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It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…

Optimization and Control · Mathematics 2026-03-20 Dan Garber

This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…

Mathematical Software · Computer Science 2018-10-18 Hongbo Rong

This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…

Numerical Analysis · Mathematics 2025-03-24 Jifeng Ge , Juan Zhang

Sparsity, which occurs in both scientific applications and Deep Learning (DL) models, has been a key target of optimization within recent ASIC accelerators due to the potential memory and compute savings. These applications use data stored…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-03-22 Eric Qin , Geonhwa Jeong , William Won , Sheng-Chun Kao , Hyoukjun Kwon , Sudarshan Srinivasan , Dipankar Das , Gordon E. Moon , Sivasankaran Rajamanickam , Tushar Krishna

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

Numerical Analysis · Computer Science 2013-01-15 Anastasios Kyrillidis , Volkan Cevher

Despite impressive performance, deep neural networks require significant memory and computation costs, prohibiting their application in resource-constrained scenarios. Sparse training is one of the most common techniques to reduce these…

Machine Learning · Computer Science 2023-12-06 Bowen Lei , Dongkuan Xu , Ruqi Zhang , Shuren He , Bani K. Mallick

In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…

Numerical Analysis · Mathematics 2022-03-17 Takeshi Iwashita , Kota Ikehara , Takeshi Fukaya , Takeshi Mifune

Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…

Information Theory · Computer Science 2025-10-16 Or Ordentlich , Yury Polyanskiy

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…

Methodology · Statistics 2011-02-14 Tony Cai , Weidong Liu , Xi Luo

We present PrecisionBatching, a quantized inference algorithm for speeding up neural network execution on traditional hardware platforms at low bitwidths without the need for retraining or recalibration. PrecisionBatching decomposes a…

Machine Learning · Computer Science 2020-03-03 Maximilian Lam , Zachary Yedidia , Colby Banbury , Vijay Janapa Reddi

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse…

Machine Learning · Computer Science 2019-08-27 Tim Dettmers , Luke Zettlemoyer

This article presents a sparse, low-memory footprint optimization algorithm for the implementation of the model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard…

Systems and Control · Electrical Eng. & Systems 2021-12-13 Pablo Krupa , Ignacio Alvarado , Daniel Limon , Teodoro Alamo

In this paper, we present a dynamically reconfigurable hardware accelerator called FADES (Fused Architecture for DEnse and Sparse matrices). The FADES design offers multiple configuration options that trade off parallelism and complexity…

Hardware Architecture · Computer Science 2023-04-18 Jose Nunez-Yanez , Andres Otero , Eduardo de la Torre

The growing demands of the worldwide IT infrastructure stress the need for reduced power consumption, which is addressed in so-called transprecision computing by improving energy efficiency at the expense of precision. For example, reducing…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-30 Andrea Borghesi , Giuseppe Tagliavini , Michele Lombardi , Luca Benini , Michela Milano

This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…

Quantum Physics · Physics 2024-09-25 Lukas Hantzko , Lennart Binkowski , Sabhyata Gupta

Matrix scaling problems with sparse cost matrices arise frequently in various domains, such as optimal transport, image processing, and machine learning. The Sinkhorn-Knopp algorithm is a popular iterative method for solving these problems,…

Optimization and Control · Mathematics 2024-06-26 Jose Rafael Espinosa Mena

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-10 Mehmet Deveci , Christian Trott , Sivasankaran Rajamanickam

The advancements of hardware technology in recent years has brought many possibilities for low-precision applications. However, the use of low precision can introduce significant computational errors, posing a considerable challenge to…

Mathematical Software · Computer Science 2024-09-30 Hongyaoxing Gu

Network pruning can reduce the computation cost of deep neural network (DNN) models. However, sparse models often produce randomly-distributed weights to maintain accuracy, leading to irregular computations. Consequently, unstructured…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-02-19 Cong Guo , Fengchen Xue , Jingwen Leng , Yuxian Qiu , Yue Guan , Weihao Cui , Quan Chen , Minyi Guo

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…

Numerical Analysis · Computer Science 2014-06-12 Huan Wang , Christos Boutsidis , Edo Liberty , Daniel Hsu