Related papers: On the Expressiveness of LARA: A Unified Language …
\textsc{Lara} is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of \textsc{Lara}'s expressive ability reports that it can represent relational algebra and most…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
We investigate the expressive power of $\mathsf{MATLANG}$, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation $\mathsf{inv}$ of inverting a matrix.…
In this extended abstract we provide a unifying framework that can be used to characterize and compare the expressive power of query languages for different data base models. The framework is based upon the new idea of valid partition, that…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic…
Analytics tasks manipulate structured data with variants of relational algebra (RA) and quantitative data with variants of linear algebra (LA). The two computational models have overlapping expressiveness, motivating a common programming…
We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic,…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…
Multi-turn intent classification is notably challenging due to the complexity and evolving nature of conversational contexts. This paper introduces LARA, a Linguistic-Adaptive Retrieval-Augmentation framework to enhance accuracy in…
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…
Large Language Models (LLMs) are powerful reasoners in natural language, but their actions are typically confined to outputting vocabulary tokens. As a result, interactions with external environments -- such as symbolic operators or…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
The goal of this paper is to provide a strong integration between constraint modelling and relational DBMSs. To this end we propose extensions of standard query languages such as relational algebra and SQL, by adding constraint modelling…