Related papers: Category Theory for Genetics
Ontologies and taxonomies of research fields are critical for managing and organising scientific knowledge, as they facilitate efficient classification, dissemination and retrieval of information. However, the creation and maintenance of…
We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the…
To make sense of massive data, we often fit simplified models and then interpret the parameters; for example, we cluster the text embeddings and then interpret the mean parameters of each cluster. However, these parameters are often…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics---with adjunctions being the primary lense. If adjunctions are so important in mathematics,…
Human languages use a wide range of grammatical categories to constrain which words or phrases can fill certain slots in grammatical patterns and to express additional meanings, such as tense or aspect, through morpho-syntactic means. These…
Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes representations, and why these representations support complex behavior remains incomplete. We…
Language models, especially transformer-based ones, have achieved colossal success in NLP. To be precise, studies like BERT for NLU and works like GPT-3 for NLG are very important. If we consider DNA sequences as a text written with an…
Neural language models are a powerful tool to embed words into semantic vector spaces. However, learning such models generally relies on the availability of abundant and diverse training examples. In highly specialised domains this…
Syllables play an important role in speech synthesis, speech recognition, and spoken document retrieval. A novel, low cost, and language agnostic approach to dividing words into their corresponding syllables is presented. A hybrid genetic…
There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be…
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context -- and for each type a set of terms of said type. This is the case for…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
The Categorical Compositional Distributional (DisCoCat) Model is a powerful mathematical model for composing the meaning of sentences in natural languages. Since we can think of biological sequences as the "language of life", it is…
State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics.…
Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and…