Advances in Quaternion-Valued Neural Networks

Author

Jeremiah P. Bill

Date of Award

9-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Operational Sciences

First Advisor

Bruce A. Cox, PhD

Abstract

This dissertation investigates the construction, optimization, and application of quaternion neural networks (QNNs) to Department of Defense (DoD) related problem sets. QNNs are a type of neural network wherein the weights, biases, and input values are all represented as quaternion numbers. This work provides a critical evaluation of the myriad different quaternion backpropagation derivations that exist in the literature, testing the performance of each on a range of regression problem sets. The optimization dynamics of QNNs are explored, presenting visualizations of QNN loss surfaces and a novel method for assessing the “smoothness” of these loss surfaces. Finally, this dissertation presents a novel integration of a QNN in a Deep Reinforcement Learning (DRL) algorithm with the Quaternion Deep Q-Network (QDQN) algorithm. QDQN represents the culmination of QNN research to date, setting the stage for further research and explorations that leverage QNNs in problem sets that take full advantage of the algebraic structure of the quaternions in advanced autonomous systems (AS) and robotic control applications

AFIT Designator

AFIT-ENS-DS-23-S-012

Comments

A 12-month embargo was observed for posting this dissertation on AFIT Scholar.

Approved for public release. PA case number on file.

Recommended Citation

Bill, Jeremiah P., "Advances in Quaternion-Valued Neural Networks" (2023). Theses and Dissertations. 7663.
https://scholar.afit.edu/etd/7663