Version 1
: Received: 15 October 2024 / Approved: 16 October 2024 / Online: 16 October 2024 (11:48:02 CEST)
How to cite:
Garayev, G.; Alili, A. Stable GANs via Fermi-Dirac Statistics and Ruppeiner Geometry. Preprints2024, 2024101286. https://doi.org/10.20944/preprints202410.1286.v1
Garayev, G.; Alili, A. Stable GANs via Fermi-Dirac Statistics and Ruppeiner Geometry. Preprints 2024, 2024101286. https://doi.org/10.20944/preprints202410.1286.v1
Garayev, G.; Alili, A. Stable GANs via Fermi-Dirac Statistics and Ruppeiner Geometry. Preprints2024, 2024101286. https://doi.org/10.20944/preprints202410.1286.v1
APA Style
Garayev, G., & Alili, A. (2024). Stable GANs via Fermi-Dirac Statistics and Ruppeiner Geometry. Preprints. https://doi.org/10.20944/preprints202410.1286.v1
Chicago/Turabian Style
Garayev, G. and Azar Alili. 2024 "Stable GANs via Fermi-Dirac Statistics and Ruppeiner Geometry" Preprints. https://doi.org/10.20944/preprints202410.1286.v1
Abstract
Generative Adversarial Networks (GANs) are powerful models for generative tasks but face significant challenges such as instability, mode collapse, and inefficient convergence. This paper introduces a theoretical framework leveraging Fermi-Dirac statistics, Ruppeiner geometry, phase transition dynamics, and graph theory to address these issues. The proposed theorems provide a robust mathematical foundation for enhancing GAN stability, diversity, and convergence. Experimental validation on the MNIST dataset demonstrates that the application of these theorems results in improved Inception Scores, reduced Fréchet Inception Distances, and stable training dynamics, as indicated by Ruppeiner curvature analysis. The findings suggest that these theoretical insights offer a comprehensive solution to the persistent challenges in GAN training, paving the way for more reliable and effective generative models.
Keywords
Supersymmetry; Generalization; Robustness; Adversarial Attacks; Parallel Transport; Loss Optimization; CIFAR-10
Subject
Computer Science and Mathematics, Artificial Intelligence and Machine Learning
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
