arXiv subjects

Rabab Alomairy

Publications and source records attributed to Rabab Alomairy.

8 recordsLinked to original sources

arXiv2026

Data-Driven Dynamic Algorithm Dispatch with Large Language Models

We introduce a large language model (LLM)-driven approach for generating dynamic algorithmic dispatch heuristics in high-performance linear algebra. By combining prompt engineering with LLaMA 3 and a curated performance database, the model learns to synthesize selection heuristics that exploit structural patterns to identify fast algorithmic choices. A case study on LU factorization demonstrates the model's ability to replicate expert-designed strategies. This work, developed as part of the DARPA-MIT SmartSolve project, highlights the promise of LLMs for algorithmic discovery and the development of more adaptive, fast linear algebra software.

cs.AI↗

arXiv2026

Cross-Model Cross-Language AI Coding Agent Performance: Accuracy and Speed of Parallel CLRS Algorithms

AI coding agents have quickly become omnipresent in software engineering. Their serial performance, both in terms of accuracy and speed, has been extensively covered. However, recent initial results suggest their parallel programming capabilities lag behind serial programming capabilities. This paper presents a cross-language evaluation of three coding agents -- Cursor's Composer 2.0, GPT 5.4, and Claude Sonnet 4.6 -- on parallel code generation across three algorithm categories -- sorting, graph traversal, and search -- in C++, Python, and Julia. For each algorithm and language pair, we prompt a coding agent to produce a parallel implementation from a serial baseline, track the prompting effort required to achieve both functional correctness and performance improvements, and measure speedup against both custom serial baselines and third-party library implementations. We find that coding agents can produce correct parallel implementations with modest prompting effort, but that achieving meaningful speedup is heavily algorithm- and language-dependent. Sonnet 4.6 delivers the strongest overall performance gains, whereas GPT 5.4 produces no measurable speedups despite consistent correctness. C++ is most consistently parallelizable for graph algorithms, while Python and Julia achieve the largest speedups on search algorithms: no single language dominates across all categories. Python and Julia each achieve speedup on some graph algorithms but regress on others. These findings underscore the impact of including runtime performance efficiency as a main LLM performance metric, in addition to accuracy, particularly for parallel implementations.

cs.SE↗

arXiv2026

Accelerating Bidiagonalization of Banded Matrices through Memory-Aware Bulge-Chasing on GPUs

The reduction of a banded matrix to bidiagonal form is a critical step in the calculation of Singular Values, a cornerstone of scientific computing and AI. Although inherently parallel, this step has traditionally been considered unsuitable for GPUs due to its memory-bound nature. However, recent advances in GPU architectures, such as increased L1 memory per Streaming Multiprocessor or Compute Unit and larger L2 caches, have shifted this paradigm. In this work, we present the first GPU-accelerated algorithm for reducing a banded matrix to bidiagonal form, integrated into an open-source software package. Our algorithm builds on prior multicore CPU cache-efficient bulge-chasing methods, adapted to modern GPU architectures to optimize throughput. Leveraging Julia's high-level array abstractions and KernelAbstractions.jl, we implement a single function that is both hardware-agnostic and data-precision-aware, running efficiently across NVIDIA, AMD, Intel, and Apple Metal GPUs. We develop a hardware-aware performance model to guide tuning and identify key hyperparameters that govern optimal GPU performance for memory-bound workloads. We show that such workloads, when carefully optimized, can achieve substantial speed-ups on modern GPUs: our implementation outperforms multithreaded CPU libraries (PLASMA,SLATE) starting from matrix sizes as small as 1024x1024, and achieves over 100x speed-up on 32k x 32k matrices. Moreover, the algorithm's performance scales linearly with the matrix bandwidth, enabling efficient reduction of matrices with larger bandwidths, previously considered impractical.

cs.DC↗

arXiv2026

Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs

Symmetric positive-definite system solvers based on Cholesky factorization are fundamental to many scientific applications, such as climate modeling. We present a portable, nested recursive mixed-precision solver designed for Matrix Processing Units (MXUs), including NVIDIA Tensor Cores (H200) and AMD Matrix Cores (MI300X), that assigns low-precision FP16 arithmetic to large off-diagonal blocks, while preserving high precision on diagonal blocks to ensure numerical stability. The solver is implemented in Julia, providing a high-level, hardware-agnostic interface. We demonstrate up to a 5.07x speedup relative to the diagonal-precision vendor baseline, with 100x better accuracy than pure half precision on H200, providing higher accuracy than low-precision at higher speed than high-precision. Positive performance trends are also observed on MI300X, demonstrating broad applicability across GPUs.

