Related papers: HPL-MxP Benchmark: Mixed-Precision Algorithms, Ite…

In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…

FPGAs have found increasing adoption in data center applications since a new generation of high-level tools have become available which noticeably reduce development time for FPGA accelerators and still provide high quality of results.…

Machine learning workflow development is a process of trial-and-error: developers iterate on workflows by testing out small modifications until the desired accuracy is achieved. Unfortunately, existing machine learning systems focus…

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…

Statistical machine learning often uses probabilistic algorithms, such as Markov Chain Monte Carlo (MCMC), to solve a wide range of problems. Probabilistic computations, often considered too slow on conventional processors, can be…

Multiplication is a core operation in modern neural network (NN) computations, contributing significantly to energy consumption. The linear-complexity multiplication (L-Mul) algorithm is specifically proposed as an approximate…

Solving a system of $m$ multivariate quadratic equations in $n$ variables over finite fields (the MQ problem) is one of the important problems in the theory of computer science. The XL algorithm (XL for short) is a major approach for…

We present a novel relaxation framework for general mixed-integer nonlinear programming (MINLP) grounded in computational geometry. Our approach constructs polyhedral relaxations by convexifying finite sets of strategically chosen points,…

We have repurposed Google Tensor Processing Units (TPUs), application-specific chips developed for machine learning, into large-scale dense linear algebra supercomputers. The TPUs' fast inter-core interconnects (ICI)s, physically…

As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…

Motivated by the increasing availability of low- and mixed-precision arithmetic on modern hardware, we develop mixed-precision variants of Lloyd's algorithm for k-means clustering. The main ingredient is a family of mixed-precision kernels…

Large Language Models (LLMs), such as GPT-4 and DeepSeek, have been applied to a wide range of domains in software engineering. However, their potential in the context of High-Performance Computing (HPC) much remains to be explored. This…

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…

The increasing number of processing elements and decreas- ing memory to core ratio in modern high-performance platforms makes efficient strong scaling a key requirement for numerical algorithms. In order to achieve efficient scalability on…

One of the hardest challenges of the current Big Data landscape is the lack of ability to process huge volumes of information in an acceptable time. The goal of this work, is to ascertain if it is useful to use typical Big Data tools to…

This study introduces a mixed-integer linear programming (MILP) model, effectively co-optimizing patrolling, damage assessment, fault isolation, repair, and load re-energization processes. The model is designed to solve a vital operational…

Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of…

Numerical features of matrix multiplier hardware units in NVIDIA and AMD data centre GPUs have recently been studied. Features such as rounding, normalisation, and internal precision of the accumulators are of interest. In this paper, we…

While many approaches have been proposed to analyze the problem of matrix multiplication parallel computing, few of them address the problem on heterogeneous processor platforms. It still remains an open question on heterogeneous processor…