[图书][B] Mean field models for spin glasses: Volume I: Basic examples

M Talagrand - 2010 - books.google.com
This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse
vol. 46:" Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two …

[图书][B] Statistical mechanics of disordered systems: a mathematical perspective

A Bovier - 2006 - books.google.com
This self-contained book is a graduate-level introduction for mathematicians and for
physicists interested in the mathematical foundations of the field, and can be used as a …

Rigorous results for the Hopfield model with many patterns

M Talagrand - Probability theory and related fields, 1998 - Springer
We perform a thorough investigation of the main aspects of the Hopfield model with many
patterns. Advances are made toward the validity of the “replica symmetric” solution. Strong …

A new mechanical approach to handle generalized Hopfield neural networks

A Barra, M Beccaria, A Fachechi - Neural Networks, 2018 - Elsevier
We propose a modification of the cost function of the Hopfield model whose salient features
shine in its Taylor expansion and result in more than pairwise interactions with alternate …

Generalized Guerra's interpolation schemes for dense associative neural networks

E Agliari, F Alemanno, A Barra, A Fachechi - Neural Networks, 2020 - Elsevier
In this work we develop analytical techniques to investigate a broad class of associative
neural networks set in the high-storage regime. These techniques translate the original …

Replica symmetry breaking in neural networks: a few steps toward rigorous results

E Agliari, L Albanese, A Barra… - Journal of Physics A …, 2020 - iopscience.iop.org
In this paper we adapt the broken replica interpolation technique (developed by Francesco
Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin …

On the storage capacity of Hopfield models with correlated patterns

M Löwe - The Annals of Applied Probability, 1998 - projecteuclid.org
We analyze the storage capacity of the Hopfield model with correlated patterns $(\xi_i^{\nu})
$. We treat both the case of semantically and spatially correlated patterns (ie, the patterns …

Hopfield models as generalized random mean field models

A Bovier, V Gayrard - Mathematical aspects of spin glasses and neural …, 1998 - Springer
Twenty years ago, Pastur and Figotin [FP1, FP2] first introduced and studied what has
become known as the Hopfield model and which turned out, over the years, to be one of the …

Dreaming neural networks: rigorous results

E Agliari, F Alemanno, A Barra… - Journal of Statistical …, 2019 - iopscience.iop.org
Recently, a daily routine for associative neural networks has been proposed: the network
Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then …

Metastates in disordered mean-field models: random field and Hopfield models

C Külske - Journal of statistical physics, 1997 - Springer
We rigorously investigate the size dependence of disordered mean-field models with finite
local spin space in terms of metastates. Thereby we provide an illustration of the framework …