Related papers: A Formal Category Theoretical Framework for Multi-…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
Data of general object images have two most common structures: (1) each object of a given shape can be rendered in multiple different views, and (2) shapes of objects can be categorized in such a way that the diversity of shapes is much…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for…
The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical…
Form understanding depends on both textual contents and organizational structure. Although modern OCR performs well, it is still challenging to realize general form understanding because forms are commonly used and of various formats. The…
This paper begins the discussion of how the Information Flow Framework can be used to provide a principled foundation for the metalevel (or structural level) of the Standard Upper Ontology (SUO). This SUO structural level can be used as a…
We observe that the existence of sequential and parallel composition supermaps in higher order theories of transformations can be formalised using enriched category theory. Encouraged by relevant examples such as unitary supermaps and…
The linear representation hypothesis is the informal idea that semantic concepts are encoded as linear directions in the representation spaces of large language models (LLMs). Previous work has shown how to make this notion precise for…
The advent of data-driven science in the 21st century brought about the need for well-organized structured data and associated infrastructure able to facilitate the applications of Artificial Intelligence and Machine Learning. We present an…
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…
Previous work has demonstrated that categories are useful and expressive models for databases. In the present paper we build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
In the paper a new approach to data representation and manipulation is described, which is called the concept-oriented data model (CODM). It is supposed that items represent data units, which are stored in concepts. A concept is a…
We establish and advocate for a novel branch of category theory, centered around strong dinatural transformations (herein known as "paranatural transformations"). Paranatural transformations generalize natural transformations to…
Tabular data forms the backbone of high-stakes decision systems in finance, healthcare, and beyond. Yet industrial tabular datasets are inherently difficult: high-dimensional, riddled with missing entries, and rarely labeled at scale. While…