Abstract
The concept of an Ω-weakly regular problem is introduced. On the basis of the Zhuravlev operator approach combined with the neural network paradigm, it is shown that, for each such problem, a correct algorithm and a six-level spatial neural network reproducing the computations executed by this algorithm can be constructed. Moreover, the set of Ω-weakly regular problems includes the set of Ω-regular problems. It turns out that a three-level spatial network (μ-block) is a forward propagation network whose inner loop under estimation of the class membership for each test object consists of a single iteration. As a result, the amount of computations required for the six-level network is reduced noticeably.
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Original Russian Text © A.E. Dyusembaev, M.V. Grishko, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 2.
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Dyusembaev, A.E., Grishko, M.V. On Correctness Conditions for Algebra of Recognition Algorithms with μ-Operators over Pattern Problems with Binary Data. Dokl. Math. 98, 421–424 (2018). https://doi.org/10.1134/S1064562418060078
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DOI: https://doi.org/10.1134/S1064562418060078