THE SHAPE OF WORDS
Stephen Fitz ◼ Tokyo, Japan ◼ 2022
"The Shape of Words" project aims to investigate topological and geometric aspects of natural language data, models, and representations. Over the past century, we saw an emergence of new branches of Mathematics exploring properties of high-dimensional objects. These ideas came initially from the Erlangen Program outlined by Felix Klein in his seminal work on the formalization of geometry as the study of invariants under algebraically defined groups of transformations. The body of research produced through this program led to the development of Category Theory as a unifying language connecting previously isolated branches of Mathematics. A particularly powerful type of such category theoretic relationship is expressed by the homotopy and homology functors, linking the realms of topology and abstract algebra. These notions belong to the branch of Mathematics known as Algebraic Topology, which has been in accelerated development over the past century, producing a set of powerful tools for probing global and local properties of manifolds. In recent years advances in hardware, availability of large data sets, as well as innovation in architectural and algorithmic design, enabled successful application of methods from Manifold Theory to real-world data. Following this general trend, this project aims to develop computational apparatus, based on ideas from Algebraic Topology, in order to gain deeper insight into linguistic structures. "The Shape of Words" is an umbrella label for a collection of research endeavors that view natural language through a topological lens.
The RESEARCH JOURNAL in the MENU below contains articles in which I develop theory and algorithms for this project. Some articles are high level, and introduce possible research directions in general terms. Other articles distill in full rigor mathematical and algorithmic notions behind my current research, which will be converted into academic publications.
If you would like to collaborate on research inspired by these ideas, or something tangential to the projects developed here, feel free to contact me (email in the about section of my website https://stephenfitz.net).