[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 …
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 …
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 …
patterns. Advances are made toward the validity of the “replica symmetric” solution. Strong …
A new mechanical approach to handle generalized Hopfield neural networks
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 …
shine in its Taylor expansion and result in more than pairwise interactions with alternate …
Generalized Guerra's interpolation schemes for dense associative neural networks
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 …
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
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 …
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 …
$. We treat both the case of semantically and spatially correlated patterns (ie, the patterns …
Hopfield models as generalized random mean field models
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 …
become known as the Hopfield model and which turned out, over the years, to be one of the …
Dreaming neural networks: rigorous results
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 …
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 …
local spin space in terms of metastates. Thereby we provide an illustration of the framework …