相关论文: Dynamical mean-field analysis of adaptive Langevin…

A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…

Feature learning (FL), where neural networks adapt their internal representations during training, remains poorly understood. Using methods from statistical physics, we derive a tractable, self-consistent mean-field (MF) theory for the…

Dynamical Mean-Field Theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered $p$-spin…

We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…

Sampling is a fundamental and arguably very important task with numerous applications in Machine Learning. One approach to sample from a high dimensional distribution $e^{-f}$ for some function $f$ is the Langevin Algorithm (LA). Recently,…

We study posterior sampling for inverse problems in discrete state spaces using discrete diffusion models as generative priors. While continuous diffusion models have become widely used for inverse problems, their discrete counterparts…

Dynamical mean field theory (DMFT) is a tool that allows to analyze the stochastic dynamics of $N$ interacting degrees of freedom in terms of a self-consistent $1$-body problem. In this work, focusing on models of ecosystems, we present the…

Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge…

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…

We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a…

While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…

We propose and analyze a class of adaptive sampling algorithms for multimodal distributions on a bounded domain, which share a structural resemblance to the classic overdamped Langevin dynamics. We first demonstrate that this class of…

We discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit…

Bayesian inference allows to obtain useful information on the parameters of models, either in computational statistics or more recently in the context of Bayesian Neural Networks. The computational cost of usual Monte Carlo methods for…

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 introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In…

We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization…

Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown…

The study of nonequilibrium phenomena in correlated lattice systems has developed into an active and exciting branch of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of…

We present an inhomogeneous dynamical mean field theory (I-DMFT) that is suitable to investigate electron-lattice interactions in non-translationally invariant and/or inhomogeneous systems. The presented approach, whose only assumption is…