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Modern processors rely heavily on speculation to keep the pipeline filled and consequently execute and commit instructions as close to maximum capacity as possible. To improve instruction-level parallelism, the processor core needs to fetch…
Simulation-based Inference (SBI) is a widely used set of algorithms to learn the parameters of complex scientific simulation models. While primarily run on CPUs in HPC clusters, these algorithms have been shown to scale in performance when…
This paper introduces hybrid LU-QR al- gorithms for solving dense linear systems of the form Ax = b. Throughout a matrix factorization, these al- gorithms dynamically alternate LU with local pivoting and QR elimination steps, based upon…
We evaluate optimized parallel sparse matrix-vector operations for two representative application areas on widespread multicore-based cluster configurations. First the single-socket baseline performance is analyzed and modeled with respect…
Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to…
We are interested in parallelizing the Least Angle Regression (LARS) algorithm for fitting linear regression models to high-dimensional data. We consider two parallel and communication avoiding versions of the basic LARS algorithm. The two…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
A novel fault-tolerant computation technique based on array Belief Propagation (BP)-decodable XOR (BP-XOR) codes is proposed for distributed matrix-matrix multiplication. The proposed scheme is shown to be configurable and suited for modern…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…
Structured sparsity has been proposed as an efficient way to prune the complexity of modern Machine Learning (ML) applications and to simplify the handling of sparse data in hardware. The acceleration of ML models - for both training and…
ShyLU-node is an open-source software package that implements linear solvers and preconditioners on shared-memory multicore CPUs or on a GPU. It is part of the Trilinos software framework and designed to provide a robust and efficient…
In sparse LU factorization, nonzero elements after symbolic factorization tend to distribute in diagonal and right-bottom region of sparse matrices. However, regular 2D blocking on this non-uniform distribution structure may lead to…
Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…
Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…
Graph search and sparse data-structure traversal workloads contain challenging irregular memory patterns on global data structures that need to be modified atomically. Distributed processing of these workloads has relied on server threads…
Bayesian networks (BNs) are attractive, because they are graphical and interpretable machine learning models. However, exact inference on BNs is time-consuming, especially for complex problems. To improve the efficiency, we propose a fast…
This paper describes REAP, a software-hardware approach that enables high performance sparse linear algebra computations on a cooperative CPU-FPGA platform. REAP carefully separates the task of organizing the matrix elements from the…