On May 8, 2024, the next All-Institute seminar was held at the Ministry of Science and Education of the Republic of Azerbaijan Institute of Mathematics and Mechanics. At the seminar, the head of the department “Theory of Functions” of the Institute of Mathematics and Mechanics, doctor of medical sciences, Professor Vugar Elman oglu Ismailov made a report on the topic “Some problems in the theory of approximation of ridge functions.”Ridge functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. The report discusses various approximation-theoretical properties of ridge functions.In addition, the properties of generalized ridge functions, their connection with linear superpositions and with the famous Kolmogorov theorem on superpositions were considered.

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