The problem surrounding convolutional neural network robustness and noise immunity is currently of great interest. In this paper, we propose a technique that involves robustness estimation and stability improvement. We also examined the noise immunity of convolutional neural networks and estimated the influence of uncertainty in the training and testing datasets on recognition probability. For this purpose, we estimated the recognition accuracies of multiple datasets with different uncertainties; we analyzed these data and provided the dependence of recognition accuracy on the training dataset uncertainty. We hypothesized and proved the existence of an optimal (in terms of recognition accuracy) amount of uncertainty in the training data for neural networks working with undefined uncertainty data. We have shown that the determination of this optimum can be performed using statistical modeling. Adding an optimal amount of uncertainty (noise of some kind) to the training dataset can be used to improve the overall recognition quality and noise immunity of convolutional neural networks.

The challenge of mobile subscribers’ groups and crowd’s behavior prediction during the mass events is now increasingly important. Operative methods application of this task solution is difficult; accordingly, development and application of technical methods is necessary. The method of this problem solution consists of subscribers’ telephone conversations recording in a zone of mass action, and the following speech recognition, the semantic analysis and statistical processing application. However, there is a tendency demand decrease for mobile systems voice services with simultaneous demand growth for data traffic nowadays. The purpose of this paper is to create a mathematical model of mobile networks subscribers’ mutual placement types, applicable for automatization of the subscribers’ activities nature prediction systems. The research method consists of mathematical simulation model development for pseudo-random examples generation of subscribers’ mutual placement types set, creation of training dataset, convolution neural network training and usage of training results to recognize the new examples. The results obtained. A mathematical model is proposed allowing to create a representative training and validation dataset of mobile networks subscribers’ mutual placement types for neural network training and testing. The convolution neural network trained using these samples has shown high classification accuracy results with a wide class of subscribers’ mutual placement types.

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A number of modern techniques for neural network training and recognition enhancement are based on their structures’ symmetry. Such approaches demonstrate impressive results, both for recognition practice, and for understanding of data transformation processes in various feature spaces. This survey examines symmetrical neural network architectures—Siamese and triplet. Among a wide range of tasks having various mathematical formulation areas, especially effective applications of symmetrical neural network architectures are revealed. We systematize and compare different architectures of symmetrical neural networks, identify genetic relationships between significant studies of different authors’ groups, and discuss opportunities to improve the element base of such neural networks. Our survey builds bridges between a large number of isolated studies with significant practical results in the considered area of knowledge, so that the presented survey acquires additional relevance.

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