Approximation of binary functions based on two-layer artificial neural network
https://doi.org/10.37661/1816-0301-2025-22-3-72-82
Abstract
O b j e c t i v e s. The article examines the features of using two-layer artificial neural network in problems of approximating binary functions of many binary variables. The issues of choosing the initial values of the model weights and choosing the number of neurons on the hidden layer are studied.
M e t h o d s. The problem of approximating a binary function using an artificial neural network is reduced to the geometric problem of dividing the vertices of a multidimensional cube by hyperplanes. Combinatorial methods are used to prove lemmas on ways of dividing a hypercube by a hyperplane and to construct a lower estimate for the number of binary functions that can be approximated using one neuron on the hidden layer.
R e s u l t s. The features of setting the initial values of weights of an artificial neural network are considered. A lower bound is constructed for the number of binary functions that can be approximated using an artificial neural network with one neuron on the hidden layer. The algorithmic complexity of calculating such an estimate is found. Numerical results are presented for using two-layer artificial neural networks to approximate binary functions in information security problems.
C o n c l u s i o n. The results of the article allow choosing the parameters of an artificial neural network to improve the accuracy of approximation of binary functions of many variables.
About the Authors
K. V. Latushkin
Research Institute of Applied Problems of Mathematics and Informatics of the Belarusian State University
Belarus
Belarus
Konstantin V. Latushkin - Junior Researcher
Nezavisimosti av., 4, Minsk, 220030
Yu. S. Kharin
Research Institute of Applied Problems of Mathematics and Informatics of the Belarusian State University
Belarus
Belarus
Yuriy S. Kharin - D. Sc. (Phys.-Math.), Acad. of the National Academy of Science of Belarus, Prof.
Nezavisimosti av., 4, Minsk, 220030
References
1. Gohr A. Improving attacks on round-reduced speck32/64 using deep learning. Advances in Cryptology – CRYPTO 2019: 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, 18–22 August 2019, pt. II, рр. 150–179.
2. Picek S., Perin G., Mariot L., Wu L., Batina L. Deep learning-based physical side-channel analysis. ACM Computing Surveys, 2023, vol. 55(11), pp. 1–35.
3. Boanca S. Exploring patterns and assessing the security of pseudorandom number generators with machine learning. 16th International Conference on Agents and Artificial Intelligence, Rome, Italy, 24–26 February 2024, vol. 3, рр. 186–193.
4. Betelin V. B., Galkin V. A. Mathematical problems of artificial intelligence and artificial neural networks. Uspekhi kibernetiki [Russian Journal of Cybernetics], 2021, vol. 2, no. 4, pp. 6–14 (In Russ.). DOI: 10.51790/2712-9942-2021-2-4-1.
5. Nikolenko S., Kadurin A., Arkhangelskaya E. Glubokoe obuchenie. Pogruzhenie v mir nejronnyh setej. Deep Learning. Dive into the World of Neural Networks. Saint Petersburg, Piter, 2018, 480 p. (In Russ.).
6. Glorot X., Bengio Y. Understanding the difficulty of training deep feedforward neural networks. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, Sardinia, Italy, 13–15 May 2010, vol. 9, рр. 249–256.
7. He K., Zhang X., Ren S., Sun J. Delving deep into rectifiers: surpassing human-level performance on ImageNet classification. Proceedings of the 2015 IEEE International Conference on Computer Vision, Santiago, Chile, 7–13 December 2015, рр. 1026–1034.
8. Kharin Yu. S., Agievich S. V., Vasilyev D. V., Matveev G. V. Kriptologiya. Cryptology. Minsk, Belorusskij gosudarstvennyj universitet, 2023, 511 p. (In Russ.).
9. Dubrova E. A list of maximum period NLFSRs. Cryptology ePrint Archive, 2012. Available at: https://eprint.iacr.org/2012/166 (accessed 18.04.2025).
10. Domashev A. V., Gruntovich M. M., Popov V. O., Pravikov D. I., Shcherbakov A. Y., Prokofyev I. V. Programmirovanie algoritmov zashhity informacii. Programming of Information Security Algorithms. Moscow, Nolidzh, 2002, 416 p. (In Russ.).
Review
For citations:
Latushkin K.V., Kharin Yu.S. Approximation of binary functions based on two-layer artificial neural network. Informatics. 2025;22(3):72-82. (In Russ.) https://doi.org/10.37661/1816-0301-2025-22-3-72-82
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