Обучение многослойного перцептрона с учителем в задаче распознавания с помощью корреляционного показателя

The article deals with the problem of recognition of handwritten digits using feedforward neural networks (perceptrons) using a correlation indicator. The proposed method is based on the mathematical model of the neural network as an oscillatory system similar to the information transmission system. The article uses theoretical developments of the authors to search for the global extremum of the error function in artificial neural networks. The handwritten digit image is considered as a one-dimensional input discrete signal representing a combination of perfect digit writing and noise, which describes the deviation of the input implementation from perfect writing. The ideal observer criterion (Kotelnikov criterion), which is widely used in information transmission systems and describes the probability of correct recognition of the input signal, is used to form the loss function. In the article is carried out a comparative analysis of the convergence of learning and experimentally obtained sequences on the basis of the correlation indicator and widely used in the tasks of classification of the function CrossEntropyLoss with the use of the optimizer and without it. Based on the experiments carried out, it is concluded that the proposed correlation indicator has an advantage of 2-3 times.