Related papers: GBLA -- Gr\"obner Basis Linear Algebra Package
The Deep Graph Library (DGL) was designed as a tool to enable structure learning from graphs, by supporting a core abstraction for graphs, including the popular Graph Neural Networks (GNN). DGL contains implementations of all core graph…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
Designing flexible graph kernels that can run well on various platforms is a crucial research problem due to the frequent usage of graphs for modeling data and recent architectural advances and variety. In this work, we propose a novel…
Bloom filters are a fundamental data structure for approximate membership queries, with applications ranging from data analytics to databases and genomics. Several variants have been proposed to accommodate parallel architectures. GPUs,…
We present a generic and executable formalization of signature-based algorithms (such as Faug\`ere's $F_5$) for computing Gr\"obner bases, as well as their mathematical background, in the Isabelle/HOL proof assistant. Said algorithms are…
In Scientific Computing and modern Machine Learning (ML) workloads, sequences of dependent General Matrix Multiplications (GEMMs) often dominate execution time. While state-of-the-art BLAS libraries aggressively optimize individual GEMM…
We present a parallel algorithm and scalable implementation for genome analysis, specifically the problem of finding overlaps and alignments for data from "third generation" long read sequencers. While long sequences of DNA offer enormous…
General Matrix Multiplication or GEMM kernels take centre place in high performance computing and machine learning. Recent NVIDIA GPUs include GEMM accelerators, such as NVIDIA's Tensor Cores. Their exploitation is hampered by the…
Gradient Boosting (GB) is a popular methodology used to solve prediction problems by minimizing a differentiable loss function, $L$. GB performs very well on tabular machine learning (ML) problems; however, as a pure ML solver it lacks the…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
Graph neural networks (GNNs) have extended the success of deep neural networks (DNNs) to non-Euclidean graph data, achieving ground-breaking performance on various tasks such as node classification and graph property prediction.…
Large Language Models (LLMs) have gained considerable notoriety in the field of natural language to SQL tasks (NL2SQL). In this study, we show how task decomposition can greatly benefit LLMs in database understanding and query generation in…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
Recently, tensor algebra have witnessed significant applications across various domains. Each operator in tensor algebra features different computational workload and precision. However, current general accelerators, such as VPU, GPGPU, and…
Traditional logic programming relies on symbolic computation on the CPU, which can limit performance for large-scale inference tasks. Recent advances in GPU hardware enable high-throughput matrix operations, motivating a shift toward…
In this paper, we introduce the G\"uler-type acceleration technique and utilize it to propose three acceleration algorithms: the G\"uler-type accelerated proximal gradient method (GPGM), the G\"uler-type accelerated linearized augmented…
In high-energy physics, the increasing luminosity and detector granularity at the Large Hadron Collider are driving the need for more efficient data processing solutions. Machine Learning has emerged as a promising tool for reconstructing…
We present the Glasgow Parallel Reduction Machine (GPRM), a novel, flexible framework for parallel task-composition based many-core programming. We allow the programmer to structure programs into task code, written as C++ classes, and…
Graph algorithms can be expressed in terms of linear algebra. GraphBLAS is a library of low-level building blocks for such algorithms that targets algorithm developers. LAGraph builds on top of the GraphBLAS to target users of graph…
The structure of the F5 algorithm to compute Gr\"obner bases makes it very efficient. However, while it is believed to terminate for so-called regular sequences, it is not clear whether it terminates for all inputs. This paper has two major…