ⋮ Dreaming neural networks: rigorous results ⋮ Generalized Guerra's interpolation schemes for dense associative neural networks ⋮ Non-convex multi-species Hopfield models ⋮ Large deviation principles and generalized Sherrington-Kirkpatrick models. ⋮ Fluctuations of the free energy in the high temperature Hopfield model ⋮ The replica symmetric approximation of the analogical neural network ⋮ PDE/statistical mechanics duality: relation between Guerra's interpolated \(p\)-spin ferromagnets and the Burgers hierarchy ⋮ Spontaneous Replica Symmetry Breaking and Interpolation Methods for Complex Statistical Mechanics Systems ⋮ About the ergodic regime in the analogical Hopfield neural networks: Moments of the partition function ⋮ Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit ⋮ Replica symmetry breaking in neural networks: a few steps toward rigorous results

Cites Work

• Huge random structures and mean field models for spin glasses
• The retrieval phase of the Hopfield model: A rigorous analysis of the overlap distribution
• The Sherrington-Kirkpatrick model: A challenge for mathematicians
• Rigorous results for the Hopfield model with many patterns
• Rigorous low-temperature results for the mean field \(p\)-spins interaction model
• Intersecting random half-spaces: Toward the Gardner-Derrida formula.
• Replica symmetry breaking and exponential inequalities for the Sherrington-Kirkpatrick model.
• ABOUT THE OVERLAP DISTRIBUTION IN MEAN FIELD SPIN GLASS MODELS
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