Mathematics

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    Adversarial Robustness and Fairness in Deep Learning
    (2023) Cherepanova, Valeriia; Goldstein, Tom; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    While deep learning has led to remarkable advancements across various domains, the widespread adoption of neural network models has brought forth significant challenges such as vulnerability to adversarial attacks and model unfairness. These challenges have profound implications for privacy, security, and societal impact, requiring thorough investigation and development of effective mitigation strategies. In this work we address both these challenges. We study adversarial robustness of deep learning models and explore defense mechanisms against poisoning attacks. We also explore the sources of algorithmic bias and evaluate existing bias mitigation strategies in neural networks. Through this work, we aim to contribute to the understanding and enhancement of both adversarial robustness and fairness of deep learning systems.
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    Analysis of Data Security Vulnerabilities in Deep Learning
    (2022) Fowl, Liam; Czaja, Wojciech; Goldstein, Thomas; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    As deep learning systems become more integrated into important application areas, the security of such systems becomes a paramount concern. Specifically, as modern networks require an increasing amount of data on which to train, the security of data that is collected for these models cannot be guaranteed. In this work, we investigate several security vulnerabilities and security applications of the data pipeline for deep learning systems. We systematically evaluate the risks and mechanisms of data security from multiple perspectives, ranging from users to large companies and third parties, and reveal several security mechanisms and vulnerabilities that are of interest to machine learning practitioners.
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    TOWARDS AN EFFICIENT SEMANTIC SEGMENTATION PIPELINE FOR 3D ELECTRON MICROSCOPY DATA.
    (2022) Emam, Zeyad Ali Sami; Czaja, Wojciech; Goldstein, Thomas; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In recent years, deep neural networks revolutionized many aspects of computer vision. However, their success relies on massive high-quality annotated datasets that are costly to curate. This thesis is composed of three major parts. In Chapter 3, we use novel high dimensional visualization methods to explore connections between the loss landscape of neural networks and their intriguing ability to generalize to unseen test data. Next, in Chapter 4, we tackle a difficult computer vision task, namely the segmentation of anisotropic 3D electron microscopy image volumes. Deep neural networks tend to struggle in this scenario due to the lack of sufficient training data and the 3 dimensional nature of the images, as such we develop a novel state-of-the-art architecture and training workflow to improve the overall segmentation pipeline. Finally, in Chapter 5 we propose a novel state-of-the-art deep active learning algorithm for image classification to alleviate the costs of data annotations and allow networks to train effectively using less data.
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    Nonlinear Analysis of Phase Retrieval and Deep Learning
    (2017) Zou, Dongmian; Balan, Radu V; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Nonlinearity causes information loss. The phase retrieval problem, or the phaseless reconstruction problem, seeks to reconstruct a signal from the magnitudes of linear measurements. With a more complicated design, convolutional neural networks use nonlinearity to extract useful features. We can model both problems in a frame-theoretic setting. With the existence of a noise, it is important to study the stability of the phaseless reconstruction and the feature extraction part of the convolutional neural networks. We prove the Lipschitz properties in both cases. In the phaseless reconstruction problem, we show that phase retrievability implies a bi-Lipschitz reconstruction map, which can be extended to the Euclidean space to accommodate noises while remaining to be stable. In the deep learning problem, we set up a general framework for the convolutional neural networks and provide an approach for computing the Lipschitz constants.