RT Journal Article
T1 Dynamics of Fourier Modes in Torus Generative Adversarial Networks
A1 González Prieto, José Ángel
A1 Mozo, Alberto
A1 Talavera, Edgar
A1 Gómez Canaval, Sandra
AB 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 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.
YR 2021
FD 2021-02-06
LK https://hdl.handle.net/20.500.14352/100640
UL https://hdl.handle.net/20.500.14352/100640
LA eng
NO González-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.
NO European Comission
DS Docta Complutense
RD 7 abr 2025