ntvНаучно-технический вестник информационных технологий, механики и оптикиScientific and Technical Journal of Information Technologies, Mechanics and Optics2226-14942500-0373Университет ИТМО10.17586/2226-1494-2026-26-2-428-435ntv-606Research ArticleМАТЕМАТИЧЕСКОЕ И КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕMODELING AND SIMULATIONРеализация и исследование резервуарного вычислителя на основе аппаратной модели трехэлементного импульсного нейронаImplementation and investigation of a reservoir computer based on a hardware model of three-element spiking neuronhttps://orcid.org/0000-0002-5010-1841ХолкинВ. С.KholkinV. S.

Холкин Владислав Сергеевич — ассистент

Санкт-Петербург, 197022

Vladislav S. Kholkin — Assistant

Saint Petersburg, 197022

super.holkin@mail.ruhttps://orcid.org/0009-0002-2584-1474ПчёлкоВ. А.PchelkoV. A.

Пчёлко Василий Андреевич — аспирант

Санкт-Петербург, 197022

Vasiliy A. Pchelko — PhD Student

Saint Petersburg, 197022

vapchelko@stud.etu.ruhttps://orcid.org/0009-0009-3966-9880КленинВ. Л.KleninV. L.

Кленин Владислав Леонидович — кандидат технических наук, доцент; заместитель генерального директора

Санкт-Петербург, 197022

Санкт-Петербург, 195196

Vladislav L. Klenin — PhD, Associate Professor; Deputy General Director

Saint Petersburg, 197022

Saint Petersburg, 195196

vklenin@akvamarinnpc.ruhttps://orcid.org/0000-0002-9860-8211КаримовТ. И.KarimovT. I.

Каримов Тимур Искандарович — кандидат технических наук, доцент, доцент

Санкт-Петербург, 197022

sc 56703060800

Timur I. Karimov — PhD, Associate Professor, Associate Professor

Saint Petersburg, 197022

sc 56703060800

tikarimov@etu.ruhttps://orcid.org/0000-0002-5953-255XКопецЕ. Е.KopetsE. E.

Копец Екатерина Евгеньевна — кандидат технических наук, доцент

Санкт-Петербург, 197022

sc 57200196143

Ekaterina E. Kopets — PhD, Associate Professor

Saint Petersburg, 197022

sc 57200196143

eekopets@etu.ruСанкт-Петербургский государственный электротехнический университет «ЛЭТИ» им. В.И. Ульянова (Ленина)РоссияSaint Petersburg Electrotechnical University “LETI”Russian FederationСанкт-Петербургский государственный электротехнический университет «ЛЭТИ» им. В.И. Ульянова (Ленина); АО «НПЦ «АквамаринРоссияSaint Petersburg Electrotechnical University “LETI”; AO NPTS “AKVAMARIN”Russian Federation202620042026262428435Copyright © Холкин В.С., Пчёлко В.А., Кленин В.Л., Каримов Т.И., Копец Е.Е., 20262026Холкин В.С., Пчёлко В.А., Кленин В.Л., Каримов Т.И., Копец Е.Е.Kholkin V.S., Pchelko V.A., Klenin V.L., Karimov T.I., Kopets E.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ntv.elpub.ru/jour/article/view/606

Введение. Исследованы варианты поиска новых компьютерных архитектур для аппаратной реализации динамических (импульсных) нейросетей, способных заменить современные сети, построенные на нейронах со статической функцией активации. Метод. Впервые предложено использование разработанной компактной аналоговой модели импульсного нейрона, состоящей из трех элементов (волатильного мемристора, туннельного диода и конденсатора), в качестве базового элемента резервуарного вычислителя типа жидкостный конечный автомат (Liquid State Machine). Предложена компьютерная модель резервуара, включающая 7480 импульсных нейронов и около 254 тыс. связей, с топологией, сформированной по биологически мотивированному алгоритму. Основные результаты. Результаты предложенного решения продемонстрированы на задаче распознавания рукописных цифр из набора данных Modified National Institute of Standards and Technology. Достигнута точность классификации 93 %, что сопоставимо с известными реализациями жидкостных конечных автоматов. Оценки быстродействия предлагаемого резервуара при будущей аппаратной реализации превосходят показатели существующих аналогов на порядок, а по энергоэффективности — на 3–4 порядка. Обсуждение. Впервые показана практическая применимость трехэлементной нейронной модели для задач машинного обучения и доказана ее перспективность как базового элемента для построения масштабируемых и энергоэффективных нейроморфных вычислительных систем.

