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We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…

Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…

The proliferation of methods for modeling of human meaning-making constitutes a powerful class of instruments for the analysis of complex semiotic systems. However, the field lacks a general theoretical framework for describing these…

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…

Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are…

The rapid development of artificial intelligence (AI) systems has created an urgent need for their scientific quantification. While their fluency across a variety of domains is impressive, AI systems fall short on tests requiring…

Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…

This paper provides a review of past approaches to the use of deep-learning frameworks for the analysis of discrete irregular-patterned complex sequential datasets. A typical example of such a dataset is financial data where specific events…

This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…

Safety constraints are crucial to the development of mission-critical systems. The practice of developing software for systems of this type requires reliable methods for identifying and analysing project artefacts. This paper proposes a…

This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. Hypercomplex neural networks are machine learning models that feature higher-dimension numbers as parameters, inputs, and…

Data-driven approaches are becoming more common as problem-solving techniques in many areas of research and industry. In most cases, machine learning models are the key component of these solutions, but a solution involves multiple such…

We introduce an information-theoretic framework that views learning as universal prediction under log loss, characterized through regret bounds. Central to the framework is an effective notion of architecture-based model complexity, defined…

We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern…

Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and…

Against the backdrop of rapid advances in artificial intelligence, legal argument mining has emerged as an important research area linking legal texts with intelligent analysis, carrying significant theoretical and practical implications.…

We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower…