相关论文: Echo State Condition at the Critical Point

In recent years, more and more works have appeared devoted to the analog (hardware) implementation of artificial neural networks, in which neurons and the connection between them are based not on computer calculations, but on physical…

We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate…

We propose a simple model that aims at describing, in a stylized manner, how local breakdowns due unbalances or congestion propagate in real dynamical networks. The model converges to a self-organized critical stationary state in which the…

Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to…

In information theory the reliability function and its bounds, describing the exponential behavior of the error probability, are the most important quantitative characteristics of the channel performance. From a general point of view, these…

Interconnected networks are mathematical representation of systems where two or more simple networks are coupled to each other. Depending on the coupling weight between the two components, the interconnected network can function in two…

In this paper we analyze a cognitive radio network with one primary and one secondary transmitter, in which the primary transmitter has bursty arrivals while the secondary node is assumed to be saturated (i.e. always has a packet waiting to…

In this article, a correlation metric $\kappa_C$ is proposed for the inference of the dynamical state of neuronal networks. $\kappa_C$ is computed from the scaling of the correlation length with the size of the observation region, which…

Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This…

A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that…

In this article, a study of the mean-square error (MSE) performance of linear echo-state neural networks is performed, both for training and testing tasks. Considering the realistic setting of noise present at the network nodes, we derive…

The topology of a sensor network changes very frequently due to node failures because of power constraints or physical destruction. Robustness to topology changes is one of the important design factors of wireless sensor networks which…

We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…

For a class of irreducible Markov chains with an infinitely countable set of states, we establish a new verifiable necessary and sufficient condition for recurrence and transience. We show that if one of the basic assumptions is not…

Network models are routinely downscaled compared to nature in terms of numbers of nodes or edges because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long…

Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of…

In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…

Irreversibility, in which a transient perturbation leaves a system in a new state, is an emergent property in systems of interacting entities. This property has well-established implications in statistical physics but remains underexplored…

1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and…

What is a neural model with minimum architectural complexity that exhibits reasonable language learning capability? To explore such a simple but sufficient neural language model, we revisit a basic reservoir computing (RC) model, Echo State…