Related papers: GBLA -- Gr\"obner Basis Linear Algebra Package

The inference and training stages of Graph Neural Networks (GNNs) are often dominated by the time required to compute a long sequence of matrix multiplications between the sparse graph adjacency matrix and its embedding. To accelerate these…

We consider the problem of computing a grevlex Gr\"obner basis for the set $F_r(M)$ of minors of size $r$ of an $n\times n$ matrix $M$ of generic linear forms over a field of characteristic zero or large enough. Such sets are not regular…

We present the first end-to-end demonstration of fine-tuning and serving Google's Gemma 4 31B model on TPU hardware, providing an empirical comparison of TPU and GPU platforms for large language model adaptation. Using LoRA on a Google TPU…

The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for…

There is a stage in the GPU computing pipeline where a grid of thread-blocks, in \textit{parallel space}, is mapped onto the problem domain, in \textit{data space}. Since the parallel space is restricted to a box type geometry, the mapping…

We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that…

GPUs are uniquely suited to accelerate (SQL) analytics workloads thanks to their massive compute parallelism and High Bandwidth Memory (HBM) -- when datasets fit in the GPU HBM, performance is unparalleled. Unfortunately, GPU HBMs remain…

The famous F5 algorithm for computing Gr\"obner basis was presented by Faug\`ere in 2002 without complete proofs for its correctness. The current authors have simplified the original F5 algorithm into an F5 algorithm in Buchberger's style…

Fine-tuning Large Language Models (LLMs) has become a crucial technique for adapting pre-trained models to downstream tasks. However, the enormous size of LLMs poses significant challenges in terms of computational complexity and resource…

In this work, we extend modular techniques for computing Gr\"obner bases involving rational coefficients to (two-sided) ideals in free algebras. We show that the infinite nature of Gr\"obner bases in this setting renders the classical…

Deep learning (DL) frameworks take advantage of GPUs to improve the speed of DL inference and training. Ideally, DL frameworks should be able to fully utilize the computation power of GPUs such that the running time depends on the amount of…

Training modern deep learning models is increasingly constrained by GPU memory and compute limits. While Randomized Numerical Linear Algebra (RandNLA) offers proven techniques to compress these models, the lack of a unified,…

We present a customizable soft architecture which allows for the execution of GPGPU code on an FPGA without the need to recompile the design. Issues related to scaling the overlay architecture to multiple GPGPU multiprocessors are…

The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…

Loopy Belief Propagation (LBP) is a widely used approximate inference algorithm in probabilistic graphical models, with applications in computer vision, error correction codes, protein folding, program analysis, etc. However, LBP faces…

The LLL lattice reduction has been widely used to decrease the bit error rate (BER) of the Babai point, but its running time varies much from matrix to matrix. To address this problem, some fixed-complexity LLL reductions (FCLLL) have been…

GPUs are dedicated processors used for complex calculations and simulations and they can be effectively used for tropical algebra computations. Tropical algebra is based on max-plus algebra and min-plus algebra. In this paper we proposed…

Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, GNNs have been shown to be a…

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…

Graph partitioning, a well studied problem of parallel computing has many applications in diversified fields such as distributed computing, social network analysis, data mining and many other domains. In this paper, we introduce FGPGA, an…