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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