80 citations · 645 across the 38 of their papers we have counts for
7 papers · 1 filter
Topological properties of hierarchical networks
Elena Agliari, Adriano Barra, Andrea Galluzzi +3
Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical m…
Hierarchical neural networks perform both serial and parallel processing
Elena Agliari, Adriano Barra, Andrea Galluzzi +3
In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance.…
Legendre Duality of Spherical and Gaussian Spin Glasses
Giuseppe Genovese, Daniele Tantari
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin…
A walk in the statistical mechanical formulation of neural networks
Elena Agliari, Adriano Barra, Andrea Galluzzi +2
Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of sci…
Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
Elena Agliari, Adriano Barra, Andrea Galluzzi +3
In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems à la Mattis, by thinking at the Dyson model a…
From Dyson to Hopfield: Processing on hierarchical networks
Elena Agliari, Adriano Barra, Andrea Galluzzi +3
We consider statistical-mechanical models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling d…