Abstract
In the circuit of two thermally coupled VO2 oscillators, we studied a higher-order synchronization effect, which can be used in object classification techniques to increase the number of possible synchronous states of the oscillator system. We developed the phase-locking estimation method to determine the values of subharmonic ratio and synchronization effectiveness. In our experiment, the number of possible synchronous states of the oscillator system was twelve, and subharmonic ratio distributions were shaped as Arnold’s tongues. In the model, the number of states may reach the maximum value of 150 at certain levels of coupling strength and noise. The long-range synchronization effect in a one-dimensional chain of oscillators occurs even at low values of synchronization effectiveness for intermediate links. We demonstrate a technique for storing and recognizing vector images, which can used for reservoir computing. In addition, we present the implementation of analog operation of multiplication, the synchronization-based logic for binary computations and the possibility to develop the interface between spike neural network and a computer. Based on the universal physical effects, the high-order synchronization can be applied to any spiking oscillators with any coupling type, enhancing the practical value of the presented results to expand spike neural network capabilities.
Similar content being viewed by others
References
Yu Q, Tang H, Hu J, Tan Chen K (2017) Neuromorphic cognitive systems. Springer, Berlin. https://doi.org/10.1007/978-3-319-55310-8
Rubio JDJ, Garcia E, Ochoa G, Elias I, Cruz DR, Balcazar R, Lopez J, Novoa JF (2019) Unscented Kalman filter for learning of a solar dryer and a greenhouse. J Intell Fuzzy Syst 37:6731–6741. https://doi.org/10.3233/JIFS-190216
Aquino G, Rubio JDJ, Pacheco J, Gutierrez GJ, Ochoa G, Balcazar R, Cruz DR, Garcia E, Novoa JF, Zacarias A (2020) Novel nonlinear hypothesis for the delta parallel robot modeling. IEEE Access 8:46324–46334. https://doi.org/10.1109/ACCESS.2020.2979141
Rubio JDJ (2009) SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans Fuzzy Syst 17:1296–1309. https://doi.org/10.1109/TFUZZ.2009.2029569
Meda-Campaña JA (2018) On the estimation and control of nonlinear systems with parametric uncertainties and noisy outputs. IEEE Access 6:31968–31973. https://doi.org/10.1109/ACCESS.2018.2846483
Volgushev M, Chauvette S, Mukovski M, Timofeev I (2006) Precise long-range synchronization of activity and silence in neocortical neurons during slow-wave sleep. J Neurosci 26:5665–5672. https://doi.org/10.1523/JNEUROSCI.0279-06.2006
Lachaux JP, Rodriguez E, Martinerie J, Varela FJ (1999) Measuring phase synchrony in brain signals. Hum Brain Mapp 8:194–208
Barraza P, Gómez DM, Oyarzún F, Dartnell P (2014) Long-distance neural synchrony correlates with processing strategies to compare fractions. Neurosci Lett 567:40–44. https://doi.org/10.1016/J.NEULET.2014.03.021
Ponulak F, Kasinski A (2011) Introduction to spiking neural networks: information processing, learning and applications. Acta Neurobiol Exp (Wars) 71:409–433
Belyaev M, Velichko A (2019) A spiking neural network based on the model of VO2—neuron. Electronics 8:1065. https://doi.org/10.3390/electronics8101065
Velichko A, Belyaev M, Putrolaynen V, Boriskov P (2018) A new method of the pattern storage and recognition in oscillatory neural networks based on resistive switches. Electronics 7:266. https://doi.org/10.3390/electronics7100266
