Related papers: Oscillator neural network model with distributed n…

Many network applications rely on the synchronization of coupled oscillators. For example, such synchronization can provide networked devices with a common temporal reference necessary for coordinating actions or decoding transmitted…

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different…

Federated learning enables collaborative training without sharing raw data, but struggles under client heterogeneity and streaming distribution shifts, where drift and novel data can impair convergence and cause forgetting. We propose a…

We study a way to set the natural frequency of a newly added oscillator in a growing network to enhance synchronization. Population growth is one of the typical features of many oscillator systems for which synchronization is required to…

Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is…

Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…

A new mathematical model of neural networks described by diffusive FitzHugh-Nagumo equations with memristors and linear synaptic coupling is proposed and investigated. The existence of absorbing set for the solution semiflow in the energy…

We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…

Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb's rule and the contrastive divergence…

We analyze partial synchronization patterns in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report a dynamical asymmetry between the hemispheres, induced by the…

The brain modifies its synaptic strengths during learning in order to better adapt to its environment. However, the underlying plasticity rules that govern learning are unknown. Many proposals have been suggested, including Hebbian…

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…

In this paper, we present a neural network system related to about memory and recall that consists of one neuron group (the "cue ball") and a one-layer neural net (the "recall net"). This system realizes the bidirectional memorization…

We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system…

The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…

Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to…

Spiking Neural Networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…

Processing sequential inputs is a fundamental brain function, underlying tasks such as sensory perception, language, and motor control. A challenge in sequence processing is to represent not only the order of events, but also their precise…