Related papers: The Little-Hopfield model on a Random Graph
We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be…
Superconducting optoelectronic loop neurons are a class of circuits potentially conducive to networks for large-scale artificial cognition. These circuits employ superconducting components including single-photon detectors, Josephson…
We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…
We study normal approximation of subgraph counts in a model of spatial scale-free random networks known as the age-dependent random connection model. In the light-tailed regime where only moments of order $(2 + \varepsilon)$ are finite, we…
The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…
High-order extensions of the Hopfield model are known to exhibit dramatically enhanced storage capacity at equilibrium, while their dynamical retrieval properties remain less well understood. In our previous work, we carried out a dynamical…
Standard large deviation estimates or the use of the Hubbard-Stratonovich transformation reduce the analysis of the distribution of the overlap parameters essentially to that of an explicitly known random function $\Phi_{N,\b}$ on $\R^M$.…
The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian…
In this paper we study, via equilibrium statistical mechanics, the properties of the internal energy of an Hopfield neural network whose patterns are stored continuously (Gaussian distributed). The model is shown to be equivalent to a…
The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
We include p-spin interactions in a spherical version of a soluble mean-field spin-glass model proposed by van Hemmen. Due to the simplicity of the solutions, which do not require the use of the replica trick, we are able to carry out a…
Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists…
We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…
In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects of stochastic spiking…
In Hopfield neural networks with up to 10^8 nodes we store two patterns through Hebb couplings. Then we start with a third random pattern which is supposed to evolve into one of the two stored patterns, simulating the cognitive process of…
The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…