arXiv - CS - Mathematical Software最新文献_第4页

On the Average Runtime of an Open Source Binomial Random Variate Generation Algorithm 论开源二项式随机变量生成算法的平均运行时间

arXiv - CS - Mathematical Software Pub Date : 2024-03-16 DOI: arxiv-2403.11018

Vincent A. Cicirello

引用次数: 0

On a vectorized basic linear algebra package for prototyping codes in MATLAB 关于用于 MATLAB 代码原型开发的矢量化基本线性代数软件包

arXiv - CS - Mathematical Software Pub Date : 2024-03-15 DOI: arxiv-2404.16039

Alexej Moskovka, Talal Rahman, Jan Valdman, Jon Eivind Vatne

{"title":"On a vectorized basic linear algebra package for prototyping codes in MATLAB","authors":"Alexej Moskovka, Talal Rahman, Jan Valdman, Jon Eivind Vatne","doi":"arxiv-2404.16039","DOIUrl":"https://doi.org/arxiv-2404.16039","url":null,"abstract":"When writing high-performance code for numerical computation in a scripting\u0000language like MATLAB, it is crucial to have the operations in a large for-loop\u0000vectorized. If not, the code becomes too slow to use, even for a moderately\u0000large problem. However, in the process of vectorizing, the code often loses its\u0000original structure and becomes less readable. This is particularly true in the\u0000case of a finite element implementation, even though finite element methods are\u0000inherently structured. A basic remedy to this is the separation of the\u0000vectorization part from the mathematics part of the code, which is easily\u0000achieved through building the code on top of the basic linear algebra\u0000subprograms that are already vectorized codes, an idea that has been used in a\u0000series of papers over the last fifteen years, developing codes that are fast\u0000and still structured and readable. We discuss the vectorized basic linear\u0000algebra package and introduce a formalism using multi-linear algebra to explain\u0000and define formally the functions in the package, as well as MATLAB pagetime\u0000functions. We provide examples from computations of varying complexity,\u0000including the computation of normal vectors, volumes, and finite element\u0000methods. Benchmarking shows that we also get fast computations. Using the\u0000library, we can write codes that closely follow our mathematical thinking,\u0000making writing, following, reusing, and extending the code easier.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"105 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Cyclical Log Annealing as a Learning Rate Scheduler 作为学习率调度器的循环对数退火法

arXiv - CS - Mathematical Software Pub Date : 2024-03-13 DOI: arxiv-2403.14685

Philip Naveen

引用次数: 0

Efficient Calculations for k-diagonal Circulant Matrices and Cyclic Banded Matrices k 对角圆周矩阵和环带矩阵的高效计算

arXiv - CS - Mathematical Software Pub Date : 2024-03-08 DOI: arxiv-2403.05048

Chen Wang, Chao Wang

引用次数: 0

TopoX: A Suite of Python Packages for Machine Learning on Topological Domains TopoX：拓扑域机器学习 Python 软件包套件

arXiv - CS - Mathematical Software Pub Date : 2024-02-04 DOI: arxiv-2402.02441

Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahem AlJabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Maneel Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prílepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, Nina Miolane

{"title":"TopoX: A Suite of Python Packages for Machine Learning on Topological Domains","authors":"Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahem AlJabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Maneel Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prílepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, Nina Miolane","doi":"arxiv-2402.02441","DOIUrl":"https://doi.org/arxiv-2402.02441","url":null,"abstract":"We introduce topox, a Python software suite that provides reliable and\u0000user-friendly building blocks for computing and machine learning on topological\u0000domains that extend graphs: hypergraphs, simplicial, cellular, path and\u0000combinatorial complexes. topox consists of three packages: toponetx facilitates\u0000constructing and computing on these domains, including working with nodes,\u0000edges and higher-order cells; topoembedx provides methods to embed topological\u0000domains into vector spaces, akin to popular graph-based embedding algorithms\u0000such as node2vec; topomodelx is built on top of PyTorch and offers a\u0000comprehensive toolbox of higher-order message passing functions for neural\u0000networks on topological domains. The extensively documented and unit-tested\u0000source code of topox is available under MIT license at\u0000https://github.com/pyt-team.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

cmaes : A Simple yet Practical Python Library for CMA-ES cmaes ：用于 CMA-ES 的简单实用的 Python 库

arXiv - CS - Mathematical Software Pub Date : 2024-02-02 DOI: arxiv-2402.01373

Masahiro Nomura, Masashi Shibata

{"title":"cmaes : A Simple yet Practical Python Library for CMA-ES","authors":"Masahiro Nomura, Masashi Shibata","doi":"arxiv-2402.01373","DOIUrl":"https://doi.org/arxiv-2402.01373","url":null,"abstract":"The covariance matrix adaptation evolution strategy (CMA-ES) has been highly\u0000effective in black-box continuous optimization, as demonstrated by its success\u0000in both benchmark problems and various real-world applications. To address the\u0000need for an accessible yet potent tool in this domain, we developed cmaes, a\u0000simple and practical Python library for CMA-ES. cmaes is characterized by its\u0000simplicity, offering intuitive use and high code readability. This makes it\u0000suitable for quickly using CMA-ES, as well as for educational purposes and\u0000seamless integration into other libraries. Despite its simplistic design, cmaes\u0000maintains enhanced functionality. It incorporates recent advancements in\u0000CMA-ES, such as learning rate adaptation for challenging scenarios, transfer\u0000learning, and mixed-integer optimization capabilities. These advanced features\u0000are accessible through a user-friendly API, ensuring that cmaes can be easily\u0000adopted in practical applications. We regard cmaes as the first choice for a\u0000Python CMA-ES library among practitioners. The software is available under the\u0000MIT license at https://github.com/CyberAgentAILab/cmaes.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"178 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139688521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reproducibility, energy efficiency and performance of pseudorandom number generators in machine learning: a comparative study of python, numpy, tensorflow, and pytorch implementations 机器学习中伪随机数生成器的可重复性、能效和性能：python、numpy、tensorflow 和 pytorch 实现的比较研究

