Related papers: Category-Theoretic Foundations of "STCLang: State …
Several methods exist today to accelerate Machine Learning(ML) or Deep-Learning(DL) model performance for training and inference. However, modern techniques that rely on various graph and operator parallelism methodologies rely on search…
Tangent category theory is a well-established categorical context for differential geometry. In a previous paper, a formal approach was adopted to provide a genuine Grothendieck construction in the context of tangent categories by…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
Cross-modal retrieval has become a highlighted research topic for retrieval across multimedia data such as image and text. A two-stage learning framework is widely adopted by most existing methods based on Deep Neural Network (DNN): The…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
Real world applications as in industry and robotics need modelling rich and diverse automated planning problems. Their resolution usually requires coordinated and concurrent action execution. In several cases, these problems are naturally…
There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…
The ability to efficiently find relevant subgraphs and paths in a large graph to a given query is important in many applications including scientific data analysis, social networks, and business intelligence. Currently, there is little…
Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model-value beyond mere comprehensible pictures. To…
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
The scientific and practical needs of the twenty-first century lead humankind to convergence of the specialized and diverse branches of science and technology. This convergence reveals the need for new mathematical theories capable of…
Large reasoning models (LRMs) generate complex reasoning traces with planning, reflection, verification, and backtracking. In this work, we introduce ReasoningFlow, a unified schema for analyzing the semantic structures of these complex…
Dataflow applications, such as machine learning algorithms, can run for days, making it desirable to have assurances that they will work correctly. Current tools are not good enough: too often the interactions between tasks are not…
This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…
We present a framework that takes a concurrent program composed of unsynchronized processes, along with a temporal specification of their global concurrent behaviour, and automatically generates a concurrent program with synchronization…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
The following work addresses the problem of frameworks for data stream processing that can be used to evaluate the solutions in an environment that resembles real-world applications. The definition of structured frameworks stems from a need…
This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices…
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…