Право и управление2224-913310.24412/2224-9133-2026-4-140-148OtherОПТИМИЗАЦИЯ ОБУЧЕНИЯ НЕЙРОННЫХ СЕТЕЙ: ФУНКЦИИ ПОТЕРЬ, ГРАДИЕНТНЫЙ СПУСК И ОБРАТНОЕ РАСПРОСТРАНЕНИЕ ОШИБКИOPTIMIZING NEURAL NETWORK TRAINING: LOSS FUNCTIONS GRADIENT DESCENT, AND BACKPROPAGATIONСеменовАлександр АлександровичSemenovAleksandr Aleksandrovichmail@law-books.ruАветисянКарэн РафаеловичAvetisyanKaren RafaelovichKaren-Avetisyan-1989@bk.ruChief Researcher, Federal State Budgetary Institution “STIS”, of the Ministry of Internal Affairs of the Russian Federationнаучный сотрудник ФКУ НПО «СТиС» МВД РоссииSenior Lecturer, Department of Information Technology, and Cybercrime Investigation Organization, Moscow Academy of the Investigative Committee, of the Russian Federation named after A. Ya. Sukharevстарший преподаватель кафедры информационных технологий, и организации расследования киберпреступлений, Московская академия Следственного комитета, Российской Федерации имени А.Я. Сухарева1405202641401482504202614052026

Работа посвящена математическим основам обучения нейронных сетей через минимизацию функции потерь как меры качества модели. Обучение формулируется как задача оптимизации, решаемая с помощью градиентного спуска с учетом его особенностей в многомерных пространствах параметров. Описываются роль размеченных данных, влияние размера батча и организации эпох на процесс обучения. Поясняется применение метода обратного распространения ошибки для эффективного вычисления градиента в сложных архитектурах нейросетей

This paper examines the mathematical foundations of neural network training through minimizing the loss function as a measure of model quality. Training is formulated as an optimization problem solved using gradient descent, taking into account itsspecific features in multidimensional parameter spaces. The role of labeled data, the influence of batch size, and epoch organization on the training process are described. The application of the backpropagation method for efficient gradient computation in complex neural network architectures is explained

нейронные сетифункция потерьлоссградиентный спускоптимизациямашинное обучениеобучение с учителемобучение безучителяразметка данныхбатчэпохаградиентчастная производнаяобратное распространение ошибкислои нейросетипрямой и обратный ходneural networksloss functionlossgradient descentoptimizationmachine learningsupervised learningunsupervised learningdata labelingbatchepochgradientpartial derivativebackpropagationneural network layersforward and backward progressionHanson A., Koutilya PNVR, Sanjukta Krishnagopal, Larry Davis Bidirectional Convolutional LSTM for the Detection of Violence in Videos. 2018. URL: https://openaccess.thecvf.com/content_ eccv_2018_workshops/w10 /html/Hanson_ Bidirectional_Convolutional_LSTM_or_the_ Detection_of_ Violence_in_ Videos_ ECCVW_2018_ paper.html (дата обращения: 15.01.2026).Howard A.G., Menglong Zhu, BoChen, Kalenichenko D. MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications. 2017. 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