Thesis Defense: On the Low-Rank Householder Expansion of Neural Networks and Its Application to Tsunami Early Warning

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 contribution 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.

Faculty Advisor: Donsub Rim