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Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…
General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines,…
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…
In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…
Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…
Sparse coding (SC) is attracting more and more attention due to its comprehensive theoretical studies and its excellent performance in many signal processing applications. However, most existing sparse coding algorithms are nonconvex and…
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing…
We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block…
We suggest a technique to reduce the storage size of sparse matrices at no loss of information. We call this technique Diagonally-Adressed (DA) storage. It exploits the typically low matrix bandwidth of matrices arising in applications. For…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…
Hyperparameter optimization is crucial for obtaining peak performance of machine learning models. The standard protocol evaluates various hyperparameter configurations using a resampling estimate of the generalization error to guide…
It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be…
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 matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on sparse matrix--vector multiplication (SpMV), Krylov subspace…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
Matrix factorization is a widely used approach for top-N recommendation and collaborative filtering. When implemented on implicit feedback data (such as clicks), a common heuristic is to upweight the observed interactions. This strategy has…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
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…