Related papers: The relativistic Hopfield model with correlated pa…
In many complex systems, elements interact via time-varying network topologies. Recent research shows that temporal correlations in the chronological ordering of interactions crucially influence network properties and dynamical processes.…
Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
The out of time order correlator (OTOC) serves as a powerful tool for investigating quantum information spreading and chaos in complex systems. We present a method employing non-equilibrium dynamical mean-field theory (DMFT) and coherent…
Correlated structures are intimately connected to intriguing phenomena exhibited by a variety of disordered systems such as soft colloidal gels, bio-polymer networks and colloidal suspensions near a shear jamming transition. The universal…
We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
We illustrate the scope of Time Dependent Density Functional Theory (TDDFT) for strongly correlated (lattice) models out of equilibrium. Using the exact many body time evolution, we reverse engineer the exact exchange correlation (xc)…
We study the effect of exponentially correlated noise on $xy-$model in the limit of small correlation time discussing the order-disorder transition in mean-field and the topological transition in two dimensions. We map the steady states of…
Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…
In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…
This article delves into the Hopfield neural network model, drawing inspiration from biological neural systems. The exploration begins with an overview of the model's foundations, incorporating insights from mechanical statistics to deepen…
We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in…
Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that…
We study a neural network model in which both neurons and synaptic interactions evolve in time simultaneously. The time evolution of synaptic interactions is described by a Langevin equation including a Hebbian learning term, and a bias…
The presence of frozen uncorrelated random on-site potential in interacting quantum systems can induce a transition from an ergodic phase to a localized one, the so-called many-body localization. Here we numerically study the effects of…
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…
In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated over time. All these features have an impact on the temporal properties of…
In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…