Related papers: A method for accelerating low precision operations…

In this paper we present two algorithms for the multiplication of sparse Laurent polynomials and Poisson series (the latter being algebraic structures commonly arising in Celestial Mechanics from the application of perturbation theories).…

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…

In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

Sparse tensor algebra computations have become important in many real-world applications like machine learning, scientific simulations, and data mining. Hence, automated code generation and performance optimizations for tensor algebra…

This is the second of two papers to describe a matrix sparsification algorithm that takes a general real or complex matrix as input and produces a sparse output matrix of the same size. The first paper presented the original algorithm, its…

Deep learning on point clouds has received increased attention thanks to its wide applications in AR/VR and autonomous driving. These applications require low latency and high accuracy to provide real-time user experience and ensure user…

Serving large-scale machine learning (ML) models efficiently and with low latency has become challenging owing to increasing model size and complexity. Quantizing models can simultaneously reduce memory and compute requirements,…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the…

Sparse matrix vector multiplication (SpMV) is an important kernel in scientific and engineering applications. The previous optimizations are sparse matrix format specific and expose the choice of the best format to application programmers.…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

Low-precision computing is essential for efficiently utilizing memory bandwidth and computing cores. While many mixed-precision algorithms have been developed for iterative sparse linear solvers, effectively leveraging half-precision (fp16)…

Efficient multiple precision linear numerical computation libraries such as MPLAPACK are critical in dealing with ill-conditioned problems. Specifically, there are optimization methods for matrix multiplication, such as the Strassen…

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…

Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP) is the bottleneck kernel of sparse tensor decomposition. In this work, we propose a GPU-based algorithm design to address the key challenges in accelerating spMTTKRP computation,…

Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…

Tensor methods have gained increasingly attention from various applications, including machine learning, quantum chemistry, healthcare analytics, social network analysis, data mining, and signal processing, to name a few. Sparse tensors and…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…