Date of Award

Spring 2022

Degree Type

Thesis

Department

Mathematics

Director of Thesis

Paula Vasquez

Second Reader

Andrei Medved

Abstract

Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to work appropriately in an analogous fashion to current models, and then explores through Monte-Carlo simulations the industry-standard measures of fit of such a model.

First Page

1

Last Page

21

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