arXiv - CS - Mathematical Software Pub Date : 2024-01-30 DOI: arxiv-2401.17345

Benjamin Antunes, David R. C Hill

{"title":"Reproducibility, energy efficiency and performance of pseudorandom number generators in machine learning: a comparative study of python, numpy, tensorflow, and pytorch implementations","authors":"Benjamin Antunes, David R. C Hill","doi":"arxiv-2401.17345","DOIUrl":"https://doi.org/arxiv-2401.17345","url":null,"abstract":"Pseudo-Random Number Generators (PRNGs) have become ubiquitous in machine\u0000learning technologies because they are interesting for numerous methods. The\u0000field of machine learning holds the potential for substantial advancements\u0000across various domains, as exemplified by recent breakthroughs in Large\u0000Language Models (LLMs). However, despite the growing interest, persistent\u0000concerns include issues related to reproducibility and energy consumption.\u0000Reproducibility is crucial for robust scientific inquiry and explainability,\u0000while energy efficiency underscores the imperative to conserve finite global\u0000resources. This study delves into the investigation of whether the leading\u0000Pseudo-Random Number Generators (PRNGs) employed in machine learning languages,\u0000libraries, and frameworks uphold statistical quality and numerical\u0000reproducibility when compared to the original C implementation of the\u0000respective PRNG algorithms. Additionally, we aim to evaluate the time\u0000efficiency and energy consumption of various implementations. Our experiments\u0000encompass Python, NumPy, TensorFlow, and PyTorch, utilizing the Mersenne\u0000Twister, PCG, and Philox algorithms. Remarkably, we verified that the temporal\u0000performance of machine learning technologies closely aligns with that of\u0000C-based implementations, with instances of achieving even superior\u0000performances. On the other hand, it is noteworthy that ML technologies consumed\u0000only 10% more energy than their C-implementation counterparts. However, while\u0000statistical quality was found to be comparable, achieving numerical\u0000reproducibility across different platforms for identical seeds and algorithms\u0000was not achieved.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Shortcutting Cross-Validation: Efficiently Deriving Column-Wise Centered and Scaled Training Set $mathbf{X}^mathbf{T}mathbf{X}$ and $mathbf{X}^mathbf{T}mathbf{Y}$ Without Full Recomputation of Matrix Products or Statistical Moments 交叉验证捷径：在不重新计算矩阵乘积或统计矩的情况下，高效地得出列居中和缩放的训练集 $mathbf{X}^mathbf{T}mathbf{X}$ 和 $mathbf{X}^mathbf{T}mathbf{Y}$

arXiv - CS - Mathematical Software Pub Date : 2024-01-24 DOI: arxiv-2401.13185

Ole-Christian Galbo Engstrøm

{"title":"Shortcutting Cross-Validation: Efficiently Deriving Column-Wise Centered and Scaled Training Set $mathbf{X}^mathbf{T}mathbf{X}$ and $mathbf{X}^mathbf{T}mathbf{Y}$ Without Full Recomputation of Matrix Products or Statistical Moments","authors":"Ole-Christian Galbo Engstrøm","doi":"arxiv-2401.13185","DOIUrl":"https://doi.org/arxiv-2401.13185","url":null,"abstract":"Cross-validation is a widely used technique for assessing the performance of\u0000predictive models on unseen data. Many predictive models, such as Kernel-Based\u0000Partial Least-Squares (PLS) models, require the computation of\u0000$mathbf{X}^{mathbf{T}}mathbf{X}$ and $mathbf{X}^{mathbf{T}}mathbf{Y}$\u0000using only training set samples from the input and output matrices,\u0000$mathbf{X}$ and $mathbf{Y}$, respectively. In this work, we present three\u0000algorithms that efficiently compute these matrices. The first one allows no\u0000column-wise preprocessing. The second one allows column-wise centering around\u0000the training set means. The third one allows column-wise centering and\u0000column-wise scaling around the training set means and standard deviations.\u0000Demonstrating correctness and superior computational complexity, they offer\u0000significant cross-validation speedup compared with straight-forward\u0000cross-validation and previous work on fast cross-validation - all without data\u0000leakage. Their suitability for parallelization is highlighted with an\u0000open-source Python implementation combining our algorithms with Improved Kernel\u0000PLS.","PeriodicalId":501256,"journal":{"name":"arXiv - CS - Mathematical Software","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139559558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Theorem Discovery Amongst Cyclic Polygons 循环多边形中的定理发现

arXiv - CS - Mathematical Software Pub Date : 2024-01-22 DOI: arxiv-2401.13002

Philip ToddSaltire Software

引用次数: 0

A Simulation of Optimal Dryness When Moving in the Rain or Snow Using MATLAB 使用 MATLAB 模拟在雨雪中移动时的最佳干燥度

arXiv - CS - Mathematical Software Pub Date : 2024-01-22 DOI: arxiv-2401.12023

Neil Zhao, Emilee Brockner, Asia Winslow, Megan Seraydarian

引用次数: 0