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Dynamics of Fourier Modes in Torus Generative Adversarial Networks

dc.contributor.authorGonzález Prieto, José Ángel
dc.contributor.authorMozo, Alberto
dc.contributor.authorTalavera, Edgar
dc.contributor.authorGómez Canaval, Sandra
dc.date.accessioned2024-02-08T21:45:13Z
dc.date.available2024-02-08T21:45:13Z
dc.date.issued2021-02-06
dc.description.abstractGenerative Adversarial Networks (GANs) are powerful machine learning models capable of generating fully synthetic samples of a desired phenomenon with a high resolution. Despite their success, the training process of a GAN is highly unstable, and typically, it is necessary to implement several accessory heuristics to the networks to reach acceptable convergence of the model. In this paper, we introduce a novel method to analyze the convergence and stability in the training of generative adversarial networks. For this purpose, we propose to decompose the objective function of the adversary min–max game defining a periodic GAN into its Fourier series. By studying the dynamics of the truncated Fourier series for the continuous alternating gradient descent algorithm, we are able to approximate the real flow and identify the main features of the convergence of GAN. This approach is confirmed empirically by studying the training flow in a 2-parametric GAN, aiming to generate an unknown exponential distribution. As a by-product, we show that convergent orbits in GANs are small perturbations of periodic orbits so the Nash equilibria are spiral attractors. This theoretically justifies the slow and unstable training observed in GANs.en
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipEuropean Comission
dc.description.statuspub
dc.identifier.citationGonzález-Prieto, Á.; Mozo, A.; Talavera, E.; Gómez-Canaval, S. Dynamics of Fourier Modes in Torus Generative Adversarial Networks. Mathematics 2021, 9, 325, doi:10.3390/math9040325.
dc.identifier.doi10.3390/math9040325
dc.identifier.officialurlhttps://doi.org/10.3390/math9040325
dc.identifier.relatedurlhttps://www.mdpi.com/2227-7390/9/4/325
dc.identifier.urihttps://hdl.handle.net/20.500.14352/100640
dc.journal.titleMathematics
dc.language.isoeng
dc.relation.projectIDHorizon 2020 833685 (SPIDER)
dc.rights.accessRightsopen access
dc.subject.ucmEcuaciones diferenciales
dc.subject.ucmInteligencia artificial (Informática)
dc.subject.unesco1202.19 Ecuaciones Diferenciales Ordinarias
dc.subject.unesco1203.04 Inteligencia Artificial
dc.titleDynamics of Fourier Modes in Torus Generative Adversarial Networksen
dc.typejournal article
dspace.entity.typePublication
relation.isAuthorOfPublicationc3011bfd-5025-4e49-8f0e-e16ea76da35c
relation.isAuthorOfPublication.latestForDiscoveryc3011bfd-5025-4e49-8f0e-e16ea76da35c

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