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.
摘要
提出一种新颖的分数阶记忆性神经突触加权电路. 与以往大多数整数阶神经突触加权电路不同, 该分数阶记忆性神经突触加权电路具有许多重要优点. 由于忆阻的概念已从经典的整数阶忆阻推广到分数阶忆阻 (分忆抗), 分忆抗能否实现分数阶记忆性突触成为一个具有挑战性的理论问题. 本文研究利用脉冲分忆抗桥电路实现的分数阶记忆性神经突触加权电路的特点. 首先, 利用基于脉冲的分忆抗桥电路设计分数阶记忆性神经突触加权电路结构. 其次, 从数学上证明分数阶记忆性神经突触加权电路的分数阶学习能力. 最后, 通过实验研究分数阶记忆性神经突触加权电路的电特性. 分数阶记忆性神经突触加权电路在解释学习和记忆基础的细胞机制方面具有很强的能力, 优于传统的整数阶神经突触加权电路, 是该电路的主要优势.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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. https://doi.org/10.1109/TNNLS.2012.2204770
Adhikari SP, Kim H, Budhathoki RK, et al., 2014. Learning with memristor bridge synapse-based neural networks. Proc 14th Int Workshop on Cellular Nanoscale Networks and Their Applications, p.1–2. https://doi.org/10.1109/CNNA.2014.6888623
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. https://doi.org/10.1109/TCSI.2014.2359717
Battiti R, 1992. First- and second-order methods for learning: between steepest descent and Newton’s method. Neur Comput, 4(2):141–166. https://doi.org/10.1162/neco.1992.4.2.141
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. https://doi.org/10.1523/JNEUROSCI.18-24-10464.1998
Bliss TVP, Lømo 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. https://doi.org/10.1113/jphysiol.1973.sp010273
Bliss TVP, Collingridge GL, 1993. A synaptic model of memory: long-term potentiation in the hippocampus. Nature, 361(6407):31–39. https://doi.org/10.1038/361031a0
Bohte SM, Kok JN, Poutré HL, 2002. Error-backpropagation in temporally encoded networks of spiking neurons. Neurocomputing, 48(1–4):17–37. https://doi.org/10.1016/S0925-2312(01)00658-0
Borghetti J, Snider GS, Kuekes PJ, et al., 2010. ‘Memristive’ switches enable ‘stateful’ logic operations via material implication. Nature, 464(7290):873–876. https://doi.org/10.1038/nature08940
Brown BD, Card HC, 2001a. Stochastic neural computation. I. Computational elements. IEEE Trans Comput, 50(9):891–905. https://doi.org/10.1109/12.954505
Brown BD, Card HC, 2001b. Stochastic neural computation. II. Soft competitive learning. IEEE Trans Comput, 50(9):906–920. https://doi.org/10.1109/12.954506
Chua L, 1971. Memristor—the missing circuit element. IEEE Trans Circ Theory, 18(5):507–519. https://doi.org/10.1109/TCT.1971.1083337
Chua L, 1978a. Introduction to Nonlinear Network Theory, Part 1, Foundations of Nonlinear Network Theory. Robert E Krieger Publishing Company, New York, USA.
Chua L, 1978b. Introduction to Nonlinear Network Theory, Part 2, Resistive Nonlinear Networks. Robert E Krieger Publishing Company, New York, USA.
Chua L, 1980a. Device modeling via nonlinear circuit elements. IEEE Trans Circ Syst, 27(11):1014–1044. https://doi.org/10.1109/TCS.1980.1084742
Chua L, 1980b. Dynamic nonlinear networks: state-of-the-art. IEEE Trans Circ Syst, 27(11):1059–1087. https://doi.org/10.1109/TCS.1980.1084745
Chua L, 2003. Nonlinear circuit foundations for nanodevices. I. The four-element torus. Proc IEEE, 91(11):1830–1859. https://doi.org/10.1109/JPROC.2003.818319
Chua L, 2011. Resistance switching memories are memristors. Appl Phys A, 102(4):765–783. https://doi.org/10.1007/s00339-011-6264-9
Chua L, 2012. The fourth element. Proc IEEE, 100(6):1920–1927. https://doi.org/10.1109/JPROC.2012.2190814
Chua L, 2013. Memristor, Hodgkin—Huxley, and edge of chaos. Nanotechnology, 24(38):383001. https://doi.org/10.1088/0957-4484/24/38/383001
Chua L, Kang SM, 1976. Memristive devices and systems. Proc IEEE, 64(2):209–223. https://doi.org/10.1109/PROC.1976.10092
Cooke SF, Bliss TVP, 2006. Plasticity in the human central nervous system. Brain, 129(7):1659–1673. https://doi.org/10.1093/brain/awl082
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. https://doi.org/10.1002/9781444344035.ch1
Fouda ME, Radwan AG, 2013. On the fractional-order memristor model. J Fract Calc Appl, 4(1):1–7.
