Related papers: Improved Particle Approximation Error for Mean Fie…

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our…

We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…

We develop a Mean-Field (MF) view of the learning dynamics of overparametrized Artificial Neural Networks (NN) under data symmetric in law wrt the action of a general compact group $G$. We consider for this a class of generalized shallow…

Dissipative Particle Dynamics (DPD) is a popular simulation model for investigating hydrodynamic behavior of systems with non-negligible equilibrium thermal fluctuations. DPD employs soft core repulsive interactions between the system…

We consider the constrained sampling problem where the goal is to sample from a target distribution $\pi(x)\propto e^{-f(x)}$ when $x$ is constrained to lie on a convex body $\mathcal{C}$. Motivated by penalty methods from continuous…

We study a normalizing flow in the latent space of a top-down generator model, in which the normalizing flow model plays the role of the informative prior model of the generator. We propose to jointly learn the latent space normalizing flow…

We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a…

Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…

We consider a system of $N$ particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as $N\to\infty$, the system takes the form of a nonlinear (McKean--Vlasov) Markov chain.…

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…

Deep neural networks (DNNs) for supervised learning can be viewed as a pipeline of a feature extractor (i.e. last hidden layer) and a linear classifier (i.e. output layer) that is trained jointly with stochastic gradient descent (SGD). In…

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced…

This paper discusses the estimation of the generalization gap, the difference between generalization performance and training performance, for overparameterized models including neural networks. We first show that a functional variance, a…

This paper studies the data-driven reconstruction of firing rate dynamics of brain activity described by linear-threshold network models. Identifying the system parameters directly leads to a large number of variables and a highly…

We tackle the general differentiable meta learning problem that is ubiquitous in modern deep learning, including hyperparameter optimization, loss function learning, few-shot learning, invariance learning and more. These problems are often…

We develop a mean-field theory for large, non-exchangeable particle (agent) systems where the states and interaction weights co-evolve in a coupled system of SDEs. A first main result is the establishment of the propagation of…

We study the global convergence of policy gradient for infinite-horizon entropy-regularized Markov decision processes (MDPs) with continuous state and action spaces. We consider log-linear softmax policies with linear function…

The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which…

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…