Velichko A, Belyaev M, Boriskov P (2019) A model of an oscillatory neural network with multilevel neurons for pattern recognition and computing. Electronics 8:75. https://doi.org/10.3390/electronics8010075
Velichko A (2019) A method for evaluating chimeric synchronization of coupled oscillators and its application for creating a neural network information converter. Electronics 8:756. https://doi.org/10.3390/electronics8070756
Pikovsky A, Rosenblum M, Kurths J (2001) Synchronization : a universal concept in nonlinear sciences. Cambridge University Press, Cambridge
Fang Y, Yashin VV, Levitan SP, Balazs AC (2016) Pattern recognition with “materials that compute”. Sci Adv 2:e1601114. https://doi.org/10.1126/sciadv.1601114
Maffezzoni P, Bahr B, Zhang Z, Daniel L (2015) Oscillator array models for associative memory and pattern recognition. IEEE Trans Circuits Syst I Regul Pap 62:1591–1598. https://doi.org/10.1109/TCSI.2015.2418851
Nikonov DE, Csaba G, Porod W, Shibata T, Voils D, Hammerstrom D, Young IA, Bourianoff GI (2015) Coupled-oscillator associative memory array operation for pattern recognition. IEEE J Explor Solid-State Comput Devices Circuits 1:85–93. https://doi.org/10.1109/JXCDC.2015.2504049
Vodenicarevic D, Locatelli N, Abreu Araujo F, Grollier J, Querlioz D (2017) A nanotechnology-ready computing scheme based on a weakly coupled oscillator network. Sci Rep 7:44772. https://doi.org/10.1038/srep44772
Meier M, Haschke R, Ritter HJ (2014) Perceptual grouping through competition in coupled oscillator networks. Neurocomputing 141:76–83. https://doi.org/10.1016/J.NEUCOM.2014.02.011
Benicasa AX, Quiles MG, Silva TC, Zhao L, Romero RAF (2016) An object-based visual selection framework. Neurocomputing 180:35–54. https://doi.org/10.1016/J.NEUCOM.2015.10.111
Yogendra K, Fan D, Shim Y, Koo M, Roy K (2016) Computing with coupled spin torque nano oscillators. In: 2016 21st Asia South Pacific design automation conference. IEEE, pp 312–317. https://doi.org/10.1109/ASPDAC.2016.7428030
Shukla N, Tsai W-Y, Jerry M, Barth M, Narayanan V, Datta S (2016) Ultra low power coupled oscillator arrays for computer vision applications. In: 2016 IEEE symposium on VLSI technology. IEEE, pp 1–2. https://doi.org/10.1109/VLSIT.2016.7573439
Lynch S (2014) Binary oscillator computing. In: Lynch S (ed) Dynamical systems with applications using MATLAB®. Springer, Cham, pp 435–455. https://doi.org/10.1007/978-3-319-06820-6_20
Coulombe JC, York MCA, Sylvestre J (2017) Computing with networks of nonlinear mechanical oscillators. PloS One 12:e0178663. https://doi.org/10.1371/journal.pone.0178663
Shukla N, Parihar A, Freeman E, Paik H, Stone G, Narayanan V, Wen H, Cai Z, Gopalan V, Engel-Herbert R, Schlom DG, Raychowdhury A, Datta S (2015) Synchronized charge oscillations in correlated electron systems. Sci Rep 4:4964. https://doi.org/10.1038/srep04964
Parihar A, Shukla N, Datta S, Raychowdhury A (2016) Computing with dynamical systems in the post-CMOS era. In: 2016 IEEE photonics society summer topicals meeting series. IEEE, pp 110–111. https://doi.org/10.1109/PHOSST.2016.7548777
Sharma AA, Bain JA, Weldon JA (2015) Phase coupling and control of oxide-based oscillators for neuromorphic computing. IEEE J Explor Solid-State Comput Devices Circuits 1:58–66. https://doi.org/10.1109/JXCDC.2015.2448417