Fouda ME, Radwan AG, 2015. Fractional-order memristor response under DC and periodic signals. Circ Syst Signal Process, 34(3):961–970. https://doi.org/10.1007/s00034-014-9886-2
Fu TD, Liu XM, Gao HY, et al., 2020. Bioinspired biovoltage memristors. Nat Commun, 11(1):1861. https://doi.org/10.1038/s41467-020-15759-y
Hebb DO, 1949. The Organization of Behavior. Wiley & Sons, New York, USA.
Hopfield JJ, 1982. Neural networks and physical systems with emergent collective computational abilities. PNAS, 79(8):2554–2558. https://doi.org/10.1073/pnas.79.8.2554
Hughes JR, 1958. Post-tetanic potentiation. Physiol Rev, 38(1):91–113. https://doi.org/10.1152/physrev.1958.38.1.91
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. https://doi.org/10.1371/journal.pcbi.1003248
Jo SH, Chang T, Ebong I, et al., 2010. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett, 10(4):1297–1301. https://doi.org/10.1021/nl904092h
Kandel ER, 2007. In Search of Memory: the Emergence of a New Science of Mind. W. W. Norton & Company, New York, USA.
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. https://doi.org/10.1109/TCSI.2005.853263
Kim H, Sah MP, Yang CJ, et al., 2012. Memristor bridge synapses. Proc IEEE, 100(6):2061–2070. https://doi.org/10.1109/JPROC.2011.2166749 ai[Koeller RC, 1984. Applications of fractional calculus to the theory of viscoelasticity. J Appl Mech, 51(2):299–307. https://doi.org/10.1115/1.3167616
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. https://doi.org/10.1063/1.5108899
Li CB, Li CD, Huang TW, et al., 2013. Synaptic memcapacitor bridge synapses. Neurocomputing, 122:370–374. https://doi.org/10.1016/j.neucom.2013.05.036
Magee JC, Johnston D, 1997. A synaptically controlled, associative signal for Hebbian plasticity in hippocampal neurons. Science, 275(5297):209–213. https://doi.org/10.1126/science.275.5297.209
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. https://doi.org/10.1126/science.275.5297.213
Massey PV, Bashir ZI, 2007. Long-term depression: multiple forms and implications for brain function. Trends Neurosci, 30(4):176–184. https://doi.org/10.1016/j.tins.2007.02.005
Oja E, 1982. Simplified neuron model as a principal component analyzer. J Math Biol, 15(3):267–273. https://doi.org/10.1007/BF00275687
Oldham KB, Spanier J, 1974. The Fractional Calculus: Integrations and Differentiations of Arbitrary Order. Academic Press, New York, USA.
Özdemir N, Karadeniz D, 2008. Fractional diffusion-wave problem in cylindrical coordinates. Phys Lett A, 372(38):5968–5972. https://doi.org/10.1016/j.physleta.2008.07.054
Pan LQ, Zeng XX, Zhang XY, et al., 2012. Spiking neural P systems with weighted synapses. Neur Process Lett, 35(1):13–27. https://doi.org/10.1007/s11063-011-9201-1
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.