cs.DC↗

arXiv2025

Leveraging Hardware-Aware Computation in Mixed-Precision Matrix Multiply: A Tile-Centric Approach

General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic necessitates a reevaluation of numerical algorithms to leverage mixed-precision computations, achieving improved performance and energy efficiency. This research introduces an adaptive mixed-precision GEMM framework that supports different precision formats at fine-grained tile/block levels. We utilize the PaRSEC runtime system to balance workloads across various architectures. The performance scales well on ARM CPU-based Fugaku supercomputer, Nvidia GPU-based A100 DGX, and AMD GPU-based Frontier supercomputer. This research aims to enhance computational efficiency and accuracy by bridging algorithmic advancements and hardware innovations, driving transformative progress in various applications.

cs.DC↗

arXiv2025

Performant Unified GPU Kernels for Portable Singular Value Computation Across Hardware and Precision

This paper presents a portable, GPU-accelerated implementation of a QR-based singular value computation algorithm in Julia. The singular value ecomposition (SVD) is a fundamental numerical tool in scientific computing and machine learning, providing optimal low-rank matrix approximations. Its importance has increased even more in large-scale machine learning pipelines, including large language models (LLMs), where it enables low-rank adaptation (LoRA). The implemented algorithm is based on the classic two-stage QR reduction, consisting of successive matrix reduction to band form and bidiagonal form. Our implementation leverages Julia's multiple dispatch and metaprogramming capabilities, integrating with the GPUArrays and KernelAbstractions frameworks to provide a unified type and hardware-agnostic function. It supports diverse GPU architectures and data types, and is, to our knowledge, the first GPU-accelerated singular value implementation to support Apple Metal GPUs and half precision. Performance results on multiple GPU backends and data types demonstrate that portability does not require sacrificing performance: the unified function outperforms most linear algebra libraries (MAGMA, SLATE, rocSOLVER, oneMKL) for matrix sizes larger than 1024x1024, and achieves 80%-90% of the performance of cuSOLVER for large matrices.

cs.DC↗

arXiv2025

Toward Portable GPU Performance: Julia Recursive Implementation of TRMM and TRSM

This paper presents a performant and portable recursive implementation of triangular matrix-matrix multiplication (TRMM) and triangular solve (TRSM) in Julia for GPUs, two kernels that underlie many linear-algebra algorithms. We restructure TRMM and TRSM so that most work is executed as general matrix-matrix multiplication (GEMM), improving use of the GPU memory hierarchy and reducing latency. Exploiting Julia's multiple dispatch and metaprogramming together with the GPUArrays and KernelAbstractions frameworks, we expose a single hardware-agnostic API that runs on NVIDIA, AMD, and Apple Silicon GPUs. For large matrices the recursive code reaches throughput comparable to vendor libraries such as cuBLAS and rocBLAS, while providing these routines on Apple Silicon for the first time. The entire implementation is only a few hundred lines of code, showing that unified Julia programs can deliver near-vendor performance across heterogeneous architectures.

cs.MS↗

arXiv2024

Toward Capturing Genetic Epistasis From Multivariate Genome-Wide Association Studies Using Mixed-Precision Kernel Ridge Regression

We exploit the widening margin in tensor-core performance between [FP64/FP32/FP16/INT8,FP64/FP32/FP16/FP8/INT8] on NVIDIA [Ampere,Hopper] GPUs to boost the performance of output accuracy-preserving mixed-precision computation of Genome-Wide Association Studies (GWAS) of 305K patients from the UK BioBank, the largest-ever GWAS cohort studied for genetic epistasis using a multivariate approach. Tile-centric adaptive-precision linear algebraic techniques motivated by reducing data motion gain enhanced significance with low-precision GPU arithmetic. At the core of Kernel Ridge Regression (KRR) techniques for GWAS lie compute-bound cubic-complexity matrix operations that inhibit scaling to aspirational dimensions of the population, genotypes, and phenotypes. We accelerate KRR matrix generation by redesigning the computation for Euclidean distances to engage INT8 tensor cores while exploiting symmetry.We accelerate solution of the regularized KRR systems by deploying a new four-precision Cholesky-based solver, which, at 1.805 mixed-precision ExaOp/s on a nearly full Alps system, outperforms the state-of-the-art CPU-only REGENIE GWAS software by five orders of magnitude.

q-bio.GN↗