Related papers: Categories of Semantic Concepts
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
Distributed word representations have been demonstrated to be effective in capturing semantic and syntactic regularities. Unsupervised representation learning from large unlabeled corpora can learn similar representations for those words…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
Concepts play a central role in many applications. This includes settings where concepts have to be modelled in the absence of sentence context. Previous work has therefore focused on distilling decontextualised concept embeddings from…
Distributed representations of words have been shown to capture lexical semantics, as demonstrated by their effectiveness in word similarity and analogical relation tasks. But, these tasks only evaluate lexical semantics indirectly. In this…
The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Topic models aim to reveal latent structures within a corpus of text, typically through the use of term-frequency statistics over bag-of-words representations from documents. In recent years, conceptual entities -- interpretable,…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…
The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification…
Mechanisms are a fundamental concept in many areas of science. Nonetheless, there has been little effort to develop structures to represent mechanisms. We explore the issues in developing a basic semantic modeling framework for describing…
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Taxonomies are semantic hierarchies of concepts. One limitation of current taxonomy learning systems is that they define concepts as single words. This position paper argues that contextualized word representations, which recently achieved…
Foundation models like chatGPT have demonstrated remarkable performance on various tasks. However, for many questions, they may produce false answers that look accurate. How do we train the model to precisely understand the concepts? In…