Similar articles

Abstract: We propose a novel circuit for the fractional-order memristive neural synaptic weighting (FMNSW). The introduced circuit is different from the majority of the previous integer-order approaches and offers important advantages. Since the concept of memristor has been generalized from the classic integer-order memristor to the fractional-order memristor (fracmemristor), a challenging theoretical problem would be whether the fracmemristor can be employed to implement the fractional-order memristive synapses or not. In this research, characteristics of the FMNSW, realized by a pulse-based fracmemristor bridge circuit, are investigated. First, the circuit configuration of the FMNSW is explained using a pulse-based fracmemristor bridge circuit. Second, the mathematical proof of the fractional-order learning capability of the FMNSW is analyzed. Finally, experimental work and analyses of the electrical characteristics of the FMNSW are presented. Strong ability of the FMNSW in explaining the cellular mechanisms that underlie learning and memory, which is superior to the traditional integer-order memristive neural synaptic weighting, is considered a major advantage for the proposed circuit.

基于脉冲分忆抗桥电路的分数阶记忆性神经突触加权

[1]Adhikari SP, Yang CJ, Kim H, et al., 2012. Memristor bridge synapse-based neural network and its learning. IEEE Trans Neur Netw Learn Syst, 23(9):1426-1435.

[2]Adhikari SP, Kim H, Budhathoki RK, et al., 2014. Learning with memristor bridge synapse-based neural networks. Proc 14^th Int Workshop on Cellular Nanoscale Networks and Their Applications, p.1-2.

[3]Adhikari SP, Kim H, Budhathoki RK, et al., 2015. A circuit-based learning architecture for multilayer neural networks with memristor bridge synapses. IEEE Trans Circ Syst I Regul Pap, 62(1):215-223.

[4]Battiti R, 1992. First- and second-order methods for learning: between steepest descent and Newton’s method. Neur Comput, 4(2):141-166.

[5]Bi GQ, Poo MM, 1998. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci, 18(24):10464-10472.

[6]Bliss TVP, Lomo T, 1973. Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. J Physiol, 232(2):331-356.

[7]Bliss TVP, Collingridge GL, 1993. A synaptic model of memory: long-term potentiation in the hippocampus. Nature, 361(6407):31-39.

[8]Bohte SM, Kok JN, Poutré HL, 2002. Error-backpropagation in temporally encoded networks of spiking neurons. Neurocomputing, 48(1-4):17-37.

[9]Borghetti J, Snider GS, Kuekes PJ, et al., 2010. ‘Memristive’ switches enable ‘stateful’ logic operations via material implication. Nature, 464(7290):873-876.

[10]Brown BD, Card HC, 2001a. Stochastic neural computation. I. Computational elements. IEEE Trans Comput, 50(9):891-905.

[11]Brown BD, Card HC, 2001b. Stochastic neural computation. II. Soft competitive learning. IEEE Trans Comput, 50(9):906-920.

[12]Chua L, 1971. Memristor—the missing circuit element. IEEE Trans Circ Theory, 18(5):507-519.

[13]Chua L, 1978a. Introduction to Nonlinear Network Theory, Part 1, Foundations of Nonlinear Network Theory. Robert E Krieger Publishing Company, New York, USA.

[14]Chua L, 1978b. Introduction to Nonlinear Network Theory, Part 2, Resistive Nonlinear Networks. Robert E Krieger Publishing Company, New York, USA.

[15]Chua L, 1980a. Device modeling via nonlinear circuit elements. IEEE Trans Circ Syst, 27(11):1014-1044.

[16]Chua L, 1980b. Dynamic nonlinear networks: state-of-the-art. IEEE Trans Circ Syst, 27(11):1059-1087.

[17]Chua L, 2003. Nonlinear circuit foundations for nanodevices. I. The four-element torus. Proc IEEE, 91(11):1830-1859.

[18]Chua L, 2011. Resistance switching memories are memristors. Appl Phys A, 102(4):765-783.

[19]Chua L, 2012. The fourth element. Proc IEEE, 100(6):1920-1927.

[20]Chua L, 2013. Memristor, Hodgkin–Huxley, and edge of chaos. Nanotechnology, 24(38):383001.

