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Large Language Models (LLMs) have shown outstanding performance across a variety of tasks, partly due to advanced prompting techniques. However, these techniques often require lengthy prompts, which increase computational costs and can…

This paper introduces Force Matching (ForM), a novel framework for generative modeling that represents an initial exploration into leveraging special relativistic mechanics to enhance the stability of the sampling process. By incorporating…

In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…

Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…

Cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Geier \textit{et al.}, Phys. Rev. E \textbf{63}, 066705 (2006)] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D)…

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…

In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…

This paper proposes SMADMM, a single-loop Stochastic Momentum Alternating Direction Method of Multipliers for solving a class of nonconvex and nonsmooth composite optimization problems. SMADMM achieves the optimal oracle complexity of…

Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochastic optimization, sampling, and integration of mathematical objective functions, in particular, in the context of Bayesian inverse problems and parameter estimation. For…

Momentum is a popular technique for improving convergence rates during gradient descent. In this research, we experiment with adding momentum to the Baum-Welch expectation-maximization algorithm for training Hidden Markov Models. We compare…

We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is…

Cascaded lattice-Boltzmann method (Cascaded-LBM) employs a new class of collision operators aiming to improve numerical stability. It achieves this and distinguishes from other collision operators, such as in the standard single or multiple…

The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded…

Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify collision…

In traditional boosting algorithms, the focus on misclassified training samples emphasizes their importance based on difficulty during the learning process. While using a standard Support Vector Machine (SVM) as a weak learner in an…

We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation…

In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…

A novel single MRT-featured lattice Boltzmann method (SmrtLBM) is introduced. The intricate algorithm of the multiple-relaxation-time (MRT) collision operator is reimagined and distilled into a streamlined, single-relaxation-time-like…

Line-level code completion requires a critical balance between high accuracy and low latency. Existing methods suffer from a trade-off: large language models (LLMs) provide high-quality suggestions but incur high latency, while small…