Date of Award

January 2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Bryce Christopherson

Abstract

Often times in machine learning there are several heuristic choices that one makes during model selection, training, and validation. These choices include the type of training used, the width and depth of the model, type activation function and many more. These choices are general rules of thumb and best practices when creating a machine learning algorithm to achieve acceptable results. For example, in the case of image processing, this may mean determining whether or not a given image contains a tumor. Decisions made during the design process create several variations of machine learning algorithms, all with various properties with pros and cons. Things like, how many layers the network has, what activation function you are using, or what error function is used to update parameters are examples of theses decisions one needs to make while specify a machine learning algorithm. This thesis explores the use of category theory to document the structure, and provide a language to describe, the changes hyperparameters have in machine learning algorithms.

A specific case of using category theory to capture how regularization changes the structure of machine learning models is given. Then a brief inventory of various hyperparameters such as network width and activation functions are given with their potential categorical constructions are outlined. The resulting categorification of various hyperparameters show that using category theory is a valid way to specify model constraints at the beginning of an ML design process and subsequently track said constraints to the final implementation of the model.

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