Related papers: Topos Theory for Generative AI and LLMs

By reformulating a learning process of a set system L as a game between Teacher (presenter of data) and Learner (updater of the abstract independent set), we define the order type dim L of L to be the order type of the game tree. The theory…

Large Language Model-based Multi-Agent Systems (MASs) have emerged as a powerful paradigm for tackling complex tasks through collaborative intelligence. However, the topology of these systems--how agents in MASs should be configured,…

We propose WHISPER-GPT: A generative large language model (LLM) for speech and music that allows us to work with continuous audio representations and discrete tokens simultaneously as part of a single architecture. There has been a huge…

Recent advancements in generative artificial intelligence (AI) have demonstrated its substantial potential in various fields. However, its application in port logistics remains underexplored. Ports are complex operational environments where…

Multi-modal generative AI (Artificial Intelligence) has attracted increasing attention from both academia and industry. Particularly, two dominant families of techniques have emerged: i) Multi-modal large language models (LLMs) demonstrate…

We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…

Large language models (LLMs) are very performant connectionist systems, but do they exhibit more compositionality? More importantly, is that part of why they perform so well? We present empirical analyses across four LLM families (12…

We introduce SymbolicAI, a versatile and modular framework employing a logic-based approach to concept learning and flow management in generative processes. SymbolicAI enables the seamless integration of generative models with a diverse…

LLMs have shown remarkable proficiency in general language understanding and reasoning. However, they consistently underperform in spatial reasoning that severely limits their application, particularly in embodied intelligence. Inspired by…

We show that a functor category whose domain is a colored category is a topos.The topos structure enables us to introduce cohomology of colored categories including quasi-schemoids. If the given colored category arises from an association…

One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…

We regard a geometric theory classified by a topos as a syntactic presentation for the topos and develop tools for finding such presentations. Extensions of geometric theories, which can add axioms, symbols and sorts, are treated as objects…

LLMs have revolutionized the field of artificial intelligence and have emerged as the de-facto tool for many tasks. The current established technology of LLMs is to process input and generate output at the token level. This is in sharp…

Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…

The development of large language models (LLMs) has successfully transformed knowledge-based systems such as open domain question nswering, which can automatically produce vast amounts of seemingly coherent information. Yet, those models…

Language models have emerged as a critical area of focus in artificial intelligence, particularly with the introduction of groundbreaking innovations like ChatGPT. Large-scale Transformer networks have quickly become the leading approach…

Topological materials occupy a frontier in condensed-matter physics thanks to their remarkable electronic and quantum properties, yet their cross-scale design remains bottlenecked by inefficient discovery workflows. Here, we introduce…

We explore a new connection between synthetic domain theory and Grothendieck topoi related to the distributive lattice classifier. In particular, all the axioms of synthetic domain theory (including the inductive fixed point object and the…

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…

Topic taxonomies, which represent the latent topic (or category) structure of document collections, provide valuable knowledge of contents in many applications such as web search and information filtering. Recently, several unsupervised…