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

It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a…

We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…

In-time particle trajectory reconstruction in the Large Hadron Collider is challenging due to the high collision rate and numerous particle hits. Using GNN (Graph Neural Network) on FPGA has enabled superior accuracy with flexible…

Large Language Models (LLMs) demand substantial computational resources, resulting in high energy consumption on GPUs. To address this challenge, we focus on Coarse-Grained Reconfigurable Arrays (CGRAs) as an effective alternative that…

In this paper we focus on the integration of high-performance numerical libraries in ab initio codes and the portability of performance and scalability. The target of our work is FLEUR, a software for electronic structure calculations…

Ciminion and Hydra are two recently introduced symmetric key Pseudo-Random Functions for Multi-Party Computation applications. For efficiency, both primitives utilize quadratic permutations at round level. Therefore, polynomial system…

The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined…

This paper is a sequel to "Computing diagonal form and Jacobson normal form of a matrix using Groebner bases", J. of Symb. Computation, 46 (5), 2011. We present a new fraction-free algorithm for the computation of a diagonal form of a…

Sparse matrix multiplication operators (i.e., SpMM and SDDMM) are widely used in deep learning and scientific computing. Modern accelerators are commonly equipped with Tensor Core Units (TCUs) and CUDA cores to accelerate sparse operators.…

The R package GFA provides a full pipeline for factor analysis of multiple data sources that are represented as matrices with co-occurring samples. It allows learning dependencies between subsets of the data sources, decomposed into latent…

Modern large language foundation models (LLM) have now entered the daily lives of millions of users. We ask a natural question whether it is possible to customize LLM for every user or every task. From system and industrial economy…

Latent Dirichlet Allocation(LDA) is a popular topic model. Given the fact that the input corpus of LDA algorithms consists of millions to billions of tokens, the LDA training process is very time-consuming, which may prevent the usage of…

Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…

Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…

In recent years, significant efforts have been directed toward adapting modern neural network architectures for tabular data. However, despite their larger number of parameters and longer training and inference times, these models often…

Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a…

Efficient execution of SPARQL queries over large RDF datasets is a topic of considerable interest due to increased use of RDF to encode data. Most of this work has followed either relational or graph-based approaches. In this paper, we…

In this paper, we make a contribution to the computation of Gr\"obner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we…

Tate introduced in [Ta71] the notion of Tate algebras to serve, in the context of analytic geometry over the-adics, as a counterpart of polynomial algebras in classical algebraic geometry. In [CVV19, CVV20] the formalism of Gr{\"o}bner…

Granular ball computing (GBC), as an efficient, robust, and scalable learning method, has become a popular research topic of granular computing. GBC includes two stages: granular ball generation (GBG) and multi-granularity learning based on…