Related papers: A Relational Matrix Algebra and its Implementation…
Prediction over tabular data is an essential task in many data science applications such as recommender systems, online advertising, medical treatment, etc. Tabular data is structured into rows and columns, with each row as a data sample…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
Relational databases (RDBs) are widely regarded as the gold standard for storing structured information. Consequently, predictive tasks leveraging this data format hold significant application promise. Recently, Relational Deep Learning…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Matrix completion has received vast amount of attention and research due to its wide applications in various study fields. Existing methods of matrix completion consider only nonlinear (or linear) relations among entries in a data matrix…
Recent advances in Large Language Models (LLMs) have significantly improved table understanding tasks such as Table Question Answering (TableQA), yet challenges remain in ensuring reliability, scalability, and efficiency, especially in…
This paper proposes Relational Similarity Machines (RSM): a fast, accurate, and flexible relational learning framework for supervised and semi-supervised learning tasks. Despite the importance of relational learning, most existing methods…
The emergence of large-language models (LLMs) has enabled a new class of semantic data processing systems (SDPSs) to support declarative queries against unstructured documents. Existing SDPSs are, however, lacking a unified algebraic…
Though large language models (LLMs) have demonstrated exceptional performance across numerous problems, their application to predictive tasks in relational databases remains largely unexplored. In this work, we address the notion that LLMs…
We consider an algebra with non-standard operations on the class of row monomial matrices (having one unit and rest of zeros in every row). The class of row monomial matrices is closed under multiplication, but not closed under ordinary…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA at sublinear cost -- by using much fewer memory cells and…
Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains…
In recent times Large Language Models have exhibited tremendous capabilities, especially in the areas of mathematics, code generation and general-purpose reasoning. However for specialized domains especially in applications that require…
Owing to recent advancements, Large Language Models (LLMs) can now be deployed as agents for increasingly complex decision-making applications in areas including robotics, gaming, and API integration. However, reflecting past experiences in…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
Alloy is a lightweight modeling formalism based on relational algebra. In prior work with Fisler, Giannakopoulos, Krishnamurthi, and Yoo, we have presented a tool, Alchemy, that compiles Alloy specifications into implementations that…