Related papers: A Relational Matrix Algebra and its Implementation…

Batch data analytics is a growing application for Large Language Models (LLMs). LLMs enable users to perform a wide range of natural language tasks, such as classification, entity extraction, and translation, over large datasets. However,…

Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…

Remote memory access (RMA) is an emerging high-performance programming model that uses RDMA hardware directly. Yet, accessing remote memories cannot invoke activities at the target which complicates implementation and limits performance of…

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…

This paper proposes a new neural architecture for collaborative ranking with implicit feedback. Our model, LRML (\textit{Latent Relational Metric Learning}) is a novel metric learning approach for recommendation. More specifically, instead…

Many tasks require finding groups of elements in a matrix of numbers, symbols or class likelihoods. One approach is to use efficient bi- or tri-linear factorization techniques including PCA, ICA, sparse matrix factorization and plaid…

PRAM puts agent-based models on a sound probabilistic footing as a basis for integrating agent-based and probabilistic models. It extends the themes of probabilistic relational models and lifted inference to incorporate dynamical models and…

We present a pseudocode algorithm for translating our (Elementary) Mathematical Data Model schemes into relational ones and associated sets of non-relational constraints, used by MatBase, our intelligent data and knowledge base management…

This paper investigates the novel one-sided communication methods based on remote memory access (RMA) operations in MPI for dynamic resizing of malleable applications, enabling data redistribution with minimal impact on application…

A matrix-analytic method is proposed for solving a system of linear integral equations arises in three tandem servers. The approach is by modelling the cumulative distribution function (cdf) of the service time as a matrix exponential…

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…

Relational Networks (RN) as introduced by Santoro et al. (2017) have demonstrated strong relational reasoning capabilities with a rather shallow architecture. Its single-layer design, however, only considers pairs of information objects,…

We present a method to integrate Large Language Models (LLMs) and traditional tabular data classification techniques, addressing LLMs challenges like data serialization sensitivity and biases. We introduce two strategies utilizing LLMs for…

Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…

We introduce rLLM (relationLLM), a PyTorch library designed for Relational Table Learning (RTL) with Large Language Models (LLMs). The core idea is to decompose state-of-the-art Graph Neural Networks, LLMs, and Table Neural Networks into…

Databases have been studied category-theoretically for decades. The database schema -- whose purpose is to arrange high-level conceptual entities -- is generally modeled as a category or sketch. The data itself, often called an instance, is…

Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…

Multi-relational databases are the basis of most consolidated data collections in science and industry today. Most learning and mining algorithms, however, require data to be represented in a propositional form. While there is a variety of…

In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…