Related papers: A spherical Hopfield model

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…

Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical…

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory…

Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…

This paper explores the use of artificial neural networks for the stable and data-driven selection of the frequency parameter in hyperbolic polynomial penalized splines (HP-splines). This parameter defines the underlying spline space and is…

We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and…

Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron…

Motivated by recent applications of the Lyapunov's method in artificial neural networks, which could be considered as dynamical systems for which the convergence of the system trajectories to equilibrium states is a necessity. We re-look at…

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…

Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest…

Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…

In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully…

The Hodgkin-Huxley equations constitute one of the more realistic neuronal models in literature and the most accepted one. It is well known that, depending on the value of the external stimuli current, it exhibits periodic solutions, both…

Thermofield dynamics has proven to be a very useful theory in high-energy physics, particularly since it permits the treatment of both time- and temperature-dependence on an equal footing. We here show that it also has an excellent…

Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…