Related papers: Enhanced Error-free Retrieval in Kuramoto-type Ass…
We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
This study examines the Kuramoto model with a Hebbian learning rule and second-order Fourier coupling for binary pattern recognition. The system stores memorized binary patterns as stable critical points, enabling it to identify the closest…
We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…
Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case that the fraction of…
We present an algorithm to store binary memories in a Hopfield neural network using minimum probability flow, a recent technique to fit parameters in energy-based probabilistic models. In the case of memories without noise, our algorithm…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…
Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…
Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections?…
Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This…
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others.…
The brain can reproduce memories from partial data; this ability is critical for memory recall. The process of memory recall has been studied using auto-associative networks such as the Hopfield model. This kind of model reliably converges…
Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…
Bayesian inference is a powerful tool for parameter estimation and uncertainty quantification in dynamical systems. However, for nonlinear oscillator networks such as Kuramoto models, widely used to study synchronization phenomena in…
We propose a neural network model, which, with appropriate assignment of the stability of its equilibrium points (EPs), achieves Hopfield-like associative memory. The oscillator Ising machine (OIM) is an ideal candidates for such a model,…
Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…
The Hopfield model describes a neural network that stores memories using all-to-all-coupled spins. Memory patterns are recalled under equilibrium dynamics. Storing too many patterns breaks the associative recall process because frustration…
Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation slows and diversifies inhibitory timescales, leading to improved task performance that is…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…