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 …

We consider the random fluctuations of the free energy in the $ p $-spin version of the
Sherrington–Kirkpatrick (SK) model in the high-temperature regime. Using the martingale …

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 …

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 …

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 …

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 …

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 study the asymptotic behavior of symmetric spin glass dynamics in the Sherrington–
Kirkpatrick model as proposed by Sompolinsky–Zippelius. We prove that the averaged law …

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 …

In this work we introduce a multi-species generalization of the Hopfield model for associative
memory, where neurons are divided into groups and both inter-groups and intra-groups pair …