Li S, Liu X, Nandi SK, Venkatachalam DK, Elliman RG (2017) Coupling dynamics of Nb/Nb2O5 relaxation oscillators. Nanotechnology 28:125201. https://doi.org/10.1088/1361-6528/aa5de0
Kumar A, Mohanty P (2017) Autoassociative memory and pattern recognition in micromechanical oscillator network. Sci Rep 7:411. https://doi.org/10.1038/s41598-017-00442-y
Flovik V, Macià F, Wahlström E (2016) Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model. Sci Rep 6:32528. https://doi.org/10.1038/srep32528
Csaba G, Porod W (2013) Computational study of spin-torque oscillator interactions for non-boolean computing applications. IEEE Trans Magn 49:4447–4451. https://doi.org/10.1109/TMAG.2013.2244202
Lebrun R, Tsunegi S, Bortolotti P, Kubota H, Jenkins AS, Romera M, Yakushiji K, Fukushima A, Grollier J, Yuasa S, Cros V (2017) Mutual synchronization of spin torque nano-oscillators through a long-range and tunable electrical coupling scheme. Nat Commun 8:15825. https://doi.org/10.1038/ncomms15825
Locatelli N, Hamadeh A, Abreu Araujo F, Belanovsky AD, Skirdkov PN, Lebrun R, Naletov VV, Zvezdin KA, Muñoz M, Grollier J, Klein O, Cros V, de Loubens G (2015) Efficient synchronization of dipolarly coupled vortex-based spin transfer nano-oscillators. Sci Rep 5:17039. https://doi.org/10.1038/srep17039
Erzgräber H, Wieczorek S, Krauskopf B (2009) Locking behavior of three coupled laser oscillators. Phys Rev E 80:026212. https://doi.org/10.1103/PhysRevE.80.026212
Yoshihara F, Fuse T, Ashhab S, Kakuyanagi K, Saito S, Semba K (2016) Superconducting qubit–oscillator circuit beyond the ultrastrong-coupling regime. Nat Phys 13:44–47. https://doi.org/10.1038/nphys3906
Kemeth FP, Haugland SW, Schmidt L, Kevrekidis IG, Krischer K (2016) A classification scheme for chimera states. Chaos Interdiscip J Nonlinear Sci 26:094815. https://doi.org/10.1063/1.4959804
Heltberg ML, Jensen MH (2019) Locked body clocks. Nat Phys. https://doi.org/10.1038/s41567-019-0617-2
Heltberg M, Kellogg RA, Krishna S, Tay S, Jensen MH (2016) Noise induces hopping between NF-κB entrainment modes. Cell Syst 3:532.e3–539.e3. https://doi.org/10.1016/j.cels.2016.11.014
Jerry M, Tsai W, Xie B, Li X, Narayanan V, Raychowdhury A, Datta S (2016) Phase transition oxide neuron for spiking neural networks. In: 2016 74th annual device research conference. IEEE, pp 1–2. https://doi.org/10.1109/DRC.2016.7548503
Pickett MD, Medeiros-Ribeiro G, Williams RS (2013) A scalable neuristor built with Mott memristors. Nat Mater 12:114–117. https://doi.org/10.1038/nmat3510
Boriskov P, Velichko A (2019) Switch elements with S-shaped current–voltage characteristic in models of neural oscillators. Electronics 8:922. https://doi.org/10.3390/electronics8090922
Velichko AA, Stefanovich GB, Pergament AL, Boriskov PP (2003) Deterministic noise in vanadium dioxide based structures. Tech Phys Lett 29:435–437. https://doi.org/10.1134/1.1579818
Jerry M, Parihar A, Raychowdhury A, Datta S (2017) A random number generator based on insulator-to-metal electronic phase transitions. In: 2017 75th annual device research conference. IEEE, pp 1–2. https://doi.org/10.1109/DRC.2017.7999423
Parihar A, Jerry M, Datta S, Raychowdhury A (2018) Stochastic IMT (insulator–metal-transition) neurons: an interplay of thermal and threshold noise at bifurcation. Front Neurosci 12:210. https://doi.org/10.3389/fnins.2018.00210
