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Analysis of institutional authors

Gonzalez-Prieto, ACorresponding AuthorMozo, AAuthorTalavera, EAuthorGomez-Canaval, SAuthor

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February 27, 2023
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Dynamics of Fourier Modes in Torus Generative Adversarial Networks

Publicated to: Mathematics. 9 (4): 325-28 - 2021-02-01 9(4), DOI: 10.3390/math9040325

Authors:

Gonzalez-Prieto, A; Mozo, A; Talavera, E; Gomez-Canaval, S
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Affiliations

Univ Autonoma Madrid, Fac Ciencias, Dept Matemat, Madrid 28049, Spain - Author
Univ Politecn Madrid, Escuela Tecn Super Ingn Sistemas Informat, Madrid 28031, Spain - Author
Universidad Autónoma de Madrid - Author
Universidad Politécnica de Madrid - Author
‎ Univ Autonoma Madrid, Fac Ciencias, Dept Matemat, Madrid 28049, Spain - Author
‎ Univ Politecn Madrid, Escuela Tecn Super Ingn Sistemas Informat, Madrid 28031, Spain - Author
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Abstract

Generative 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 descend algorithm, we are able to approximate the real flow and to 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 equillibria are spiral attractors. This theoretically justifies the slow and unstable training observed in GANs.
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Keywords

Dynamical systemsGenerative adversarial networksMachine learningMorse theoryNash equilibrium

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position 21/333, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.87. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 13, 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2026-04-02, the following number of citations:

  • WoS: 7
  • Scopus: 7
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-02:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 5.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 5 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 3.
  • The number of mentions on the social network X (formerly Twitter): 3 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
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Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (GONZALEZ PRIETO, JOSE ANGEL) and Last Author (GOMEZ CANAVAL, SANDRA MARIA).

the author responsible for correspondence tasks has been GONZALEZ PRIETO, JOSE ANGEL.

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Awards linked to the item

This work was supported in part by the European Union's Horizon 2020 Research and Innovation Programme under grant 833685 (SPIDER).
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