通过采样估计张量极值：确定最小/最大元素的新方法

IF 1.8 4区计算机科学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computing in Science & Engineering Pub Date : 2023-12-26 DOI:10.1109/mcse.2023.3346208

Andrei Chertkov, Gleb Ryzhakov, Georgii Novikov, Ivan Oseledets

{"title":"通过采样估计张量极值：确定最小/最大元素的新方法","authors":"Andrei Chertkov, Gleb Ryzhakov, Georgii Novikov, Ivan Oseledets","doi":"10.1109/mcse.2023.3346208","DOIUrl":null,"url":null,"abstract":"The tensor train (TT) format, widely used in computational mathematics and machine learning, offers a computationally efficient method for handling multidimensional arrays, vectors, matrices, and discretized functions in various applications. In this article, we propose a new algorithm for estimating minimum/maximum elements of TT-tensors, which leads to accurate approximations. The method consists of sequential tensor multiplications of the TT-cores with an intelligent selection of candidates for the optimum. We propose a probabilistic interpretation of the method and estimate its complexity and convergence. We perform extensive numerical experiments with random tensors and various multivariable benchmark functions with the number of input dimensions up to 100. Our approach generates a solution close to the exact optimum for all model problems on a regular laptop.","PeriodicalId":10553,"journal":{"name":"Computing in Science & Engineering","volume":"18 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tensor Extrema Estimation Via Sampling: A New Approach for Determining Minimum/Maximum Elements\",\"authors\":\"Andrei Chertkov, Gleb Ryzhakov, Georgii Novikov, Ivan Oseledets\",\"doi\":\"10.1109/mcse.2023.3346208\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The tensor train (TT) format, widely used in computational mathematics and machine learning, offers a computationally efficient method for handling multidimensional arrays, vectors, matrices, and discretized functions in various applications. In this article, we propose a new algorithm for estimating minimum/maximum elements of TT-tensors, which leads to accurate approximations. The method consists of sequential tensor multiplications of the TT-cores with an intelligent selection of candidates for the optimum. We propose a probabilistic interpretation of the method and estimate its complexity and convergence. We perform extensive numerical experiments with random tensors and various multivariable benchmark functions with the number of input dimensions up to 100. Our approach generates a solution close to the exact optimum for all model problems on a regular laptop.\",\"PeriodicalId\":10553,\"journal\":{\"name\":\"Computing in Science & Engineering\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computing in Science & Engineering\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1109/mcse.2023.3346208\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computing in Science & Engineering","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1109/mcse.2023.3346208","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

张量列车（TT）格式被广泛应用于计算数学和机器学习中，它为处理各种应用中的多维数组、向量、矩阵和离散函数提供了一种计算高效的方法。在本文中，我们提出了一种估算 TT 张量最小/最大元素的新算法，从而获得精确的近似值。该方法由 TT 核心的连续张量乘法和最优候选的智能选择组成。我们提出了该方法的概率解释，并估算了其复杂性和收敛性。我们用随机张量和各种多变量基准函数进行了广泛的数值实验，输入维数高达 100。对于所有模型问题，我们的方法都能在普通笔记本电脑上生成接近精确最优的解决方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Tensor Extrema Estimation Via Sampling: A New Approach for Determining Minimum/Maximum Elements

The tensor train (TT) format, widely used in computational mathematics and machine learning, offers a computationally efficient method for handling multidimensional arrays, vectors, matrices, and discretized functions in various applications. In this article, we propose a new algorithm for estimating minimum/maximum elements of TT-tensors, which leads to accurate approximations. The method consists of sequential tensor multiplications of the TT-cores with an intelligent selection of candidates for the optimum. We propose a probabilistic interpretation of the method and estimate its complexity and convergence. We perform extensive numerical experiments with random tensors and various multivariable benchmark functions with the number of input dimensions up to 100. Our approach generates a solution close to the exact optimum for all model problems on a regular laptop.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computing in Science & Engineering 工程技术-计算机：跨学科应用

CiteScore

4.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Physics, medicine, astronomy -- these and other hard sciences share a common need for efficient algorithms, system software, and computer architecture to address large computational problems. And yet, useful advances in computational techniques that could benefit many researchers are rarely shared. To meet that need, Computing in Science & Engineering presents scientific and computational contributions in a clear and accessible format. The computational and data-centric problems faced by scientists and engineers transcend disciplines. There is a need to share knowledge of algorithms, software, and architectures, and to transmit lessons-learned to a broad scientific audience. CiSE is a cross-disciplinary, international publication that meets this need by presenting contributions of high interest and educational value from a variety of fields, including—but not limited to—physics, biology, chemistry, and astronomy. CiSE emphasizes innovative applications in advanced computing, simulation, and analytics, among other cutting-edge techniques. CiSE publishes peer-reviewed research articles, and also runs departments spanning news and analyses, topical reviews, tutorials, case studies, and more.