Development of Interval Neural Network Architecture Intervalsqueezenet
( Pp. 13-24)
More about authors
Gonets Artem P.
postgraduate student, Department of Applied Mathematics; MIREA – Russian Technological University
MIREA – Russian Technological University
Moscow, Russian Federation Saraev Pavel V. Dr. Sci. (Eng.), Associate Professor; Professor, Department of Applied Mathematics; MIREA – Russian Technological University; Moscow, Russian Federation
MIREA – Russian Technological University
Moscow, Russian Federation Saraev Pavel V. Dr. Sci. (Eng.), Associate Professor; Professor, Department of Applied Mathematics; MIREA – Russian Technological University; Moscow, Russian Federation
Abstract:
This paper is devoted to a new type of architecture of the IntervalSqueezeNet convolutional neural network based on the integration of interval calculations into the SqueezeNet neural network model for image classification under conditions of interval uncertainty of input data. The methods of regularization and optimization of neural network models have been systematized, as well as ways to reduce computational complexity by randomly disabling Dropout neurons and using the Monte Carlo method. An overview of interval uncertainty is provided: the definition of the essence is given, the basics of interval analysis are presented, and a comparison with the probabilistic (Bayesian) approach to uncertainty modeling is performed. The existing interval neural networks, including fully connected and convolutional ones, are considered. The basic structure of SqueezeNet is described, including fire modules, compression and channel expansion operations. A new architecture of IntervalSqueezeNet with interval data processing and interval weights is proposed. Mathematical formulations of all operations are presented: interval convolution, compression and expansion operations in fire modules, interval activation functions ReLU and Softmax, interval subsampling over the average and maximum window, as well as a loss function based on cross-entropy. It is shown that the result of the classification is a probability interval, the width of which is interpreted as a quantitative measure of the confidence of the model. The advantages and disadvantages of interval convolutional neural networks are analyzed.
How to Cite:
Gonets A.P., Saraev P.V. Development of interval neural network architecture intervalsqueezenet. Computational Nanotechnology. 13, 2 (2026), 13–24. DOI: 10.33693/2313-223X-2026-13-2-13-24. EDN: YZZUQZ
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Bazhenov A.N., Zhilin S.I., Kumkov S.I., Sharyi S.P. Processing and analysis of interval data. Moscow; Izhevsk: Regular and Chaotic Dynamics, 2024. 363 p. EDN: FOKVPI.
Bazhenov A.N., Telnova A.Yu. Generalization of the Jaccard coefficient for data analysis with interval uncertainty. Izmeritelnaya tekhnika. 2022. No. 12. Pp. 15–22. (In Rus.). DOI: 10.32446/0368-1025it.2022-12-15-22. EDN: LHKUAN.
Beketov S.M., Zubkova D.A., Gintsyak A.M. et al. Modern optimization methods and their application features. Russian Technological Journal. 2025. Vol. 13. No. 4. Pp. 78–94. (In Rus.). DOI: 10.32362/2500-316X-2025-13-4-78-94. EDN: CVZOXD.
Miroshnikov A.I. Special mathematical and relational database software for interval-valued data types. Abstract of dis. ... of Cand. Sci. (Eng.). Voronezh, 2019. 156 p.
Polozova Yu.E. Development of an interval neural network identification method in information and analytical systems for managing objects with uncertainty. Abstract of dis. ... of Cand. Sci. (Eng.). Voronezh. 2019. 156 p.
Tikhonov A.N. On incorrect linear algebra problems and a stable method for solving them. Reports of the USSR Academy of Sciences. 1965. Vol. 163. No. 3. Pp. 591–594. (In Rus.)
Sharyi S.P. Strong consistency in problems of dependency reconstruction from data with interval uncertainty. In: Proceedings of the All-Russian Conference on Mathematics “MAK-2016”. Materials of the Youth Applied IT School “Mathematical Modeling in Ecology, Agroecology and Nature Management” (Barnaul, June 29 – July 1, 2016). Barnaul: Altai State University, 2016. Pp. 113–115.
Shary S.P., Androsov A.S. Polynomial curve fitting for data with interval uncertainty. Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki. 2025. Vol. 65. No. 11. Pp. 1761–1778. (In Rus.). DOI: 10.7868/S303453325110015. EDN: PKWENT.
