Abstract
Artificial neural networks play an important role in the modern world. Their main field of application is the tasks of recognizing and processing images, speech, robotics, and unmanned systems. The use of neural networks is related to high computational costs. In part, it was this fact that held back their progress, and only with the advent of high-performance computing systems did the active development of this area begin. Nevertheless, the issue of speeding up the work of neural network algorithms is still relevant. One of the promising areas is the creation of analog implementations of artificial neural networks, since analog calculations are performed orders of magnitude faster than digital ones. The memristor acts as the base element on which such systems are built. A memristor is a resistor whose conductivity depends on the total charge passed through it. Combining memristors into a matrix (crossbar) allows one layer of artificial synapses to be implemented at the hardware level. Traditionally, the Spike Timing Dependent Plasticity (STDP) method based on Hebb’s rule has been used as an analog learning method. A two-layer fully connected network with one layer of synapses is modeled. The memristive effect can manifest itself in different substances (mainly in different oxides), so it is important to understand how the characteristics of memristors affect the parameters of the neural network. Two oxides are considered: titanium oxide (TiO2) and hafnium oxide (HfO2). For each oxide, a parametric identification of the corresponding mathematical model is performed for the best agreement with the experimental data. The neural network is tuned depending on the oxide used and the process of learning it to recognize five patterns is simulated.
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REFERENCES
Wong, H.-S.P., Lee, H.Y., Yu, S., Chen, Y.S., Wu, Y., Chen, P.S., Lee, B., and Frederic, T., Metal-oxide RRAM, Proc. IEEE, 2012, vol. 100, no. 6, pp. 1951–1970. https://doi.org/10.1109/JPROC.2012.2190369
Yang, J.J., Strukov, D.B., and Stewart, D.R., Memristive devices for computing, Nat. Nanotechnol., 2013, vol. 8, no. 1, pp. 13–24. https://doi.org/10.1038/nnano.2012.240
Li, C., Hu, M., Li, Y., Jiang, H., Ge, N., Montgomery, E., Zhang, J., Song, W., Dávila, N., Graves, C.E., Li, Z., Strachan, J.P., Lin, P., Wang, Z., Barnell, M., Wu, Q., Williams, R.S., Yang, J.J., and Xia, Q., Analogue signal and image processing with large memristor crossbars, Nat. Electron., 2018, vol. 1, no. 1, pp. 52–59. https://doi.org/10.1038/s41928-017-0002-z
Hu, M., Graves, C.E., Li, C., Li, Y., Ge, N., Montgomery, E., Davila, N., Jiang, H., Williams, R.S., Yang, J.J., Xia, O., and Strachan, J.P., Memristor-based analog computation and neural network classification with a dot product engine, Adv. Mater., 2018, vol. 30, no. 9, p. 1705914. https://doi.org/10.1002/adma.201705914
Morozov, A.Yu., Reviznikov, D.L., and Abgaryan, K.K., Issuues of implementing neural network algorithms on memristor crossbars, Izv. Vyssh. Uchebn. Zaved., Mater. Elektron. Tekh., 2019, vol. 22, no. 4, pp. 272–278. https://doi.org/10.17073/1609-3577-2019-4-272-278
Diehl, P. and Cook, M., Unsupervised learning of digit recognition using spike-timing-dependent plasticity, Front. Comput. Neurosci., 2015, vol. 9, p. 99. https://doi.org/10.3389/fncom.2015.00099
Ambrogio, S., Milo, V., Wang, Z.-Q., Ramaswamy, N., Balatty, S., Carboni, R., Calderoni, A., and Lelmibi, D., Neuromorphic learning and recognition with one-transistor-one-resistor synapses and bistable metal oxide RRAM, IEEE Trans. Electron Dev., 2016, vol. 63, no. 4, pp. 1508–1515. https://doi.org/10.1109/TED.2016.2526647
Guo, Y., Wu, H., Gao, B., and Qian, H., Unsupervised learning on resistive memory array based spiking neural networks, Front. Neurosci., 2019, vol. 13, art. 812. https://doi.org/10.3389/fnins.2019.00812
Milo V. Laudato, M., Ambrosi, E., Chicca, E., Pedretti, G., Bricalli, A., Bianchi, S., and Ielmini, D., Resistive switching synapses for unsupervised learning in feed-forward and recurrent neural networks, in Proceedings of the International Symposium on Circuits and Systems, Florence, Italy: IEEE, 2018, pp. 1–5. https://doi.org/10.1109/ISCAS.2018.8351824
Pedretti, G., Bianchi, S., Milo, V., Calderoni, A., Ramaswamy, N., and Ielmini, D., Modeling-based design of brain-inspired spiking neural networks with RRAM learning synapses, in Proceedings of the International Electron Devices Meeting, San Francisco, CA, IEEE, 2017, pp. 28.1.1–28.1.4. https://doi.org/10.1109/IEDM.2017.8268467
Milo, V., Ielmini, D., and Chicca, E., Attractor networks and associative memories with STDP learning in RRAM synapses, in Proceedings of the International Electron Devices Meeting, San Francisco, CA, IEEE, 2017, pp. 11.2.1–11.2.4. https://doi.org/10.1109/IEDM.2017.8268369
Strukov, D.B., Snider, G.S., Stewart, D.R., and Williams, R.S., The missing memristor found, Nature (London, U.K.), 2008, vol. 453, no. 7191, pp. 80–83. https://doi.org/10.1038/nature06932
Yang, J.J., Pickett, M.D., Xuema, L., Ohlberg, D.A.A., Stewart, D.R., and Williams, R.S., Memristive switching mechanism for metal/oxide/metal nanodevices, Nat. Nanotechnol., 2008, vol. 3, no. 7, pp. 429–433. https://doi.org/10.1038/nnano.2008.160
Pickett, M.D., Stukov, D.B., Borghetti, J.L., Yang, J.J., Snider, G.S., Stewart, D.R., and Williams, R.S., Switching dynamics in titanium dioxide memristive devices, J. Appl. Phys., 2009, vol. 106, no. 7, art. 074508. https://doi.org/10.1063/1.3236506
Joglekar, Y.N. and Wolf, S.J., The elusive memristor: Properties of basic electrical circuits, Eur. J. Phys., 2009, vol. 30, no. 4, p. 661. https://doi.org/10.1088/0143-0807/30/4/001
Biolek, Z., Biolek, D., and Biolkova, V., SPICE model of memristor with nonlinear dopant drift, Radioengineering, 2009, vol. 18, no. 2, pp. 210–214. https://www. radioeng.cz/fulltexts/2009/09_02_210_214.pdf.
