相关论文: Concentration inequalities for sequential dynamica…

Standard attention-based transformers are known to exhibit instability under learning rate overspecification during training, particularly at high learning rates. While various methods have been proposed to improve resilience to such…

A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This…

Fine-tuning pretrained image classifiers is standard practice, yet which individual samples are forgotten during this process, and whether forgetting patterns are stable or architecture dependent, remains unclear. Understanding these…

In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on $[0,1]$. We consider a parametrization of Beta distributions in terms of mean and scale parameters and…

We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system.…

We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…

This paper investigates the dynamical properties of tokens in pre-trained Transformer models and explores their application to improving Transformers. To this end, we analyze the dynamical system governing the continuous-time limit of the…

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for…

Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…

In this article we obtain concentration inequalities for Poisson $U$-statistics $F_m(f,\eta)$ of order $m\ge 1$ with kernels $f$ under general assumptions on $f$ and the intensity measure $\gamma \Lambda$ of underlying Poisson point process…

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

We consider a Boolean model $Z$ driven by a Poisson particle process $\eta$ on a metric space $\mathbb{Y}$. We study the random variable $\rho(Z)$, where $\rho$ is a (deterministic) measure on $\mathbb{Y}$. Due to the interaction of…

The study of escape rates for a ball in a dynamical systems has been much studied. Understanding the asymptotic behavior of the escape rate as the radius of the ball tends to zero is an especially subtle problem. In the case of hyperbolic…

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…

Two mode squeezed vacuum states allow Bell's inequality violation (BIQV) for all non-vanishing squeezing parameter $(\zeta)$. Maximal violation occurs at $\zeta \to \infty$ when the parity of either component averages to zero. For a given…

We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…

Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…

This paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time. These results extend previously established Freedman and Bernstein inequalities for series of random matrices to…