Related papers: The high-dimensional asymptotics of first order me…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries.…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…
In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the…
One of the primary challenges of system identification is determining how much data is necessary to adequately fit a model. Non-asymptotic characterizations of the performance of system identification methods provide this knowledge. Such…
We study the high-dimensional training dynamics of a shallow neural network with quadratic activation in a teacher-student setup. We focus on the extensive-width regime, where the teacher and student network widths scale proportionally with…
We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study…
Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…
In recent years, researchers proposed several algorithms that compute metric quantities of real-world complex networks, and that are very efficient in practice, although there is no worst-case guarantee. In this work, we propose an…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…
We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…
We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where…
Change point detection in high dimensional data has found considerable interest in recent years. Most of the literature either designs methodology for a retrospective analysis, where the whole sample is already available when the…
Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n^{1/2} one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…