Architecture and Formal-mathematical Justification of Generative Adversarial Networks

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.