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We investigate a recently proposed model for cortical computation which performs relational inference. It consists of several interconnected, structurally equivalent populations of leaky integrate-and-fire (LIF) neurons, which are trained…
We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group…
Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states . Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: at random time intervals, the process $x_n$…
The paper deals with non-linear Poisson neuron network models with bounded memory dynamics, that can include both Hebbian learning mechanisms and refractory periods. The state of a network is described by the times elapsed since its neurons…
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…
We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample…
Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to…
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of…
We study dynamics of a reverberating neural net by means of computer simulation. The net, which is composed of 9 leaky integrate-and-fire (LIF) neurons arranged in a square lattice, is fully connected with interneuronal communication delay…
We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model…
To be effective in sequential data processing, Recurrent Neural Networks (RNNs) are required to keep track of past events by creating memories. While the relation between memories and the network's hidden state dynamics was established over…
We investigate dense higher-order associative memories in the high storage regime when the stored patterns are biased, namely when the entries of the patterns are not symmetrically distributed around zero. In this setting, the standard…
We study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian;…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
A recurrent neural network is considered that can retrieve a collection of patterns, as well as slightly perturbed versions of this `pure' set of patterns via fixed points of its dynamics. By replacing the set of dynamical constraints,…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal…
Biological neural networks self-organize according to local synaptic modifications to produce stable computations. How modifications at the synaptic level give rise to such computations at the network level remains an open question.…