Abdar M., Pourpanah F., Hussain S. et al. A review of uncertainty quantification in deep learning: Techniques, applications and challenges. Information Fusion. 2021. Vol. 76. Pp. 243–297. DOI: 10.1016/j.inffus.2021.05.008.
Amnuaypongsa W., Songsiri J. Large width penalization for neural network-based prediction interval estimation. arXiv preprint. 2024. Pp. 1–28. DOI: 10.48550/arXiv.2411.19181.
Chinnapnan R.R., Sundaram D. Image enhancement framework combining interval-valued intuitionistic fuzzy sets and fractional sobel operator. Artificial Intelligence Review. 2025. Vol. 58. Art. 291. DOI: 10.1007/s10462-025-11294-8.
Fase M., Broggi M., Patelli E. et al. Inverse quantification of epistemic uncertainty under scarce data: Bayesian or Interval approach? In: Proceedings of the 13th International Conference on Applications of Statistics and Probability on Civil Engineering (Seoul, South Korea, May 26–30, 2019). Seoul, 2019. Pp. 226–233. DOI: 10.22725/ICASP13.060.
Ferah M.A., Kumbasar T. Beyond prediction: Interval neural networks for uncertainty-aware system identification. arXiv preprint. 2026. Pp. 1–37. DOI: 10.48550/arXiv.2605.11460.
Ferah M.A., Kumbasar T. Introducing interval neural networks for uncertainty-aware system identification. arXiv preprint. 2025. Pp. 1–7. DOI: 10.48550/arXiv.2504.18845.
Iandola F.N., Han S., Moskewicz M.W. et al. SqueezeNet: AlexNet-level accuracy with 50× fewer. In: International Conference on Learning Representations (Toulon, France, April 24–26, 2017). Toulon, 2017. DOI: 10.48550/arXiv.1602.07360.
Kabir S., Wagner C., Ellerby Z. Towards handling uncertainty-at-source in AI – a review and next steps for interval regression. IEEE Transactions on Artificial Intelligence. 2024. Vol. 5. Issue 1. Pp. 3–22. DOI: 10.1109/TAI.2023.3234930.
Kingma D.P., Ba J.L. Adam: A method for stochastic optimization. arXiv preprint. 2014. DOI: 10.48550/arXiv.1412.6980.
Llorente F., Martino L., Read J., Delgado D. A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABC. International Statistical Review. 2025. Vol. 93. No. 1. Pp. 18–61. DOI: 10.1111/insr.12573.
Lopez-Molina C., Marco-Detchart C., Cerron J. et al. Gradient extraction operators for discrete interval-valued data. In: Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (Gijon, Spain, June 30 – July 3, 2015). Gijon, 2015. Pp. 836–843. DOI: 10.2991/ifsa-eusflat-15.2015.118.
Lyra A. Uma fundamentação matemática para o processamento de imagens digitais intervalares. Tese (Doutorado em Ciências) – Curso de Pós Graduação em Engenharia Elétrica. Natal: Universidade Federal do Rio Grande do Norte, 2003. 183 p.
Macdonald J., Marz M., Oala L., Samek W. Interval neural networks as instability detectors for image reconstructions. arXiv preprint. 2020. DOI: 10.48550/arXiv.2003.13471.
Srivastava N., Hinton G., Krizhevsky A. et al. Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research. 2014. Vol. 15. Pp. 1929–1958. DOI: 10.5555/2627435.2670313.
Steim I. Uma proposta de arquitetura de rede neural convolucional intervalar para o processamento de imagens intervalares. Dissertação (Mestrado em Ciências da Computação) – Programa de Pós-Graduação em Ciências da Computação, Centro de Desenvolvimento Tecnológico. Pelotas: Universidade Federal de Pelotas, 2017. 113 p.
Tretiak K., Schollmeyer G., Ferson S. Neural network model for imprecise regression with interval dependent variables. Neural Networks. 2023. Vol. 161. Pp. 550–564. DOI: 10.1016/j.neunet.2023.02.005.
Keywords:
SqueezeNet. IntervalSqueezeNet, interval analysis, uncertainty, interval convolutional neural networks, optimization, SqueezeNet, IntervalSqueezeNet.
