Architecture and Formal-mathematical Justification of Generative Adversarial Networks

2024;
: pp. 15 - 22
Authors:
1
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Department of Artificial Intelligence

 

The purpose of the work is to analyze the features of generative adversarial networks. The object of research is the process of machine learning algorithmization. The subject of the research is mathematical methods used in the generation of semantically related text. This article explores the architecture and mathematical justification of such a type of generative models as generative adversarial networks. Generative adversarial networks are a powerful tool in the field of artificial intelligence, capable of generating realistic data, including photos, videos, sounds, etc. The architecture of generative competition defines its structure, the interaction of components and a general description of the learning process. Mathematical justification, in turn, includes a theoretical analysis of the principles, algorithms and functions underlying these networks.

The article examines the general architecture of generative adversarial networks, examines each of its components (namely, the two main network models – generator and discriminator, their input and output data vectors) and its role in the operation of the algorithm. The author also defined the mathematical principles of generative adversarial networks, focusing on game theory and optimization methods (in particular, special attention is paid to minimax and maximin problems, zero-sum game, saddle points, Nash equilibrium) used in their study. The cost function and the process of deriving it using the Nash equilibrium in a zero-sum game for generative adversarial networks are described, and the learning algorithm using the method of stochastic gradient descent and the mini-batch approach in the form of a pseudocode, its iterations, is visualized network architecture.

Finally, the conclusion that generative adversarial networks is an effective tool for creating realistic and believable data samples based on the use of elements of game theory is substantiated. Due to the high quality of generated data, generative adversarial networks can be used in various fields, including: cyber security, medicine, commerce, science, art, etc.

  1. Arjovsky, M., Chintala, S., & Bottou, L. (2017). Wasserstein generative adversarial networks. In International conference on machine learning (ICML). Proceedings of the 34th International Conference on Machine Learning, PMLR, 70: 214–223. DOI: https://doi.org/10.48550/arXiv.1701.07875
  2. Bengio, Y. (2009). Learning deep architectures for AI. Now Publishers. Foundations and Trends® in Machine Learning, 2: 1, 1–127. DOI: http://dx.doi.org/10.1561/2200000006
  3. Glorot, X., Bordes, A., and Bengio, Y. (2011). Deep sparse rectifier neural networks. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR, 15: 315–323.
  4. Goodfellow, I. et al. (2020). Generative adversarial networks Communications of the ACM, November, 63(11), 139–144. DOI: https://doi.org/10.1145/3422622
  5. Goodfellow, I. J. et al. (2013). Maxout networks. In ICML’2013 JMLR WCP, 28 (3): 1319–1327.  DOI:.https://doi.org/10.48550/arXiv.1302.4389
  6. Goodfellow, I. J. et al. (2014) Generative Adversarial Nets. Proceedings of the 27th International Conference on Neural Information Processing Systems, 2, 2672–2680 URL: https://arxiv.org/pdf/1406.2661.pdf. DOI:    https://doi.org/10.48550/arXiv.1406.2661
  7. Hinton, G. et al. (2012). Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups, in IEEE Signal Processing Magazine, 29 (6), 82–97, Nov. 2012. DOI: 10.1109/MSP.2012.2205597
  8. Jarrett, K. et al. (2009). What is the best multi-stage architecture for object recognition? IEEE 12th International Conference on Computer Vision, Kyoto, Japan, 2146–2153. DOI: 10.1109/ICCV.2009.5459469.
  9. Knudson, K. C. et al. (2014). Advances in Neural Information Processing Systems 27, eds. Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, 1215–1223. URL: https://pillowlab.princeton.edu/pubs/Knudson_COMP_NIPS14.pdf
  10. Krizhevsky, A., Sutskever, I., and Hinton, G. (2012). ImageNet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, 25 (NIPS 2012) Communications of the ACM, (6), 84–90. DOI: https://doi.org/10.1145/3065386
  11. Krizhevsky, A., Sutskever, I., and Hinton, G. (2012). ImageNet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, 25 (NIPS 2012) Communications of the ACM, (6), 84–90. DOI: https://doi.org/10.1145/3065386
  12. Mirza, M., Osindero, S. (2014). Conditional generative adversarial Nets Computing Research Repository. URL: https://arxiv.org/abs/1411.1784
  13. Radford, A., Metz, L., & Chintala, S. (2015). Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434. International Conference on Learning Representations. DOI: https://doi.org/10.48550/arXiv.1511.06434
  14. Schmidhuber, J. (1991). Adaptive confidence and adaptive curiosity. Technical Report FKI-149-91, Inst.f. Informatik, Tech. Univ. Munich, April. URL: https://people.idsia.ch/~juergen/FKI-149-91ocr.pdf
  15. Schmidhuber, J. (1992). Learning Factorial Codes by Predictability Minimization. Neural Comput.; 4 (6): 863–879. DOI: https://doi.org/10.1162/neco.1992.4.6.863
  16. Shatri, E. A review on Generative Adversarial Networks. How did the GANs change the way machine learning works? URL: HTTPS://TOWARDSDATASCIENCE.COM/A-REVIEW-OF-GENERATIVE- ADVERSARIAL-NETWORKS-9AF21E94BDA4
  17. Springenberg, J. T. (2016). Unsupervised and Semi-supervised Learning with Categorical Generative Adversarial Networks. URL: https://arxiv.org/abs/1511.06390
  18. Zhu, J. Y. et al. (2017). Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision (ICCV). DOI: 10.1109/ICCV.2017.244.