This paper investigates new computer architectures for the hardware implementation of dynamic (spiking) neural networks capable to replace up-to-date networks built on neurons with a static activation function. We propose for the first time the use of a recently developed compact analog model of a spiking neuron, consisting of only three elements (a volatile memristor, a tunnel diode, and a capacitor), as the basic element of a reservoir computer of Liquid State Machine (LSM) type. A computer model of the reservoir is proposed, including 7,480 neurons and approximately 254,000 connections, with a topology formed using the biologically motivated LSM stochastic synapse distribution algorithm. The results of the proposed solution are demonstrated on the task of recognizing handwritten digits from the MNIST dataset. A classification accuracy of 93 % is achieved, which is comparable to known LSM implementations. Estimates for the proposed reservoir performance of the future hardware implementation exceed those of existing analogs by an order, and in terms of energy efficiency by 3-4 orders. Thus, the proposed study demonstrates for the first time the practical applicability of the three-element neuron model for machine learning tasks and confirms its potential as a basic element for constructing scalable and energy-efficient neuromorphic computing systems.

резервуарный вычислительимпульсный нейронжидкостный конечный автоматнейроморфные вычисленияклассификация MNISTклассы возбудимостианалоговая модель нейронаreservoir computerspiking neuronliquid state machine (LSM)neuromorphic computingMNIST classificationexcitability classesanalog neuron modelРабота поддержана Российским научным фондом, проект № 25-71-10049 «Исследовательское проектирование перспективных нейроморфных вычислителей».The research was supported by the Russian Science Foundation, project No. 25-71-10049 “Research design of promising neuromorphic computers”.ReferencesTavanaei A., Ghodrati M., Kheradpisheh S.R., Masquelier T., Maida A. Deep learning in spiking neural networks // Neural Networks. 2019. V. 111. P. 47–63. https://doi.org/10.1016/j.neunet.2018.12.002Tavanaei A., Ghodrati M., Kheradpisheh S.R., Masquelier T., Maida A. Deep learning in spiking neural networks // Neural Networks. 2019. V. 111. P. 47–63. https://doi.org/10.1016/j.neunet.2018.12.002Philipp G., Song D., Carbonell J.G. The exploding gradient problem demystified — definition, prevalence, impact, origin, tradeoffs, and solutions // arXiv. 2017. arXiv:1712.05577. https://doi.org/10.48550/arXiv.1712.05577Philipp G., Song D., Carbonell J.G. The exploding gradient problem demystified — definition, prevalence, impact, origin, tradeoffs, and solutions // arXiv. 2017. arXiv:1712.05577. https://doi.org/10.48550/arXiv.1712.05577Kirkpatrick J., Pascanu R., Rabinowitz N., Veness J., Desjardins G., Rusu A.A., et al. Overcoming catastrophic forgetting in neural networks // Proc. of the National Academy of Sciences of the United States of America. 2017. V. 114. N 13. P. 3521–3526. https://doi.org/10.1073/pnas.1611835114Kirkpatrick J., Pascanu R., Rabinowitz N., Veness J., Desjardins G., Rusu A.A., et al. Overcoming catastrophic forgetting in neural networks // Proc. of the National Academy of Sciences of the United States of America. 2017. V. 114. N 13. P. 3521–3526. https://doi.org/10.1073/pnas.1611835114Davidson S., Furber S.B. Comparison of artificial and spiking neural networks on digital hardware // Frontiers in Neuroscience. 2021. V. 15. P. 651141. https://doi.org/10.3389/fnins.2021.651141Davidson S., Furber S.B. Comparison of artificial and spiking neural networks on digital hardware // Frontiers in Neuroscience. 2021. V. 15. P. 651141. https://doi.org/10.3389/fnins.2021.651141Przyczyna D., Pecqueur S., Vuillaume D., Szaciłowski K. Reservoir computing for sensing: an experimental approach // arXiv. 2020. arXiv:2001.04342. https://doi.org/10.48550/arXiv.2001.04342Przyczyna D., Pecqueur S., Vuillaume D., Szaciłowski K. Reservoir computing for sensing: an experimental approach // arXiv. 