Related papers: Phase transitions from linear to nonlinear informa…

Filtering signal from noise is fundamental to accurately assessing spillover effects in financial markets. This study investigates denoised return and volatility spillovers across a diversified set of markets, spanning developed and…

We identify a noise model that ensures the functioning of an echo state network employing a gate-based quantum computer for reservoir computing applications. Energy dissipation induced by amplitude damping drastically improves the…

Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…

This paper investigates in detail the effects of noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic…

We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…

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…

Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to…

Biological information processing manifests a huge variety in its complexity and capability among different organisms, which presumably stems from the evolutionary optimization under limited computational resources. Starting from the…

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…

Recurrent Neural Networks (RNN) are extensively employed for processing sequential data such as time series. Reservoir computing (RC) has drawn attention as an RNN framework due to its fixed network that does not require training, making it…

To discover intrinsic inter-class transition probabilities underlying data, learning with noise transition has become an important approach for robust deep learning on corrupted labels. Prior methods attempt to achieve such transition…

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving…

We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…

A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir…

A short review is presented of a recently developed computational approach which allows the study of the resistance noise over the full range of bias values, from the linear regime up to electrical breakdown. Resistance noise is described…

We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the…

Despite the significance of short-term memory in cognitive function, the process of encoding and sustaining the input information in neural activity dynamics remains elusive. Herein, we unveiled the significance of transient neural dynamics…

Stochastic resonance is a non-linear phenomenon, in which the sensitivity of signal detectors can be enhanced by adding random noise to the detector input. Here, we demonstrate that noise can also improve the information flux in recurrent…

Supralinear and sublinear pre-synaptic and dendritic integration is considered to be responsible for nonlinear computation power of biological neurons, emphasizing the role of nonlinear integration as opposed to nonlinear output…

We consider signal transaction in a simple neuronal model featuring intrinsic noise. The presence of noise limits the precision of neural responses and impacts the quality of neural signal transduction. We assess the signal transduction…