Related papers: Lara: A Key-Value Algebra underlying Arrays and Re…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

Querying tables with unstructured data is challenging due to the presence of text (or image), either embedded in the table or in external paragraphs, which traditional SQL struggles to process, especially for tasks requiring semantic…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…

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…

The ubiquity and value of tables as semi-structured data across various domains necessitate advanced methods for understanding their complexity and vast amounts of information. Despite the impressive capabilities of large language models…

This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic…

Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs) for solving question-answer (QA) tasks. The state-of-the-art RAG approaches often use the graph data as the…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data…

Large language models (LLMs) are primarily designed to understand unstructured text. When directly applied to structured formats such as tabular data, they may struggle to discern inherent relationships and overlook critical patterns. While…

In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…

Graph machine learning has led to a significant increase in the capabilities of models that learn on arbitrary graph-structured data and has been applied to molecules, social networks, recommendation systems, and transportation, among other…

Large language models are often adapted using parameter-efficient techniques such as Low-Rank Adaptation (LoRA), formulated as $y = W_0x + BAx$, where $W_0$ is the pre-trained parameters and $x$ is the input to the adapted layer. While…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

Recent advancements in language models (LMs) have notably enhanced their ability to reason with tabular data, primarily through program-aided mechanisms that manipulate and analyze tables. However, these methods often require the entire…

Graph algorithms play an important role in many computer science areas. In order to solve problems that can be modeled using graphs, it is necessary to use a data structure that can represent those graphs in an efficient manner. On top of…

Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…

Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…