相关论文: Topos Theory for Generative AI and LLMs
Current Artificial Intelligence (AI) systems are frequently built around monolithic models that entangle perception, reasoning, and decision-making, a design that often conflicts with established software architecture principles. Large…
Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to…
Current research has explored how Generative AI can support the brainstorming process for content creators, but a gap remains in exploring support-tools for the pre-writing process. Specifically, our research is focused on supporting users…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Generalized Category Discovery (GCD) is a crucial task that aims to recognize both known and novel categories from a set of unlabeled data by utilizing a few labeled data with only known categories. Due to the lack of supervision and…
In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g.,…
Artificial Intelligence is moving from models that only generate text to Agentic AI, where systems behave as autonomous entities that can perceive, reason, plan, and act. Large Language Models (LLMs) are no longer used only as passive…
In mid-20th century, the linguist Noam Chomsky established generative linguistics, and made significant contributions to linguistics, computer science, and cognitive science by developing the computational and philosophical foundations for…
Converging evidence suggests that human systems of semantic categories achieve near-optimal compression via the Information Bottleneck (IB) complexity-accuracy tradeoff. Large language models (LLMs) are not trained for this objective, which…
We propose a hybrid approach to machine Theory of Mind (ToM) that uses large language models (LLMs) as a mechanism for generating hypotheses and likelihood functions with a Bayesian inverse planning model that computes posterior…
We develop a discrete gauge-theoretic framework for superposition in large language models (LLMs) that replaces the single-global-dictionary premise with a sheaf-theoretic atlas of local semantic charts. Contexts are clustered into a…
Vision-language models (VLMs) and the recent surge of Multimodal Large Language Models (MLLMs) have revolutionized artificial intelligence with unprecedented cross-modal alignment and zero-shot generalization. However, enabling them to…
The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ($\sim 10^1$ dimensions), modern LLMs…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
This paper proposes a novel framework for understanding large language models (LLMs) by reconceptualizing them as semiotic machines rather than as imitations of human cognition. Drawing from structuralist and post-structuralist theories of…
Knowledge graphs (KGs) are crucial for representing and reasoning over structured information, supporting a wide range of applications such as information retrieval, question answering, and decision-making. However, their effectiveness is…
Large collections of tabular data from data lakes, web tables and open data portals often originate from heterogeneous sources, leading to representational inconsistencies. Understanding and organizing such repositories therefore remains a…
Large collections of tabular data from data lakes, web tables and open data portals often originate from heterogeneous sources, leading to representational inconsistencies. Understanding and organizing such repositories therefore remains a…
As Large Language Models (LLMs) and other forms of Generative AI permeate various aspects of our lives, their application for learning and education has provided opportunities and challenges. This paper presents an investigation into the…
The rapid adoption of large language models (LLMs) has enabled new forms of AI-assisted reasoning across scientific, technical, and organizational domains. However, prevailing modes of LLM use remain cognitively unstructured: problem…