Related papers: Improvement of random LHD for high dimensions

Large Language Model (LLM) based coding tools have been tremendously successful as software development assistants, yet they are often designed for general purpose programming tasks and perform poorly for more specialized domains such as…

Random field models have been widely employed to develop a predictor of an expensive function based on observations from an experiment. The traditional framework for developing a predictor with random field models can fail due to the…

There is increasing interest in modeling high-dimensional longitudinal outcomes in applications such as developmental neuroimaging research. Growth curve model offers a useful tool to capture both the mean growth pattern across individuals,…

We develop a set of algorithms to solve a broad class of Design of Experiment (DoE) problems efficiently. Specifically, we consider problems in which one must choose a subset of polymers to test in experiments such that the learning of the…

Decoding strategies for generative large language models (LLMs) are a critical but often underexplored aspect of text generation tasks. Guided by specific hyperparameters, these strategies aim to transform the raw probability distributions…

Large Language Models (LLMs) have demonstrated impressive capability in many natural language tasks. However, the auto-regressive generation process makes LLMs prone to produce errors, hallucinations and inconsistent statements when…

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When…

While there has been significant progress on algorithmic aspects of the Lov\'{a}sz Local Lemma (LLL) in recent years, a noteworthy exception is when the LLL is used in the context of random permutations. The breakthrough algorithm of Moser…

The modern status of large extra dimensional (LED) approaches, highlights of their manifestation and short prehistory are discussed in this paper.

Designs for Order-of-Addition (OofA) experiments have received growing attention due to their impact on responses based on the sequence of component addition. In certain cases, these experiments involve heterogeneous groups of units, which…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Parallel programs in high performance computing (HPC) continue to grow in complexity and scale in the exascale era. The diversity in hardware and parallel programming models make developing, optimizing, and maintaining parallel software…

The design and implementation of unit tests is a complex task many programmers neglect. This research evaluates the potential of Large Language Models (LLMs) in automatically generating test cases, comparing them with manual tests. An…

Access to large amounts of diverse design solutions can support designers during the early stage of the design process. In this paper, we explore the efficacy of large language models (LLM) in producing diverse design solutions,…

This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. A novel and efficient algorithm for ridge-penalized quadratic regression is proposed, leveraging the matrix structures of the…

We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…

We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that…

Traditional simulations on High-Performance Computing (HPC) systems typically involve modeling very large domains and/or very complex equations. HPC systems allow running large models, but limits in performance increase that have become…

We consider enhancing large language models (LLMs) for complex planning tasks. While existing methods allow LLMs to explore intermediate steps to make plans, they either depend on unreliable self-verification or external verifiers to…

Large language models (LLMs) have revolutionized natural language processing and broadened their applicability across diverse commercial applications. However, the deployment of these models is constrained by high inference time in…