Podlubny I, Petráš I, Vinagre BM, et al., 2002. Analogue realizations of fractional-order controllers. Nonl Dynam, 29(1–4):281–296. https://doi.org/10.1023/A:1016556604320
Powell MJD, 1977. Restart procedures for the conjugate gradient method. Math Programm, 12(1):241–254. https://doi.org/10.1007/BF01593790
Prodromakis T, Toumazou C, Chua L, 2012. Two centuries of memristors. Nat Mater, 11(6):478–481. https://doi.org/10.1038/nmat3338
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. https://doi.org/10.1109/ACCESS.2016.2585818
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. https://doi.org/10.1109/ACCESS.2016.2585819
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. https://doi.org/10.1109/ACCESS.2016.2606160
Pu YF, Yuan X, 2016. Fracmemristor: fractional-order memristor. IEEE Access, 4:1872–1888. https://doi.org/10.1109/ACCESS.2016.2557818
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. https://doi.org/10.1142/S0129065717500034
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. https://doi.org/10.1109/TNNLS.2016.2582512
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. https://doi.org/10.1109/TCSI.2018.2789907
Pu YF, Siarry P, Chatterjee A, et al., 2018b. A fractional-order variational framework for retinex: fractional-order partial differential equation-based formulation for multiscale nonlocal contrast enhancement with texture preserving. IEEE Trans Image Process, 27(3):1214–1229. https://doi.org/10.1109/TIP.2017.2779601
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. https://doi.org/10.1115/1.3101682
Sah MP, Yang CJ, Kim H, et al., 2012. A voltage mode memristor bridge synaptic circuit with memristor emulators. Sensors, 12(3):3587–3604. https://doi.org/10.3390/s120303587
Shettleworth SJ, 2009. Cognition, Evolution, and Behavior (2nd Ed.). Oxford University Press, New York, USA.
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. https://doi.org/10.1007/978-981-10-6373-2_70
Snider GS, 2007. Self-organized computation with unreliable, memristive nanodevices. Nanotechnology, 18(36): 365202. https://doi.org/10.1088/0957-4484/18/36/365202
Squire LR, Kandel ER, 2003. Memory: from Mind to Molecules. Macmillan, London, UK, p.69.
Strukov DB, Snider GS, Stewart DR, et al., 2008. The missing memristor found. Nature, 453(7191):80–83. https://doi.org/10.1038/nature06932
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.
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. https://doi.org/10.1016/j.neucom.2005.11.023
Yang CJ, Adhikari SP, Kim H, 2018. Excitatory and inhibitory actions of a memristor bridge synapse. Sci China Inform Sci, 61(6):060427. https://doi.org/10.1007/s11432-017-9348-3
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). https://doi.org/10.7498/aps.64.238401.
Yu YJ, Bao BC, Kang HY, et al., 2015. Calculating area of fractional-order memristor pinched hysteresis loop. J Eng, 2015(11):325–327. https://doi.org/10.1049/joe.2015.0154
Zhang CX, Chen Y, Yi MD, et al., 2018. Recent progress in memristors for stimulating synaptic plasticity. Sci Sin Inform, 48(2):115–142. https://doi.org/10.1360/N112017-00022
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. https://doi.org/10.1021/acs.nanolett.9b00525
Zhou L, Yang SW, Ding GQ, et al., 2019. Tunable synaptic behavior realized in C3N composite based memristor. Nano Energy, 58:293–303. https://doi.org/10.1016/j.nanoen.2019.01.045
Author information
Authors and Affiliations
Contributions
Yifei PU designed the research. Bo YU and Qiuyan HE processed the data. Yifei PU and Qiuyan HE drafted the manuscript. Bo YU and Xiao YUAN helped organize the manuscript. Yifei PU, Bo YU, Qiuyan HE, and Xiao YUAN revised and finalized the paper.
Corresponding authors
Ethics declarations
Yifei PU, Bo YU, Qiuyan HE, and Xiao YUAN declare that they have no conflict of interest.
Additional information
Project supported by the National Key Research and Development Program of China (No. 2018YFC0830300) and the National Natural Science Foundation of China (No. 61571312)
Rights and permissions
About this article
Cite this article
Pu, Y., Yu, B., He, Q. et al. Fractional-order memristive neural synaptic weighting achieved by pulse-based fracmemristor bridge circuit. Front Inform Technol Electron Eng 22, 862–876 (2021). https://doi.org/10.1631/FITEE.2000085
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.2000085
Key words
- Fractional calculus
- Fracmemristor
- Fracmemristance
- Fractional-order memristor
- Fractional-order memristive synapses