Related papers: Improvement of random LHD for high dimensions

Large Language Models (LLMs) have demonstrated remarkable in-context learning capabilities, enabling flexible utilization of limited historical information to play pivotal roles in reasoning, problem-solving, and complex pattern recognition…

We combine MAP-Elites and highly parallelisable simulation to explore the design space of a class of large legged robots, which stand at around 2m tall and whose design and construction is not well-studied. The simulation is modified to…

The recent development of Large Language Models (LLMs) has been accompanied by an effervescence of novel ideas and methods to better optimize the loss of deep learning models. Claims from those methods are myriad: from faster convergence to…

Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…

We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these…

In this talk, I first present the motivation for theories wherein extra spacetime dimensions can be compactified to have large magnitudes. In particular, I discuss the Arkani-Hamed, Dimopoulos, Dvali (ADD) scenario. I present the…

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…

Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…

Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

A $k$-plane of a $d$-dimensional array is a subarray formed by fixing $d-k$ coordinates and allowing the remaining $k$ coordinates to vary freely. A Latin hypercube of dimension $d$ and order $n$ is an $n\times n\times\cdots\times n$ array…

This brief paper: (1) Discusses strategies to generate random test cases that can be used to extensively test any Linear Distance Program (LDP) software. (2) Gives three numerical examples of input cases generated by this strategy that…

Large Language Models can lead researchers in the design of robots.

The use of Large Language Models (LLMs) has drawn growing interest within the scientific community. LLMs can handle large volumes of textual data and support methods for evidence synthesis. Although recent studies highlight the potential of…

We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…

We introduce a hybrid quantum-classical deep learning architecture for large language model fine-tuning. The classical portion of the architecture is a sentence transformer that is powerful enough to display significant accuracy for complex…

Large Language Models (LLMs) are large-scale pretrained models that have achieved remarkable success across diverse domains. These successes have been driven by unprecedented complexity and scale in both data and computations. However, due…

An important question that arises in the study of high dimensional vector representations learned from data is: given a set $\mathcal{D}$ of vectors and a query $q$, estimate the number of points within a specified distance threshold of…