[21]Chua L, Kang SM, 1976. Memristive devices and systems. Proc IEEE, 64(2):209-223.

[22]Cooke SF, Bliss TVP, 2006. Plasticity in the human central nervous system. Brain, 129(7):1659-1673.

[23]Fennell CT, 2012. Habituation procedures. In: Hoff E (Ed.), Research Methods in Child Language: a Practical Guide. Blackwell Publishing Ltd., Malden, USA, p.1-16.

[24]Fouda ME, Radwan AG, 2013. On the fractional-order memristor model. J Fract Calc Appl, 4(1):1-7.

[25]Fouda ME, Radwan AG, 2015. Fractional-order memristor response under DC and periodic signals. Circ Syst Signal Process, 34(3):961-970.

[26]Fu TD, Liu XM, Gao HY, et al., 2020. Bioinspired bio-voltage memristors. Nat Commun, 11(1):1861.

[27]Hebb DO, 1949. The Organization of Behavior. Wiley & Sons, New York, USA.

[28]Hopfield JJ, 1982. Neural networks and physical systems with emergent collective computational abilities. PNAS, 79(8):2554-2558.

[29]Hughes JR, 1958. Post-tetanic potentiation. Physiol Rev, 38(1):91-113.

[30]Iyer R, Menon V, Buice M, et al., 2013. The influence of synaptic weight distribution on neuronal population dynamics. PLoS Comput Biol, 9(10):e1003248.

[31]Jo SH, Chang T, Ebong I, et al., 2010. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett, 10(4):1297-1301.

[32]Kandel ER, 2007. In Search of Memory: the Emergence of a New Science of Mind. W. W. Norton & Company, New York, USA.

[33]Kim H, Son H, Roska T, et al., 2005. High-performance Viterbi decoder with circularly connected 2-D CNN unilateral cell array. IEEE Trans Circ Syst I Regul Pap, 52(10):2208-2218.

[34]Kim H, Sah MP, Yang CJ, et al., 2012. Memristor bridge synapses. Proc IEEE, 100(6):2061-2070.

[35]Koeller RC, 1984. Applications of fractional calculus to the theory of viscoelasticity. J Appl Mech, 51(2):299-307.

[36]Krishnaprasad A, Choudhary N, Das S, et al., 2019. Electronic synapses with near-linear weight update using MoS₂/graphene memristors. Appl Phys Lett, 115(10):103104.

[37]Li CB, Li CD, Huang TW, et al., 2013. Synaptic memcapacitor bridge synapses. Neurocomputing, 122:370-374.

[38]Magee JC, Johnston D, 1997. A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons. Science, 275(5297):209-213.

[39]Markram H, Lübke J, Frotscher M, et al., 1997. Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science, 275(5297):213-215.

[40]Massey PV, Bashir ZI, 2007. Long-term depression: multiple forms and implications for brain function. Trends Neurosci, 30(4):176-184.

[41]Oja E, 1982. Simplified neuron model as a principal component analyzer. J Math Biol, 15(3):267-273.

[42]Oldham KB, Spanier J, 1974. The Fractional Calculus: Integrations and Differentiations of Arbitrary Order. Academic Press, New York, USA.

[43]Özdemir N, Karadeniz D, 2008. Fractional diffusion-wave problem in cylindrical coordinates. Phys Lett A, 372(38):5968-5972.

[44]Pan LQ, Zeng XX, Zhang XY, et al., 2012. Spiking neural P systems with weighted synapses. Neur Process Lett, 35(1):13-27.

[45]Podlubny I, 1998. Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, New York, USA.

[46]Podlubny I, Petráš I, Vinagre BM, et al., 2002. Analogue realizations of fractional-order controllers. Nonl Dynam, 29(1-4):281-296.

[47]Powell MJD, 1977. Restart procedures for the conjugate gradient method. Math Programm, 12(1):241-254.

[48]Prodromakis T, Toumazou C, Chua L, 2012. Two centuries of memristors. Nat Mater, 11(6):478-481.

[49]Pu YF, 2016a. Measurement units and physical dimensions of fractance-part I: position of purely ideal fractor in Chua’s axiomatic circuit element system and fractional-order reactance of fractor in its natural implementation. IEEE Access, 4:3379-3397.

