Related papers: The relativistic Hopfield model with correlated pa…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
Associative memory models retrieve stored information through content-based addressing, mimicking the neural processes of animal brains. The classical Hopfield network-based models store memories as vectors of discrete values and have good…
We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory…
Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynamics of higher-order out-of-time-order…
We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an…
Relaxation and correlation times are two parameters used frequently in approximate descriptions of the time development of hadronizing system from some initial state towards distributions observed experimentally. Chosen to reproduce the…
Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they…
We investigate transport properties of topologically disordered, three-dimensional, one-particle, tight binding models, featuring site distance dependent hopping terms. We start from entirely disordered systems into which we gradually…
The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
A functional time series approach is proposed for investigating spatial correlation in daily maximum temperature forecast errors for 111 cities spread across the U.S. The modelling of spatial correlation is most fruitful for longer forecast…
Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…
Time-irreversibility is a distinctive feature of non-equilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical…
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…
In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both…
We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
We discuss a relativistic model for heat conduction, building on a convective variational approach to multi-fluid systems where the entropy is treated as a distinct dynamical entity. We demonstrate how this approach leads to a relativistic…
The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this…
Neural dynamics of energy-based models are governed by energy minimization and the patterns stored in the network are retrieved when the system reaches equilibrium. However, when the system is driven by time-varying external input, the…