Analogies, Metaphors, Allegories: Categorical architectures of general intelligence

This thesis presents a bird eye view of Artificial General Intelligence (AGI) and Hypercomputing through the lens of Category Theory and Topos Theory. The work discusses various frameworks for AGI development, focusing on explainability and alignment with human values. It examines the use of Hyper Dimensional Computing (HDC) and Vector Symbolic Architectures (VSA) as tools for bridging Symbolic and Connectionist approaches, aiming to unify diverse paradigms in AI. The thesis also delves into the cognitive structures necessary for creating self aware, interpretable AGI systems capable of making ethical decisions in dynamic environments. Category theory and Topos Theory in particular are the background mathematical theories in which the present contributions find a natural language to be discussed, since they provide the foundations for modeling cognitive architectures and describe their inner processes. The present work explores how to generalise the paradigm of Manifold Learning by leveraging concepts from Category Theory, such as (co)limits, enrichment and allegories, envisioning autonomous artificial agents capable of reasoning about geometric patterns in abstract spaces. Besides contributing to the theoretical foundations for AGI, the present work addresses future challenges in aligning AI development with ethical considerations, proposing models that integrate explainability at their core. Finally, we propose an implementation of an Episodic Memory SubModule (EMSM) within the context of Retrieval Augmented Generation (RAG) architectures, exploring its role in enhancing contextual understanding and memory retention in AI systems.