[50]Pu YF, 2016b. Measurement units and physical dimensions of fractance-part II: fractional-order measurement units and physical dimensions of fractance and rules for fractors in series and parallel. IEEE Access, 4:3398-3416.

[51]Pu YF, 2016c. Analog circuit realization of arbitrary-order fractional Hopfield neural networks: a novel application of fractor to defense against chip cloning attacks. IEEE Access, 4:5417-5435.

[52]Pu YF, Yuan X, 2016. Fracmemristor: fractional-order memristor. IEEE Access, 4:1872-1888.

[53]Pu YF, Yi Z, Zhou JL, 2017a. Defense against chip cloning attacks based on fractional Hopfield neural networks. Int J Neur Syst, 27(4):1750003.

[54]Pu YF, Yi Z, Zhou JL, 2017b. Fractional Hopfield neural networks: fractional dynamic associative recurrent neural networks. IEEE Trans Neur Netw Learn Syst, 28(10):2319-2333.

[55]Pu YF, Yuan X, Yu B, 2018a. Analog circuit implementation of fractional-order memristor: arbitrary-order lattice scaling fracmemristor. IEEE Trans Circ Syst I Regul Pap, 65(9):2903-2916.

[56]Pu YF, Siarry P, Chatterjee A, et al., 2018b. A fractional-order variational framework for retinex: fractional-order partial differential equation-based formulation for multi-scale nonlocal contrast enhancement with texture preserving. IEEE Trans Image Process, 27(3):1214-1229.

[57]Rossikhin YA, Shitikova MV, 1997. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl Mech Rev, 50(1):15-67.

[58]Sah MP, Yang CJ, Kim H, et al., 2012. A voltage mode memristor bridge synaptic circuit with memristor emulators. Sensors, 12(3):3587-3604.

[59]Shettleworth SJ, 2009. Cognition, Evolution, and Behavior (2^nd Ed.). Oxford University Press, New York, USA.

[60]Shi M, Hu SL, 2017. Pinched hysteresis loop characteristics of a fractional-order HP TiO₂ memristor. Proc Intelligent Computing, Networked Control, and Their Engineering Applications, p.705-713.

[61]Snider GS, 2007. Self-organized computation with unreliable, memristive nanodevices. Nanotechnology, 18(36):365202.

[62]Squire LR, Kandel ER, 2003. Memory: from Mind to Molecules. Macmillan, London, UK, p.69.

[63]Strukov DB, Snider GS, Stewart DR, et al., 2008. The missing memristor found. Nature, 453(7191):80-83.

[64]Wang LD, Wang XD, Duan SK, et al., 2015. A spintronic memristor bridge synapse circuit and the application in memrisitive cellular automata. Neurocomputing, 167:346-351.

[65]Wu QX, McGinnity TM, Maguire LP, et al., 2006. Learning under weight constraints in networks of temporal encoding spiking neurons. Neurocomputing, 69(16-18):1912-1922.

[66]Yang CJ, Adhikari SP, Kim H, 2018. Excitatory and inhibitory actions of a memristor bridge synapse. Sci China Inform Sci, 61(6):060427.

[67]Yu YJ, Wang ZH, 2015. A fractional-order memristor model and the fingerprint of the simple series circuits including a fractional-order memristor. Acta Phys Sin, 64(23):238401 (in Chinese).

[68]Yu YJ, Bao BC, Kang HY, et al., 2015. Calculating area of fractional-order memristor pinched hysteresis loop. J Eng, 2015(11):325-327.

[69]Zhang CX, Chen Y, Yi MD, et al., 2018. Recent progress in memristors for stimulating synaptic plasticity. Sci Sin Inform, 48(2):115-142.

[70]Zhang P, Xia M, Zhuge FW, et al., 2019. Nanochannel-based transport in an interfacial memristor can emulate the analog weight modulation of synapses. Nano Lett, 19(7):4279-4286.

[71]Zhou L, Yang SW, Ding GQ, et al., 2019. Tunable synaptic behavior realized in C₃N composite based memristor. Nano Energy, 58:293-303.