Generation of Pseudo-Random Sequences Using Generative Predictive Neural Network Transformers

The paper considers the problem of generating pseudo-random sequences using artificial neural networks. The problem can be applied in many fields of knowledge, such as cryptography, game theory, and system identification. The main problem with generating sequences is that any pseudo-random generator with a finite number of internal states will repeat itself after a very long sequence of numbers. To improve pseudo-random sequences, the work proposes to use the generative predictive principle (a modification of the generative adversarial approach, which has proven itself well in image generation) and the attention mechanism that is used in modern large language models. This approach allowed us to achieve better statistical performance for the generated sequences under the null hypothesis. A by-product of the work is a predictive model that can predict the next values of random sequences with an error less than the standard deviation and the mean absolute deviation.