Jerry M, Parihar A, Grisafe B, Raychowdhury A, Datta S (2017) Ultra-low power probabilistic IMT neurons for stochastic sampling machines. In: 2017 symposium on VLSI technology. IEEE, pp T186–T187. https://doi.org/10.23919/VLSIT.2017.7998148
Czanner G, Sarma SV, Ba D, Eden UT, Wu W, Eskandar E, Lim HH, Temereanca S, Suzuki WA, Brown EN (2015) Measuring the signal-to-noise ratio of a neuron. Proc Natl Acad Sci U S A 112:7141–7146. https://doi.org/10.1073/pnas.1505545112
Faisal AA, Selen LPJ, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292–303. https://doi.org/10.1038/nrn2258
Branco T, Staras K (2009) The probability of neurotransmitter release: variability and feedback control at single synapses. Nat Rev Neurosci 10:373–383. https://doi.org/10.1038/nrn2634
Velichko A, Belyaev M, Putrolaynen V, Perminov V, Pergament A (2018) Modeling of thermal coupling in VO2-based oscillatory neural networks. Solid State Electron 139:8–14. https://doi.org/10.1016/j.sse.2017.09.014
Velichko A, Belyaev M, Putrolaynen V, Perminov V, Pergament A (2018) Thermal coupling and effect of subharmonic synchronization in a system of two VO2 based oscillators. Solid State Electron 141:40–49. https://doi.org/10.1016/j.sse.2017.12.003
Velichko A, Belyaev M, Putrolaynen V, Pergament A, Perminov V (2017) Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks. Int J Mod Phys B 31:1650261. https://doi.org/10.1142/S0217979216502611
Lowet E, Roberts MJ, Bonizzi P, Karel J, De Weerd P (2016) Quantifying neural oscillatory synchronization: a comparison between spectral coherence and phase-locking value approaches. PloS One 11:e0146443. https://doi.org/10.1371/journal.pone.0146443
Parihar A, Shukla N, Jerry M, Datta S, Raychowdhury A (2017) Vertex coloring of graphs via phase dynamics of coupled oscillatory networks. Sci Rep 7:911. https://doi.org/10.1038/s41598-017-00825-1
Shukla N, Parihar A, Cotter M, Barth M, Li X, Chandramoorthy N, Paik H, Schlom DG, Narayanan V, Raychowdhury A, Datta S (2014) Pairwise coupled hybrid vanadium dioxide-MOSFET (HVFET) oscillators for non-boolean associative computing. In: 2014 IEEE international electron devices meeting. IEEE, pp 28.7.1–28.7.4. https://doi.org/10.1109/IEDM.2014.7047129
Von NJ (1954) Non-linear capacitance or inductance switching, amplifying, and memory organs. US2815488A. https://patents.google.com/patent/US2815488. Accessed 19 Mar 2018
Roychowdhury J (2015) Boolean computation using self-sustaining nonlinear oscillators. Proc IEEE 103:1958–1969. https://doi.org/10.1109/JPROC.2015.2483061
Pergament A, Velichko A, Belyaev M, Putrolaynen V (2018) Electrical switching and oscillations in vanadium dioxide. Phys B Condens Matter 536:239–248. https://doi.org/10.1016/j.physb.2017.10.123
Belyaev MA, Boriskov PP, Velichko AA, Pergament AL, Putrolainen VV, Ryabokon’ DV, Stefanovich GB, Sysun VI, Khanin SD (2018) Switching channel development dynamics in planar structures on the basis of vanadium dioxide. Phys Solid State 60:447–456. https://doi.org/10.1134/S1063783418030046
Pergament A, Stefanovich G, Velichko A (2017) Relaxation oscillations in circuits containing sandwich switches based on vanadium dioxide. Phase Transit 90:351–361. https://doi.org/10.1080/01411594.2016.1201818
Belyaev M, Velichko A, Putrolaynen V, Perminov V, Pergament A (2017) Electron beam modification of vanadium dioxide oscillators. Phys Status Solidi Curr Top Solid State Phys. https://doi.org/10.1002/pssc.201600236
