相关论文: Some Remarks on Preconditioning Molecular Dynamics

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental…

The bias-variance trade-off is a central concept in supervised learning. In classical statistics, increasing the complexity of a model (e.g., number of parameters) reduces bias but also increases variance. Until recently, it was commonly…

The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…

In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…

This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

We consider a prospect theoretic version of the classical Q-learning algorithm for discounted reward Markov decision processes, wherein the controller perceives a distorted and noisy future reward, modeled by a nonlinearity that accentuates…

Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…

Stochastic Langevin dynamics has been traditionally used as a tool to describe non-equilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their…

We study Langevin dynamics with noise projected onto the directions orthogonal to an isometric group action. This mathematical model is introduced to shed new light on the effects of symmetry on stochastic gradient descent for…

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…

In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space,…

Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood…

We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to…

This article deals with the realisation of constraints in underdamped Langevin dynamics via soft-constrained dynamics. Specifically, we study systems with a large (or small) parameter that controls the constraint mechanisms, e.g. the…

We propose an ab-initio molecular dynamics method, capable to reduce dramatically the autocorrelation time required for the simulation of classical and quantum particles at finite temperature. The method is based on an efficient…

One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects,…

This article fills a gap in the mathematical analysis of Adaptive Biasing algorithms, which are extensively used in molecular dynamics computations. Given a reaction coordinate, ideally, the bias in the overdamped Langevin dynamics would be…