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We present a mechanism to symbolically gather performance-relevant operation counts from numerically-oriented subprograms (`kernels') expressed in the Loopy programming system, and apply these counts in a simple, linear model of kernel run…

Performance · Computer Science 2016-04-19 James Stevens , Andreas Klöckner

The Nvidia GPU architecture has introduced new computing elements such as the \textit{tensor cores}, which are special processing units dedicated to perform fast matrix-multiply-accumulate (MMA) operations and accelerate \textit{Deep…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-03-12 Roberto Carrasco , Raimundo Vega , Cristóbal A. Navarro

A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these…

Performance · Computer Science 2021-10-29 Eliza Wszola , Celestine Mendler-Dünner , Martin Jaggi , Markus Püschel

Face recognition is the important field in machine learning and pattern recognition research area. It has a lot of applications in military, finance, public security, to name a few. In this paper, the combination of the tensor sparse PCA…

Computer Vision and Pattern Recognition · Computer Science 2020-08-12 Loc Hoang Tran , Linh Hoang Tran

We consider the problem of low-rank approximation of massive dense non-negative tensor data, for example to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting…

Numerical Analysis · Mathematics 2019-09-04 Srinivas Eswar , Koby Hayashi , Grey Ballard , Ramakrishnan Kannan , Michael A. Matheson , Haesun Park

Improving the computational efficiency of quantum many-body calculations from a hardware perspective remains a critical challenge. Although field-programmable gate arrays (FPGAs) have recently been exploited to improve the computational…

Strongly Correlated Electrons · Physics 2026-02-06 Songtai Lv , Yang Liang , Rui Zhu , Qibin Zheng , Haiyuan Zou

Achieving high efficiency with numerical kernels for sparse matrices is of utmost importance, since they are part of many simulation codes and tend to use most of the available compute time and resources. In addition, especially in large…

Performance · Computer Science 2013-05-07 Tobias Scharpff , Klaus Iglberger , Georg Hager , Ulrich Ruede

We investigate the energy efficiency of a library designed for parallel computations with sparse matrices. The library leverages high-performance, energy-efficient Graphics Processing Unit (GPU) accelerators to enable large-scale scientific…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-16 Massimo Bernaschi , Alessandro Celestini , Pasqua D'Ambra , Giorgio Richelli

We extend an existing approach for efficient use of shared mapped memory across Chapel and C++ for graph data stored as 1-D arrays to sparse tensor data stored using a combination of 2-D and 1-D arrays. We describe the specific extensions…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-10-18 S. Isaac Geronimo Anderson , Daniel M. Dunlavy

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Statistics Theory · Mathematics 2021-02-08 Rungang Han , Rebecca Willett , Anru R. Zhang

Today, many scientific and engineering areas require high performance computing to perform computationally intensive experiments. For example, many advances in transport phenomena, thermodynamics, material properties, computational…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-07-15 K. G. Kapanova , J. M. Sellier

Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…

Mathematical Software · Computer Science 2018-10-23 Ewout van den Berg

The KeOps library provides a fast and memory-efficient GPU support for tensors whose entries are given by a mathematical formula, such as kernel and distance matrices. KeOps alleviates the major bottleneck of tensor-centric libraries for…

Machine Learning · Computer Science 2021-04-10 Benjamin Charlier , Jean Feydy , Joan Alexis Glaunès , François-David Collin , Ghislain Durif

Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…

Machine Learning · Computer Science 2020-04-28 Fei Sun , Minghai Qin , Tianyun Zhang , Liu Liu , Yen-Kuang Chen , Yuan Xie

In this paper, we explore the acceleration of tensor product operations in finite element methods, leveraging the computational power of the NVIDIA A100 GPU Tensor Cores. We provide an accessible overview of the necessary mathematical…

Mathematical Software · Computer Science 2024-07-16 Cu Cui

Future computing systems, from handhelds to supercomputers, will undoubtedly be more parallel and heterogeneous than todays systems to provide more performance and energy efficiency. Thus, GPUs are increasingly being used to accelerate…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-18 Saeed Taheri , Apan Qasem , Martin Burtscher

We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse…

Numerical Analysis · Mathematics 2024-01-30 HanQin Cai , Zehan Chao , Longxiu Huang , Deanna Needell

The trend towards highly parallel multi-processing is ubiquitous in all modern computer architectures, ranging from handheld devices to large-scale HPC systems; yet many applications are struggling to fully utilise the multiple levels of…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-07-19 Michael Lange , Gerard Gorman , Michele Weiland , Lawrence Mitchell , Xiaohu Guo , James Southern

While loop reordering and fusion can make big impacts on the constant-factor performance of dense tensor programs, the effects on sparse tensor programs are asymptotic, often leading to orders of magnitude performance differences in…

Mathematical Software · Computer Science 2023-10-13 Willow Ahrens , Fredrik Kjolstad , Saman Amarasinghe

We introduce a code generator that converts unoptimized C++ code operating on sparse data into vectorized and parallel CPU or GPU kernels. Our approach unrolls the computation into a massive expression graph, performs redundant expression…

Programming Languages · Computer Science 2022-03-15 Philipp Herholz , Xuan Tang , Teseo Schneider , Shoaib Kamil , Daniele Panozzo , Olga Sorkine-Hornung