Jerry M, Ni K, Parihar A, Raychowdhury A, Datta S (2018) Stochastic insulator-to-metal phase transition-based true random number generator. IEEE Electron Device Lett 39:139–142. https://doi.org/10.1109/LED.2017.2771812
Somers D, Kopell N (1993) Rapid synchronization through fast threshold modulation. Biol Cybern 68:393–407. https://doi.org/10.1007/BF00198772
Yamamoto H, Matsumura R, Takaoki H, Katsurabayashi S, Hirano-Iwata A, Niwano M (2016) Unidirectional signal propagation in primary neurons micropatterned at a single-cell resolution. Appl Phys Lett 109:043703. https://doi.org/10.1063/1.4959836
Tanaka G, Yamane T, Héroux JB, Nakane R, Kanazawa N, Takeda S, Numata H, Nakano D, Hirose A (2019) Recent advances in physical reservoir computing: a review. Neural Netw 115:100–123. https://doi.org/10.1016/j.neunet.2019.03.005
Zhou W, Goh WL, Gao Y (2019) A 3-MHz 17.3-μW 0.015% period jitter relaxation oscillator with energy efficient swing boosting. IEEE Trans Circuits Syst II Express Briefs 1:1. https://doi.org/10.1109/tcsii.2019.2948032
Callan R (1998) Essence of neural networks. Prentice Hall PTR, Upper Saddle River
Kernel method—Wikipedia, (2005). https://en.wikipedia.org/wiki/Kernel_method. Accessed 29 Mar 2020
Lukoševičius M, Jaeger H (2009) Reservoir computing approaches to recurrent neural network training. Comput Sci Rev 3:127–149. https://doi.org/10.1016/j.cosrev.2009.03.005
Hoppensteadt FCFC, Izhikevich EMEM (2000) Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans Neural Netw 11:734–738. https://doi.org/10.1109/72.846744
Romera M, Talatchian P, Tsunegi S, Abreu Araujo F, Cros V, Bortolotti P, Trastoy J, Yakushiji K, Fukushima A, Kubota H, Yuasa S, Ernoult M, Vodenicarevic D, Hirtzlin T, Locatelli N, Querlioz D, Grollier J (2018) Vowel recognition with four coupled spin-torque nano-oscillators. Nature 563:230–234. https://doi.org/10.1038/s41586-018-0632-y
Jerominek H, Renaud M, Swart NR, Picard F, Pope TD, Levesque M, Lehoux M, Bilodeau G, Pelletier M, Audet D, Lambert P (1996) Micromachined VO2-based uncooled IR bolometric detector arrays with integrated CMOS readout electronics. In: Micromachined devices components II, SPIE, pp 111–121. https://doi.org/10.1117/12.250694
Kumar S, Strachan JP, Williams RS (2017) Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing. Nature 548:318–321. https://doi.org/10.1038/nature23307
Wang L, Ren W, Wen J, Xiong B (2018) Overview of phase-change electrical probe memory. Nanomaterials. https://doi.org/10.3390/nano8100772
Foong A, Hady F (2016) Storage as fast as rest of the system. In: 2016 IEEE 8th international memory work, IMW 2016. Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/IMW.2016.7495289
Acknowledgements
This research was supported by Russian Science Foundation (Grant no. 16-19-00135). The authors express their gratitude to Dr. Andrei Rikkiev for the valuable comments in the course of the article translation and revision.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Velichko, A., Putrolaynen, V. & Belyaev, M. Higher-order and long-range synchronization effects for classification and computing in oscillator-based spiking neural networks. Neural Comput & Applic 33, 3113–3131 (2021). https://doi.org/10.1007/s00521-020-05177-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-020-05177-y