相关论文: The directed landscape is a black noise

We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)]. The static…

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…

Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…

Gradient descent is commonly used to find minima in rough landscapes, particularly in recent machine learning applications. However, a theoretical understanding of why good solutions are found remains elusive, especially in strongly…

In this paper we discuss the well known Kardar Parisi Zhang (KPZ) equation driven by temporally correlated noise. We use a self consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the…

The behavior of one-dimensional Hegselmann-Krause (HK) dynamics driven by noise has been extensively studied. Previous research has indicated that within no matter the bounded or the unbounded space of one dimension, the HK dynamics attain…

We design a control law for two agents to successfully track a level curve in the plane without explicitly estimating the field gradient. The velocity of each agent is decomposed along two mutually perpendicular directions, and separate…

When the drive which causes the level crossing in a qubit is slow, the probability, P_{LZ}, of the Landau-Zener transition is close to 1. We show that in this regime, which is most promising for applications, the noise due to the coupling…

We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features.…

The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified…

We discuss the behavior of bounded slope quenched noise invasion models in high dimensions. We first observe that the roughness of such a steady state interface is generated by the combination of the roughness of the invasion process…

Distributed Acoustic Sensing (DAS) is promising for traffic monitoring, but its extensive data and sensitivity to vibrations, causing noise, pose computational challenges. To address this, we propose a two-step deep-learning workflow with…

In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…

We explain how the claims of the KPZ scaling theory are confirmed by a recent proof of Borodin and Corwin on the asymptotics of the semi-discrete directed polymer.

While the convergence behaviors of stochastic gradient methods are well understood \emph{in expectation}, there still exist many gaps in the understanding of their convergence with \emph{high probability}, where the convergence rate has a…

We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…

Noise-assisted transport in quantum systems occurs when quantum time-evolution and decoherence conspire to produce a transport efficiency that is higher than what would be seen in either the purely quantum or purely classical cases. In…

We numerically study the collective dynamics of dense particle assemblies driven by non-reciprocal pairwise forces of amplitude $\kappa$. At a critical value $\kappa_{\rm c}$, the system undergoes a dynamical phase transition from an…

We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…