Related papers: Topos Theory for Generative AI and LLMs

The rapid advancement of generative models has empowered modern AI systems to comprehend and produce highly sophisticated content, even achieving human-level performance in specific domains. However, these models are fundamentally…

A generalization of topos theory is proposed giving an abstract realization of such categories as, say, the categories of manifolds and of Grothendieck schemes on the one hand, and permitting one, on the other hand, a view on…

The rapid development of AI and LLMs has driven new methods of SDLC, in which a large portion of code, technical, and business documentation is generated automatically. However, since there is no single architectural framework that can…

The field of Artificial Intelligence (AI) continues to drive transformative innovations, with significant progress in conversational interfaces, autonomous vehicles, and intelligent content creation. Since the launch of ChatGPT in late…

Our study demonstrates the effective use of Large Language Models (LLMs) for automating the classification of complex datasets. We specifically target proposals of Decentralized Autonomous Organizations (DAOs), as the clas-sification of…

This paper presents a novel methodological framework for detecting and classifying latent constructs, including frames, narratives, and topics, from textual data using Open-Source Large Language Models (LLMs). The proposed hybrid approach…

Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…

Large language models (LLMs) have not only revolutionized the field of natural language processing (NLP) but also have the potential to bring a paradigm shift in many other fields due to their remarkable abilities of language understanding,…

Large Language Models (LLMs) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive…

Large Language Models (LLMs), originally developed for natural language processing (NLP), have demonstrated the potential to generalize across modalities and domains. With their in-context learning (ICL) capabilities, LLMs can perform…

Large Language Models (LLMs) have generated considerable interest and debate regarding their potential emergence of Theory of Mind (ToM). Several recent inquiries reveal a lack of robust ToM in these models and pose a pressing demand to…

We propose a novel model- and feature-based approach to development of vehicle software systems, where the end architecture is not explicitly defined. Instead, it emerges from an iterative process of search and optimization given certain…

We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the formal theory of Kan extension in this 2-category (pointwise…

Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…

This study explored how large language models (LLMs) perform in two areas related to art: writing critiques of artworks and reasoning about mental states (Theory of Mind, or ToM) in art-related situations. For the critique generation part,…

We observe that pre-trained large language models (LLMs) are capable of autoregressively completing complex token sequences -- from arbitrary ones procedurally generated by probabilistic context-free grammars (PCFG), to more rich spatial…

We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…

In recent years, machine learning (ML) techniques have created numerous opportunities for intelligent mobile networks and have accelerated the automation of network operations. However, complex network tasks may involve variables and…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

Transformer architectures are the backbone of the modern AI revolution. However, they are based on simply stacking the same blocks in dozens of layers and processing information sequentially from one block to another. In this paper, we…