相关论文: On Convergence of Tracking Differentiator with Mul…

We study the influence of correlations among discrete stochastic excitatory or inhibitory inputs on the response of the FitzHugh-Nagumo neuron model. For any level of correlation the emitted signal exhibits at some finite noise intensity a…

Correlation Filter-based trackers have recently achieved excellent performance, showing great robustness to challenging situations exhibiting motion blur and illumination changes. However, since the model that they learn depends strongly on…

We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show…

Heavy-tailed stochastic gradient noise, commonly observed in transformer models, can destabilize the optimization process. Recent works mainly focus on developing and understanding approaches to address heavy-tailed noise in the centralized…

We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase…

Multitarget tracking in the interference environments suffers from the nonuniform, unknown and time-varying clutter, resulting in dramatic performance deterioration. We address this challenge by proposing a robust multitarget tracking…

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…

To learn and reason in the presence of uncertainty, the brain must be capable of imposing some form of regularization. Here we suggest, through theoretical and computational arguments, that the combination of noise with synchronization…

Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {\em analytically-solvable}…

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…

For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…

This paper introduces a stochastic framework for a recently proposed discrete-time delay estimation method in Laguerre-domain, i.e. with the delay block input and output signals being represented by the corresponding Laguerre series. A…

The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…

This letter reports on a new method of analysing experimentally gained time series with respect to different types of noise involved, namely, we show that it is possible to differentiate between dynamical and measurement noise. This method…

The inherent connection between noise and disturbance is one of the most fundamental features of quantum measurements. In the two well-known extreme cases a measurement either makes no disturbance but then has to be totally noisy or is as…

We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the…

In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white…

Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz…

In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…