Related papers: Topos Theory for Generative AI and LLMs

Cutting-edge Artificial Intelligence (AI) techniques keep reshaping our view of the world. For example, Large Language Models (LLMs) based applications such as ChatGPT have shown the capability of generating human-like conversation on…

Large Language Models (LLMs) have demonstrated remarkable reasoning capabilities, yet their standard generation process -- auto-regressive token prediction -- is inherently myopic and prone to cascading errors. To address this, the…

Derivations provide a way of transporting ideas from the calculus of manifolds to algebraic settings where there is no sensible notion of limit. In this paper, we consider derivations in certain monoidal categories, called codifferential…

Recently, the exponential growth in capability and pervasiveness of Large Language Models (LLMs) has led to significant work done in the field of code generation. However, this generation has been limited to code snippets. Going one step…

The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…

Transistor topology optimization is a critical step in standard cell design, directly dictating diffusion sharing efficiency and downstream routability. However, identifying optimal topologies remains a persistent bottleneck, as…

Large language model (LLM)-based multi-agent systems have shown strong potential for complex reasoning by coordinating specialized agents through structured communication. However, existing topology-evolution methods typically construct or…

Large Language Models (LLMs) are increasingly integrated into critical decision-making pipelines, a trend that raises the demand for robust and automated data analysis. Current approaches to dataset risk analysis are limited to manual…

This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…

This paper investigates how Large Language Models (LLMs) from leading providers (OpenAI, Google, Anthropic, DeepSeek, and xAI) can be applied to quantitative sector-based portfolio construction. We use LLMs to identify investable universes…

We present a tendency of large language models (LLMs) to generate absurd patterns despite their clear inappropriateness in a simple task of identifying regularities in number series. Several approaches have been proposed to apply LLMs to…

We suggest an ordering for the predicates in continuous logic so that the semantics of continuous logic can be formulated as a hyperdoctrine. We show that this hyperdoctrine can be embedded into the hyperdoctrine of subobjects of a suitable…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…

Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their…

Existing frameworks for LLM-based agent architectures describe systems from a single perspective: industry guides (Anthropic, Google, LangChain) focus on execution topology -- how data flows -- while cognitive science surveys focus on…

The use of artificial intelligence (AI) in research across all disciplines is becoming ubiquitous. However, this ubiquity is largely driven by hyperspecific AI models developed during scientific studies for accomplishing a well-defined,…

Large language models (LLMs) have greatly accelerated the automation of algorithm generation and optimization. However, current methods such as EoH and FunSearch mainly rely on predefined templates and expert-specified functions that focus…

Artificial intelligence (AI) systems, and Large Language Models (LLMs) in particular, are increasingly employed for creative tasks like scientific idea generation, constituting a form of generalization from training data unaddressed by…

Our main result states that for each finite complex L the category ${\bf TOP}$ of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all…