Prodromakis, T., Peh, B.P., Papavassiliou, C., and Toumazou, C., A versatile memristor model with nonlinear dopant kinetics, IEEE Trans. Electron Dev., 2011, vol. 58, no. 9, pp. 3099–3105. https://doi.org/10.1109/TED.2011.2158004
Zha, J., Huang, H., and Liu, Y., A novel window function for memristor model with application in programming analog circuits, IEEE Trans. Circuits Syst. II: Express Briefs, 2015, vol. 63, no. 5, pp. 423–427. https://doi.org/10.1109/TCSII.2015.2505959
Kvatinsky, S., Friedman, E.G., Kolodny, A., and Weiser, U.C., TEAM: ThrEshold adaptive memristor model, IEEE Trans. Circuits Syst. I: Reg. Papers, 2013, vol. 60, no. 1, pp. 211–221. https://doi.org/10.1109/TCSI.2012.2215714
Kvatinsky, S., Ramadan, M., Friedman, E.G., and Kolodny, A., VTEAM: a general model for voltage-controlled memristors, IEEE Trans. Circuits Syst. II: Express Briefs, 2015, vol. 62, no. 8, pp. 786–790. https://doi.org/10.1109/TCSII.2015.2433536
Yakopcic, C., Taha, T.M., Subramanyam, G., Pino, R.E., and Rogers, S., A memristor device model, IEEE Electron Dev. Lett., 2011, vol. 32, no. 10, pp. 1436–1438. https://doi.org/10.1109/LED.2011.2163292
Zheng, G., Mohanty, S.P., Kougianos, E., and Okobiah, O., Polynomial metamodel integrated Verilog-AMS for memristor-based mixed-signal system design, in Proceedings of the International Midwest Symposium on Circuits and Systems (MWSCAS), Columbus, OH, IEEE, 2013, pp. 916–919. https://doi.org/10.1109/MWSCAS.2013.6674799
Mladenov, V., Analysis of memory matrices with HfO2 memristors in a PSpice environment, Electronics, 2019, vol. 8, no. 4, p. 383. https://doi.org/10.3390/electronics8040383
Teplov, G.S. and Gornev, E.S., Multilevel bipolar memristor model considering deviations of switching parameters in the Verilog-A language, Russ. Microelectron., 2019. vol. 48, no. 3, pp. 131–142. https://doi.org/10.1134/S1063739719030107
Morozov, A.Y. and Reviznikov, D.L., Adaptive interpolation algorithm based on a kd-tree for numerical integration of systems of ordinary differential equations with interval initial conditions, Differ. Equat., 2018, vol. 54, no. 7, pp. 945–956. https://doi.org/10.1134/S0012266118070121
Morozov, A.Yu., Reviznikov, D.L., and Gidaspov, V.Yu., Adaptive interpolation algorithm based on a kd-tree for the problems of chemical kinetics with interval parameters, Math. Models Comput. Simul., 2019, vol. 11, no. 4, pp. 622–633. https://doi.org/10.1134/S2070048219040100
Morozov, A.Y., Abgaryan, K.K., and Reviznikov, D.L., Mathematical model of a neuromorphic network based on memristive elements, Chaos, Solitons Fract., 2021, vol. 143, art. 110548. https://doi.org/10.1016/j.chaos.2020.110548
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This work was supported by the Russian Foundation for Basic Research, grant no. 19-29-03051 mk.
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Morozov, A.Y., Abgaryan, K.K. & Reviznikov, D.L. Mathematical Modeling of a Self-Learning Neuromorphic Network Based on Nanosized Memristive Elements with a 1T1R-Crossbar-Architecture. Russ Microelectron 50, 628–637 (2021). https://doi.org/10.1134/S1063739721080060
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DOI: https://doi.org/10.1134/S1063739721080060