Related papers: Topos Theory for Generative AI and LLMs

Recent developments in Large Language Models (LLMs) have significantly expanded their applications across various domains. However, the effectiveness of LLMs is often constrained when operating individually in complex environments. This…

Task-oriented grasping (TOG) is more challenging than simple object grasping because it requires precise identification of object parts and careful selection of grasping areas to ensure effective and robust manipulation. While recent…

Large Language Models (LLMs), powered by Transformers, have demonstrated human-like intelligence capabilities, yet their underlying mechanisms remain poorly understood. This paper presents a novel framework for interpreting LLMs as…

Large language model (LLM)-based multi-agent systems (MAS) have demonstrated exceptional capabilities in solving complex tasks, yet their effectiveness depends heavily on the underlying communication topology that coordinates agent…

Utilizing LLMs for automated taxonomy construction presents a clear opportunity for the comprehensive, yet efficient mapping of potentially complex domains. When contending with high volumes of rapidly growing corpora, however, it becomes…

Classic AI planning problems have been revisited in the Large Language Model (LLM) era, with a focus of recent benchmarks on success rates rather than plan efficiency. We examine the degree to which frontier models reason optimally versus…

Large language models (LLMs) have emerged as powerful tools for many AI problems and exhibit remarkable in-context learning (ICL) capabilities. Compositional ability, solving unseen complex tasks that combine two or more simple tasks, is an…

Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…

A classical result of topos theory holds that the category of coalgebras for a Cartesian comonad on a topos is again a topos (Kock and Wraith, 1971). It is natural to refine this result to a topos-theoretic setting that includes universes.…

Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…

Different fields in applied machine learning such as computer vision, speech or natural language processing have been building domain-specialised solutions. Currently, we are witnessing an opposing trend towards developing more generalist…

We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…

This paper introduces the idea of applying signal processing inside a Large Language Model (LLM). With the recent explosion of generative AI, our work can help bridge two fields together, namely the field of signal processing and large…

We show that large language models (LLMs) are remarkably good at working with interpretable models that decompose complex outcomes into univariate graph-represented components. By adopting a hierarchical approach to reasoning, LLMs can…

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we…

The emergence of Large Language Models (LLMs) has transformed information access, with current LLMs also powering deep research systems that can generate comprehensive report-style answers, through planned iterative search, retrieval, and…

Homotopy Type Theory may be seen as an internal language for the $\infty$-category of weak $\infty$-groupoids which in particular models the univalence axiom. Voevodsky proposes this language for weak $\infty$-groupoids as a new foundation…

Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…

Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…