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Large language models (LLMs) are increasingly deployed on customer devices. To support them, current devices are adopting SoCs (System on Chip) with NPUs (Neural Processing Unit) installed. Although high performance is expected, LLM…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
Pipeline parallelism has emerged as a predominant approach for deploying large language models (LLMs) across distributed nodes, owing to its lower communication overhead compared to tensor parallelism. While demonstrating high throughput in…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
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…
Transpilation is a crucial process in preparing quantum circuits for execution on hardware, transforming virtual gates to match device-specific topology by introducing swap gates and basis gates, and applying optimizations that reduce…
We demonstrate algorithm-based fault tolerance for silent, transient data corruption in "black-box" preconditioners. We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both…
Krylov subspace methods are linear solvers based on matrix-vector multiplications and vector operations. While easily parallelizable, they are sensitive to rounding errors and may experience convergence issues. ILU(0), an incomplete LU…
Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…
HipMCL is a high-performance distributed memory implementation of the popular Markov Cluster Algorithm (MCL) and can cluster large-scale networks within hours using a few thousand CPU-equipped nodes. It relies on sparse matrix computations…
Consecutive matrix multiplications are commonly used in graph neural networks and sparse linear solvers. These operations frequently access the same matrices for both reading and writing. While reusing these matrices improves data locality,…
Particle-in-Cell (PIC) simulations are fundamental to plasma physics but often suffer from limited scalability due to particle-grid interaction bottlenecks and particle redistribution costs. Specifically, the particle-grid interaction…
In the last decade, an impressive increase in software adaptions has led to a surge in log data production, making manual log analysis impractical and establishing the necessity for automated methods. Conversely, most automated analysis…
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming…
While recent advances in AI SoC design have focused heavily on accelerating tensor computation, the equally critical task of tensor manipulation, centered on high,volume data movement with minimal computation, remains underexplored. This…
We introduce a new sorting algorithm that is the combination of ML-enhanced sorting with the In-place Super Scalar Sample Sort (IPS4o). The main contribution of our work is to achieve parallel ML-enhanced sorting, as previous algorithms…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…
The Lanczos method is one of the standard approaches for computing a few eigenpairs of a large, sparse, symmetric matrix. It is typically used with restarting to avoid unbounded growth of memory and computational requirements. Thick-restart…
Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty…
We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…