Effcient Implementation of Neural Network Learning Algorithms Using the Concept of a Q-determinant

It has three steps: construction of the Q-determinant of the algorithm, and description of the Q-effective implementation of the algorithm, development of a program for an realizable Q-effective implementation of the algorithm. A program is called Q-effective if it is developed using this method. A program is also called Q-effective if it performs a Q-effective implementation of an algorithm. The same set of programs corresponds to these two definitions. The application of the method of designing Q-effective programs is shown on the example of algorithms implementing stochastic gradient descent and error back propagation methods. These methods are often used to learn neural networks. Q-effective programs for shared and distributed memory parallel computing systems have been developed that implement these methods. The acceleration and efficiency of the developed programs have been evaluated using computational experiments. Computational experiments were performed on the supercomputer «Tornado» of the South Ural State University. We present conclusions based on the obtained evaluation of the dynamic characteristics of the developed programs. The values of the dynamic characteristics of a Q-effective program depend on the implemented algorithm and the conditions of development and execution of the program. The paper provides a recommendation to the developer of a Q-effective program in the case where he wants to improve the values of the dynamic characteristics of the program being developed. Therefore, the research shows that the method of designing Q-effective programs can be applied to efficiently implement neural network learning algorithms. The paper is the first to consider an efficient implementation of neural network learning algorithms using the concept of a Q-determinant. Let’s describe the necessary information about the concept of the Q-determinant.