Abstract
This dissertation investigates the inherent instability of deep learning models, specifically focusing on the origin and mitigation of adversarial examples – imperceptible input changes that lead to catastrophic prediction errors. While neural networks (NNs) have achieved state- of-the-art results in fields ranging from image classification to hazard forecasting, their lack of reliability in safety-critical applications remain a significant barrier to their deployment as alternatives to traditional, time-intensive supercomputer simulations. The core contribu- tion of this work is the application of the low-rank Householder expansion (LRHE). The expansion provides a tractable way to identify unstable singular vectors through singular vector decomposition (SVD), which represents the specific directions in input space that trigger erroneous output changes. Furthermore, the dissertation introduces a novel way to expand max pooling layers using Householder reflectors, extending the LRHE framework to more complex architectures. Finally, a new adversarial training procedure based on LRHE regularization is proposed. This research aims to enhance the reliability of neural network models and applies the adversarial training to safety-critical applications such as tsunami early warning.
Committee Chair
Donsub Rim
Committee Members
Douglas Wiens; Mladen Wickerhauser; Rachel Roberts; Renato Feres
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
8-3-2026
Language
English (en)
DOI
https://doi.org/10.7936/4ar3-f185
Recommended Citation
Johnson, Tiana Chanel, "On the Low-Rank Householder Expansion of Neural Networks and Its Application to Tsunami Early Warning" (2026). Arts & Sciences Graduate Student Theses and Dissertations. 3822.
The definitive version is available at https://doi.org/10.7936/4ar3-f185