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Cracking open the black box: a geometric and topological analysis of neural networks

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dc.contributor.authorCole, Christina, author
dc.contributor.authorKirby, Michael, advisor
dc.contributor.authorPeterson, Chris, advisor
dc.contributor.authorCheney, Margaret, committee member
dc.contributor.authorDraper, Bruce, committee member
dc.date.accessioned2024-09-09T20:52:02Z
dc.date.available2024-09-09T20:52:02Z
dc.date.issued2024
dc.description.abstractDeep learning is a subfield of machine learning that has exploded in recent years in terms of publications and commercial consumption. Despite their increasing prevalence in performing high-risk tasks, deep learning algorithms have outpaced our understanding of them. In this work, we hone in on neural networks, the backbone of deep learning, and reduce them to their scaffolding defined by polyhedral decompositions. With these decompositions explicitly defined for low-dimensional examples, we utilize novel visualization techniques to build a geometric and topological understanding of them. From there, we develop methods of implicitly accessing neural networks' polyhedral skeletons, which provide substantial computational and memory savings compared to those requiring explicit access. While much of the related work using neural network polyhedral decompositions is limited to toy models and datasets, the savings provided by our method allow us to use state-of-the-art neural networks and datasets in our analyses. Our experiments alone demonstrate the viability of a polyhedral view of neural networks and our results show its usefulness. More specifically, we show that the geometry that a polyhedral decomposition imposes on its neural network's domain contains signals that distinguish between original and adversarial images. We conclude our work with suggested future directions. Therefore, we (1) contribute toward closing the gap between our use of neural networks and our understanding of them through geometric and topological analyses and (2) outline avenues for extensions upon this work.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierCole_colostate_0053A_18393.pdf
dc.identifier.urihttps://hdl.handle.net/10217/239205
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectdeep learning
dc.subjectmachine learning
dc.subjectpolyhedral decomposition
dc.subjectlearning representation
dc.subjectdata science
dc.subjectneural networks
dc.titleCracking open the black box: a geometric and topological analysis of neural networks
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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