2020. arXiv:2001.04342. https://doi.org/10.48550/arXiv.2001.04342Jiang H., Anumasa S., De Masi G., Xiong H., Gu B. A unified optimization framework of ANN-SNN conversion: towards optimal mapping from activation values to firing rates // Proc. of the 40th International Conference on Machine Learning. 2023. P. 14945– 14974.Jiang H., Anumasa S., De Masi G., Xiong H., Gu B. A unified optimization framework of ANN-SNN conversion: towards optimal mapping from activation values to firing rates // Proc. of the 40th International Conference on Machine Learning. 2023. P. 14945– 14974.Lukoševičius M., Jaeger H. Reservoir computing approaches to recurrent neural network training // Computer Science Review. 2009. V. 3. N 3. P. 127–149. https://doi.org/10.1016/j.cosrev.2009.03.005Lukoševičius M., Jaeger H. Reservoir computing approaches to recurrent neural network training // Computer Science Review. 2009. V. 3. N 3. P. 127–149. https://doi.org/10.1016/j.cosrev.2009.03.005Morando S., Pera M.C., Yousfi Steiner N., Jemei S., Hissel D., Larger L. Reservoir Computing optimisation for PEM fuel cell fault diagnostic // Proc. of the IEEE Vehicle Power and Propulsion Conference (VPPC). 2017. P. 1–7. https://doi.org/10.1109/vppc.2017.8330981Morando S., Pera M.C., Yousfi Steiner N., Jemei S., Hissel D., Larger L. Reservoir Computing optimisation for PEM fuel cell fault diagnostic // Proc. of the IEEE Vehicle Power and Propulsion Conference (VPPC). 2017. P. 1–7. https://doi.org/10.1109/vppc.2017.8330981Zhang S., Duan X., Li C., Liang M. Pre-classified reservoir computing for the fault diagnosis of 3D printers // Mechanical Systems and Signal Processing. 2021. V. 146. P. 106961. https://doi.org/10.1016/j.ymssp.2020.106961Zhang S., Duan X., Li C., Liang M. Pre-classified reservoir computing for the fault diagnosis of 3D printers // Mechanical Systems and Signal Processing. 2021. V. 146. P. 106961. https://doi.org/10.1016/j.ymssp.2020.106961Shi C., Fu X., Wang H., Lin Y., Jiang Y., Liu L., et al. Ghost reservoir: a memory-efficient low-power and real-time neuromorphic processor of liquid state machine with on-chip learning // IEEE Transactions on Circuits and Systems II: Express Briefs. 2024. V. 71. N 10. P. 4526– 4530. https://doi.org/10.1109/TCSII.2024.3395415Shi C., Fu X., Wang H., Lin Y., Jiang Y., Liu L., et al. Ghost reservoir: a memory-efficient low-power and real-time neuromorphic processor of liquid state machine with on-chip learning // IEEE Transactions on Circuits and Systems II: Express Briefs. 2024. V. 71. N 10. P. 4526– 4530. https://doi.org/10.1109/TCSII.2024.3395415Stoliar P., Schneegans O., Rozenberg M.J. Biologically relevant dynamical behaviors realized in an ultra-compact neuron model // Frontiers in Neuroscience. 2020. V. 14. P. 421. https://doi.org/10.3389/fnins.2020.00421Stoliar P., Schneegans O., Rozenberg M.J. Biologically relevant dynamical behaviors realized in an ultra-compact neuron model // Frontiers in Neuroscience. 2020. V. 14. P. 421. https://doi.org/10.3389/fnins.2020.00421Isik I., Tagluk M.E. Analysis of the electronic integrate and fire neuron model // Neurocomputing. 2022. V. 488. P. 261–270. https://doi.org/10.1016/j.neucom.2022.02.064Isik I., Tagluk M.E. Analysis of the electronic integrate and fire neuron model // Neurocomputing. 2022. V. 488. P. 261–270. https://doi.org/10.1016/j.neucom.2022.02.064Pickett M.D., Medeiros-Ribeiro G., Williams R.S. A scalable neuristor built with Mott memristors // Nature Materials. 2013. V. 12. N 2. P. 114–117. https://doi.org/10.1038/nmat3510Pickett M.D., Medeiros-Ribeiro G., Williams R.S. A scalable neuristor built with Mott memristors // Nature Materials. 2013. V. 12. N 2. P. 114–117. https://doi.org/10.1038/nmat3510Li Y., Tang J., Gao B., Li X., Xi Y., Zhang W., et al. Oscillation neuron based on a low-variability threshold switching device for highperformance neuromorphic computing // Journal of Semiconductors. 2021. V. 42. N 6. P. 064101. https://doi.org/10.1088/1674-4926/42/6/064101Li Y., Tang J., Gao B., Li X., Xi Y., Zhang W., et al. Oscillation neuron based on a low-variability threshold switching device for highperformance neuromorphic computing // Journal of Semiconductors. 