相关论文: Concentration inequalities for sequential dynamica…
We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic…
It is shown, that Bose-Einstein statistical distributions can occur not only in quantum system, but in classical systems as well. The coherent dynamics of the system, or equivalently autocatalytic dynamics in momentum space of the system is…
We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of…
We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneously sheared suspension is shown to support exponentially growing layering…
Entanglement and its consequences - in particular the violation of Bell inequalities, which defies our concepts of realism and locality - have been proven to play key roles in Nature by many experiments for various quantum systems.…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
Inductive biases influence the behavior and performance of sequential models. In this work, we study an underexplored inductive bias in sequential modeling: continuity in time. We ask a simple question: do models motivated by…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
In this chapter, we introduce two interval observer designs for discrete-time (DT) and continuous-time (CT) nonlinear systems with bounded Jacobians that are affected by bounded uncertainties. Our proposed methods utilize the concepts of…
Artificial intelligence models trained through loss minimization have demonstrated significant success, grounded in principles from fields like information theory and statistical physics. This work explores these established connections…
Catastrophic forgetting - the tendency of neural networks to forget previously learned data when learning new information - remains a central challenge in continual learning. In this work, we adopt a behavioral approach, observing a…
We investigate in-context temporal biases in attention heads and transformer outputs. Using cognitive science methodologies, we analyze attention scores and outputs of the GPT-2 models of varying sizes. Across attention heads, we observe…
We derive explicit Bernstein-type and Bennett-type concentration inequalities for matrix-valued martingale processes with unbounded observations from the Hermitian space $\mathbb{H}(d)$. Specifically, we assume that the…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for…
The long-term dynamics of a Bonifacio-Lugiato model of optical superfluorescence is investigated. The scalar ordinary differential equation modelling the phenomenon is given by a concave-convex autonomous function of the state variable that…
In this work we investigate the information loss in (nonlinear) dynamical input-output systems and provide some general results. In particular, we present an upper bound on the information loss rate, defined as the (non-negative) difference…