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Knowledge graph reasoning (KGR) infers missing facts, with recent advances increasingly harnessing the semantic priors and reasoning abilities of Large Language Models (LLMs). However, prevailing generative paradigms are prone to memorizing…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Graph Neural Networks (GNNs) have empowered the advance in graph-structured data analysis. Recently, the rise of Large Language Models (LLMs) like GPT-4 has heralded a new era in deep learning. However, their application to graph data poses…
The use of large-scale machine learning methods is becoming ubiquitous in many applications ranging from business intelligence to self-driving cars. These methods require a complex computation pipeline consisting of various types of…
Logic rules are powerful for expressing complex reasoning and analysis problems. At the same time, they are inconvenient or impossible to use for many other aspects of applications. Integrating rules in a language with sets and functions,…
Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…
We introduce an algebra of data linkages. Data linkages are intended for modelling the states of computations in which dynamic data structures are involved. We present a simple model of computation in which states of computations are…
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its finite-dimensional representations. These functions are…
Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…
This paper presents DAALder (Database-Assisted Automata Learning, with Dutch suffix from leerder), a new algorithm for learning state machines, or automata, specifically deterministic finite-state automata (DFA). When learning state…
Tables form a central component in both exploratory data analysis and formal reporting procedures across many industries. These tables are often complex in their conceptual structure and in the computations that generate their individual…
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…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
In this article we discuss a data structure, which combines advantages of two different ways for representing graphs: adjacency matrix and collection of adjacency lists. This data structure can fast add and search edges (advantages of…
Although database systems perform well in data access and manipulation, their relational model hinders data scientists from formulating machine learning algorithms in SQL. Nevertheless, we argue that modern database systems perform well for…
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…
Transformers flexibly operate over sets of real-valued vectors representing task-specific entities and their attributes, where each vector might encode one word-piece token and its position in a sequence, or some piece of information that…
Deep learning has recently demonstrated its ability to rival the human brain for visual object recognition. As datasets get larger, a natural question to ask is if existing deep learning architectures can be extended to handle the 50+K…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Enterprises often maintain multiple databases for storing critical business data in siloed systems, resulting in inefficiencies and challenges with data interoperability. A key to overcoming these challenges lies in integrating disparate…