Related papers: An efficient multi-core implementation of a novel …
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…
We address the problem of efficient sparse fixed-rank (S-FR) matrix decomposition, i.e., splitting a corrupted matrix $M$ into an uncorrupted matrix $L$ of rank $r$ and a sparse matrix of outliers $S$. Fixed-rank constraints are usually…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
Kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines. In…
This paper presents a low-overhead optimizer for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. Architectural diversity among different processors together with structural diversity among different sparse matrices lead to…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve…
We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
To minimize data movement, state-of-the-art parallel sorting algorithms use techniques based on sampling and histogramming to partition keys prior to redistribution. Sampling enables partitioning to be done using a representative subset of…
Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
Sparse Matrix-matrix Multiplication (SpMM) and Sampled Dense-dense Matrix Multiplication (SDDMM) are important sparse operators in scientific computing and deep learning. Tensor Core Units (TCUs) enhance modern accelerators with superior…
Multiplication of a sparse matrix to a dense matrix (SpDM) is widely used in many areas like scientific computing and machine learning. However, existing works under-look the performance optimization of SpDM on modern many-core…
Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…
HQC is one of the code-based finalists in the last round of the NIST post quantum cryptography standardization process. In this process, security and implementation efficiency are key metrics for the selection of the candidates. A critical…
The recently developed Hierarchical Poincar\'e-Steklov (HPS) method is a high-order discretization technique that comes with a direct solver. Results from previous papers demonstrate the method's ability to solve Helmholtz problems to high…
This article introduces a highly parallel algorithm for molecular dynamics simulations with short-range forces on single node multi- and many-core systems. The algorithm is designed to achieve high parallel speedups for strongly…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle…