Date of Award:
5-2026
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Mathematics and Statistics
Committee Chair(s)
Kevin R. Moon
Committee
Kevin R. Moon
Committee
Ian Anderson
Committee
Soukaina Filali Boubrahimi
Committee
Mark Fels
Committee
Shuhan Yuan
Abstract
Machine learning powers many technologies we use every day, from image classification in computer vision to analyzing time series data such as sensor readings or financial trends. One way to make these systems smarter and more reliable is by using symmetry, meaning patterns that remain unchanged under certain transformations, such as rotations for images or uniform changes in signal amplitude for time series. Discovering these patterns can improve understanding of data and help build models that perform well in new situations.
Current methods for finding symmetry often rely on large neural networks and are limited to simple transformations like stretching or rotating. This research introduces a more efficient approach that uncovers more complex symmetries using principles from geometry. It also demonstrates how enforcing these symmetries during training can improve model performance. In addition to image data, new tools are developed for analyzing time-based data in a way that respects their underlying geometry.
In short, this work connects machine learning with advanced mathematical concepts, providing a versatile framework for building models that are more interpretable and robust.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Shaw, Benjamin D., "Continuous Symmetry Discovery and Enforcement Using Vector Fields With Application to Time Series and Image Data" (2026). All Graduate Theses and Dissertations, Fall 2023 to Present. 726.
https://digitalcommons.usu.edu/etd2023/726
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