{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129887"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129887","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Geometric and functional representations of stochastic neural dynamical systems: from realization theory to controlled approximation","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","abstract_has_math":false,"creators":["Veeravalli, Tanya"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Raginsky, Maxim","Srikant, Rayadurgam","Belabbas, Mohamed Ali","Zhao, Zhizhen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-07-18","date_published":"2025-07-18","updated_at":"2026-07-22T22:25:06Z","subjects":["Optimal Control","Neural Dynamical Systems","Stochastic Realization Theory","Nonlinear Controllability","Function Approximation"],"languages":["en","eng"],"rights":["Copyright 2025 Tanya Veeravalli"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129887","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Raginsky, Maxim","Srikant, Rayadurgam","Belabbas, Mohamed Ali","Zhao, Zhizhen"]},{"key":"dc:creator","label":"Author","values":["Veeravalli, Tanya"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-07-18","2025-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Optimal Control","Neural Dynamical Systems","Stochastic Realization Theory","Nonlinear Controllability","Function Approximation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Tanya Veeravalli"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129887"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Tanya Veeravalli, accepted the attached license on 2025-07-17 at 13:05.","The student, Tanya Veeravalli, submitted this Dissertation for approval on 2025-07-17 at 13:13.","This Dissertation was approved for publication on 2025-07-18 at 15:30.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22616 on 2025-10-20 at 16:58:41","There has been a great deal of interest in understanding continuous-time processes in deep learning, in particular methods related to (stochastic) control for improving diffusion models. In this work, we explore various facets of function approximation and realization problems through the lens of dynamical systems theory, neural stochastic differential equations (neural SDEs), and differential geometry. A neural SDE is an Itô diffusion process whose drift and diffusion matrices are elements of some parametric families. We cover topics from estimating the transition density of both uniformly elliptic and possibly degenerate diffusion processes by leveraging tools from sub-Riemannian geometry and stochastic control. There are many nuanced insights we can get into the behavior of deep neural networks and diffusion models by studying properties of associated problems in optimal control theory and drawing on other tools from the rich mathematical physics literature. The geometric insights explain the underlying noise structure and controllability properties of a stochastic dynamical system while also explaining the expressive power of the stochastic system."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Geometric and functional representations of stochastic neural dynamical systems: from realization theory to controlled approximation"]}]}],"canonical_facts":{"dc:contributor":["Raginsky, Maxim","Srikant, Rayadurgam","Belabbas, Mohamed Ali","Zhao, Zhizhen"],"dc:creator":["Veeravalli, Tanya"],"dc:date":["2025-07-18","2025-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms","The student, Tanya Veeravalli, accepted the attached license on 2025-07-17 at 13:05.","The student, Tanya Veeravalli, submitted this Dissertation for approval on 2025-07-17 at 13:13.","This Dissertation was approved for publication on 2025-07-18 at 15:30.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22616 on 2025-10-20 at 16:58:41","There has been a great deal of interest in understanding continuous-time processes in deep learning, in particular methods related to (stochastic) control for improving diffusion models. In this work, we explore various facets of function approximation and realization problems through the lens of dynamical systems theory, neural stochastic differential equations (neural SDEs), and differential geometry. A neural SDE is an Itô diffusion process whose drift and diffusion matrices are elements of some parametric families. We cover topics from estimating the transition density of both uniformly elliptic and possibly degenerate diffusion processes by leveraging tools from sub-Riemannian geometry and stochastic control. There are many nuanced insights we can get into the behavior of deep neural networks and diffusion models by studying properties of associated problems in optimal control theory and drawing on other tools from the rich mathematical physics literature. The geometric insights explain the underlying noise structure and controllability properties of a stochastic dynamical system while also explaining the expressive power of the stochastic system."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129887"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Tanya Veeravalli"],"dc:subject":["Optimal Control","Neural Dynamical Systems","Stochastic Realization Theory","Nonlinear Controllability","Function Approximation"],"dc:title":["Geometric and functional representations of stochastic neural dynamical systems: from realization theory to controlled approximation"],"dc:type":["text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:06Z"}