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201887 https://hdl.handle.net/2286/R.2.N.201887 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2025 172 pages Doctoral Dissertation Academic theses en Mitra, Sinjini Turaga, Pavan Papandreou-Suppappola, Antonia Dasarathy, Gautam Moraffah, Bahman Arizona State University Partial requirement for: Ph.D., Arizona State University, 2025 Field of study: Electrical Engineering Recent advances in deep learning have enabled transformative progress across fields such as medical imaging, scientific modeling, transportation analysis, and natural language processing. However, the increasing complexity of model architectures and the demand for large-scale datasets pose critical challenges - particularly in resource- constrained settings where retraining and fine-tuning are computationally intensive and often impossible. Addressing these limitations requires a broader and more nuanced definition of robustness, one that encompasses not only accuracy and generalization but also adaptability, efficiency, and ethical deployment.This dissertation explores how the geometric and structural properties of latent spaces can be leveraged to improve model robustness across diverse modalities. By projecting high-dimensional data into geometry-preserving latent representations, the studies presented here demonstrate that significant reductions in model complexity and computational burden can be achieved without sacrificing performance. Operating in these compact latent spaces facilitates resilience to input noise, missing data, and distributional shifts - key factors under modern definitions of robustness. Collectively, these works underscore the hypothesis that geometric reasoning within latent spaces is a powerful and underutilized tool in deep learning. By moving away from monolithic models that require extensive retraining, and toward structurally-aware representations that emphasize efficiency and interpretability, this body of work contributes to a growing shift in how robustness is conceptualized and implemented in real-world machine learning applications. Artificial Intelligence Geometric Approaches Machine learning Robustness in Deep Learning Geometrically Inspired Approaches For Robust Machine Learning In GenAI, Health, and Scientific Applications