Related papers: When Only Topology Matters
Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich…
Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems…
The Unified Modeling Language UML is a language for specifying visualizing and documenting object oriented systems UML combines the concepts of OOA OODOMT and OOSE and is intended as a standard in the domain of object oriented analysis and…
By virtue of linguistic compositionality, few syntactic rules and a finite lexicon can generate an unbounded number of sentences. That is, language, though seemingly high-dimensional, can be explained using relatively few degrees of…
Graphs are used as models in many areas of computer science and computer engineering. For example graphs are used to represent syntax, control and data flow, dependency, state spaces, models such as UML and other types of domain-specific…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
Text-to-image generative models are capable of producing high-quality images that often faithfully depict concepts described using natural language. In this work, we comprehensively evaluate a range of text-to-image models on numerical…
Much research has highlighted the impressive capabilities of large language models (LLMs), like GPT and Bard, for solving introductory programming exercises. Recent work has shown that LLMs can effectively solve a range of more complex…
Combining multiple knowledge graphs (KGs) across linguistic boundaries is a persistent challenge due to semantic heterogeneity and the complexity of graph environments. We propose a framework for cross-lingual graph fusion, leveraging the…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…
Algorithmic meta-theorems explain the tractability of large classes of computational problems by linking logical expressibility with structural graph properties. While extensions of first-order logic such as FO+dp admit efficient model…
Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an…
The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary,…
We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying…
Ontologies are useful for automatic machine processing of domain knowledge as they represent it in a structured format. Yet, constructing ontologies requires substantial manual effort. To automate part of this process, large language models…
Isomorphisms allow human cognition to transcribe a potentially unsolvable problem from one domain to a different domain where the problem might be more easily addressed. Current approaches only focus on transcribing structural information…
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…