2021. V. 42. N 6. P. 064101. https://doi.org/10.1088/1674-4926/42/6/064101Ostrovskii V., Karimov T., Rybin V., Bobrova Y., Arlyapov V., Butusov D. Bio-inspired neuron based on threshold selector and tunnel diode capable of excitability modulation // Neurocomputing. 2025. V. 624. P. 129454. https://doi.org/10.1016/j.neucom.2025.129454Ostrovskii V., Karimov T., Rybin V., Bobrova Y., Arlyapov V., Butusov D. Bio-inspired neuron based on threshold selector and tunnel diode capable of excitability modulation // Neurocomputing. 2025. V. 624. P. 129454. https://doi.org/10.1016/j.neucom.2025.129454Hodgkin A.L. The local electric changes associated with repetitive action in a non-medullated axon // The Journal of Physiology. 1948. V. 107. N 2. P. 165–181. https://doi.org/10.1113/jphysiol.1948.sp004260Hodgkin A.L. The local electric changes associated with repetitive action in a non-medullated axon // The Journal of Physiology. 1948. V. 107. N 2. P. 165–181. https://doi.org/10.1113/jphysiol.1948. sp004260Zhang Y., Mo L., He X., Meng X. Unsupervised spiking neural network based on liquid state machine and self-organizing map // Neurocomputing. 2025. V. 620. P. 129120. https://doi.org/10.1016/j.neucom.2024.129120Zhang Y., Mo L., He X., Meng X. Unsupervised spiking neural network based on liquid state machine and self-organizing map // Neurocomputing. 2025. V. 620. P. 129120. https://doi.org/10.1016/j.neucom.2024.129120Hua Q., Wu H., Gao B., Zhao M., Li Y., Li X., et al. A threshold switching selector based on highly ordered Ag nanodots for X-point memory applications // Advanced Science. 2019. V. 6. N 10. P. 1900024. https://doi.org/10.1002/advs.201900024Hua Q., Wu H., Gao B., Zhao M., Li Y., Li X., et al. A threshold switching selector based on highly ordered Ag nanodots for X-point memory applications // Advanced Science. 2019. V. 6. N 10. P. 1900024. https://doi.org/10.1002/advs.201900024Баюков А.В., Гитцевич А.Б., Зайцев А.А., Мокряков В.В., Петухов В.М., Хрулев А.К. Полупроводниковые приборы: диоды, тиристоры, оптоэлектронные приборы. Справочник. М.: Энергоатомиздат, 1983. 744 с.Bayukov A.V., Gitsevich A.B., Zaitsev A.A., Mokryakov V.V., Petukhov V.M., Khrulev A.K. Semiconductor Devices: Diodes, Thyristors, and Optoelectronic Devices. A Handbook. Moscow, Energoatomizdat, 1983, 744 p. (in Russian)Wijesinghe P., Srinivasan G., Panda P., Roy K. Analysis of liquid ensembles for enhancing the performance and accuracy of liquid state machines // Frontiers in Neuroscience. 2019. V. 13. P. 504. https://doi.org/10.3389/fnins.2019.00504Wijesinghe P., Srinivasan G., Panda P., Roy K. Analysis of liquid ensembles for enhancing the performance and accuracy of liquid state machines // Frontiers in Neuroscience. 2019. V. 13. P. 504. https://doi.org/10.3389/fnins.2019.00504McHugh M.L. The chi-square test of independence // Biochemia Medica. 2013. V. 23. N 2. P. 143–149. https://doi.org/10.11613/bm.2013.018McHugh M.L. The chi-square test of independence // Biochemia Medica. 2013. V. 23. N 2. P. 143–149. https://doi.org/10.11613/bm.2013.018Wang Q., Jin Y., Li P. General-purpose LSM learning processor architecture and theoretically guided design space exploration. Proc. of the IEEE Biomedical Circuits and Systems Conference (BioCAS), 2015, pp. 1–4. https://doi.org/10.1109/biocas.2015.7348397Wang Q., Jin Y., Li P. General-purpose LSM learning processor architecture and theoretically guided design space exploration. Proc. of the IEEE Biomedical Circuits and Systems Conference (BioCAS), 2015, pp. 1–4. https://doi.org/10.1109/biocas.2015.7348397Hazan H., Saunders D.J., Sanghavi D.T., Siegelmann H., Kozma R. Lattice map spiking neural networks (LM-SNNs) for clustering and classifying image data. Annals of Mathematics and Artificial Intelligence, 2020, vol. 88, no. 11, pp. 1237–1260. https://doi.org/10.1007/s10472-019-09665-3Hazan H., Saunders D.J., Sanghavi D.T., Siegelmann H., Kozma R. Lattice map spiking neural networks (LM-SNNs) for clustering and classifying image data. Annals of Mathematics and Artificial Intelligence, 2020, vol. 88, no. 11, pp. 1237–1260. https://doi.org/10.1007/s10472-019-09665-3

The authors declare that there are no conflicts of interest present.