A biomorphic neuron model and principles of designing a neural network with memristor synapses for a biomorphic neuroprocessor

Abstract

This paper presents an original biomorphic neuron model, which differs from common IT models by a more complex synapse structure and from biological models by replacement of differential equations that describe the change in potential over time with explicit recurrence expressions by approximation of experimental data in the cortical neuron, and therefore, by transition from the spiking information coding to the coding using the average frequency of action potentials per a simulation step. This approach ensures sufficiently simple and efficient calculation of an ultra-large neural network in the stand-alone hardware with limited computing resources. The model consists of three separate functional parts: dendrites, soma, and axon, which allows implementing any connections between functional parts of different neurons, thus making the neural network architecture more flexible. To perform functional testing of the neuron model, the test neural network performing simple association and constructed as a consequent stack of functional blocks with primary connections organized using experimental neurophysiological data was simulated. It is shown that encoding of the information transmitted by the impulses, similar to biological ones, allows using memristors for calculating recurrence expressions that describe the change in the quantity of neurotransmitter receptors of the dendrite membrane. The elaborated biomorphic neuron model, defined conceptual principles of a neural network construction based on it, as well as replacement of synapses in the neural network with memristors will allow building an ultra-large biomorphic neural network that simulates the functioning of a separate brain cortical column in the stand-alone hardware—a biomorphic neuroprocessor.

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References

  1. 1.

    Udovichenko SY, Pisarev AD, Busygin AN, Maevsky OV (2018) Neuroprocessor based on combined memristor-diode crossbar. Nanoindustry 5:344–355. https://doi.org/10.22184/1993-8578.2018.84.5.344.355

    Article  Google Scholar 

  2. 2.

    Pisarev A, Busygin A, Udovichenko S, Maevsky O (2018) 3D memory matrix based on a composite memristor-diode crossbar for a neuromorphic processor. Microelectron Eng 198:1–7. https://doi.org/10.1016/j.mee.2018.06.008

    Article  Google Scholar 

  3. 3.

    Udovichenko S, Pisarev A, Busygin A, Maevsky O (2017) 3D CMOS memristor nanotechnology for creating logical and memory matrices of neuroprocessor. Nanoindustry 5:26–34. https://doi.org/10.22184/1993-8578.2017.76.5.26.34

    Article  Google Scholar 

  4. 4.

    Maevsky OV, Pisarev AD, Busygin AN, Udovichenko SY (2018) Complementary memristor-diode cell for a memory matrix in neuromorphic processor. Int J Nanotechnol 15(4/5):388–393. https://doi.org/10.1504/IJNT.2018.094795

    Article  Google Scholar 

  5. 5.

    Pisarev AD, Busygin AN, Udovichenko SYu, Bobylev AN, Maevsky OV (2018) A biomorphic neuroprocessor based on the composite memristor-diode crossbar. Book of abstracts of international workshop from RERAM and Memristors to new Computing Paradigms (MEM-Q):25

  6. 6.

    Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544. https://doi.org/10.1113/jphysiol.1952.sp004764

    Article  Google Scholar 

  7. 7.

    Merolla РА, Arthur JV, Alvarez-Icaza R et al (2014) A million spiking-neuron integrated circuit with a scalable communication network and interface. Science 345:668–672. https://doi.org/10.1126/science.1254642

    Article  Google Scholar 

  8. 8.

    Prezioso M, Merrikh-Bayat F, Hoskins BD, Adam GC, Likharev KK, Strukov DB (2015) Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature 521:61–64. https://doi.org/10.1038/nature14441

    Article  Google Scholar 

  9. 9.

    Kim K-H, Gaba S, Wheeler D, Cruz-Albrecht JM, Hussain T, Srinivasa N, Lu W (2012) A functional hybrid memristor crossbar-array/CMOS system for data storage and neuromorphic applications. Nano Lett 12:389–395. https://doi.org/10.1021/nl203687n

    Article  Google Scholar 

  10. 10.

    Bobylev AN, Busygin AN, Pisarev AD, Udovichenko SYu, Filippov VA (2017) Neuromorphic coprocessor prototype based on mixed metal oxide memristors. Int J Nanotechnol 14(7/8):698–704. https://doi.org/10.1504/IJNT.2017.083444

    Article  Google Scholar 

  11. 11.

    Govoreanu B, Kar GS, Chen Y-Y et al. (2011) 10 × 10 nm2 Hf/HfOx crossbar resistive RAM with excellent performance, reliability and low-energy operation. In: Proceedings of 2011 IEEE international electron devices meeting (IEDM), pp 31.6.1–31.6.4. https://doi.org/10.1109/IEDM.2011.6131652

  12. 12.

    Bobylev AN, Udovichenko SYu (2016) The electrical properties of memristor devices TiN/TixAl1−xOy/TiN produced by magnetron sputtering. Russ Microlectron 45(6):396–401. https://doi.org/10.1134/S1063739716060020

    Article  Google Scholar 

  13. 13.

    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

    Article  Google Scholar 

  14. 14.

    Wang Z, Wang X (2018) A novel memristor-based circuit implementation of full-function Pavlov associative memory accorded with biological feature. IEEE Trans Circuits Syst I Regul Pap 65(7):2210–2220. https://doi.org/10.1109/TCSI.2017.2780826

    Article  Google Scholar 

  15. 15.

    Yang L, Zeng Z, Huang Y, Wen S (2018) Memristor-based circuit implementations of recognition network and recall network with forgetting stages. IEEE Trans Cogn Dev Syst 10(4):1133–1142. https://doi.org/10.1109/TCDS.2018.2859303

    Article  Google Scholar 

  16. 16.

    Zhang X, Long K (2019) Improved learning experience memristor model and application as neural network synapse. IEEE Access 7:15262–15271. https://doi.org/10.1109/ACCESS.2019.2894634

    Article  Google Scholar 

  17. 17.

    Wang Z, Rao M, Han J-W et al (2018) Capacitive neural network with neuro-transistors. Nat Commun 9:3208. https://doi.org/10.1038/s41467-018-05677-5

    Article  Google Scholar 

  18. 18.

    Liu J, Huang Y, Luo Y, Harkin J, McDaid L (2019) Bio-inspired fault detection circuits based on synapse and spiking neuron models. Neurocomputing 331:473–482. https://doi.org/10.1016/j.neucom.2018.11.078

    Article  Google Scholar 

  19. 19.

    Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 534(7191):80–83. https://doi.org/10.1038/nature06932

    Article  Google Scholar 

  20. 20.

    Liu J, Harkin J, Maguire LP et al (2017) SPANNER: a self-repairing spiking neural network hardware architecture. IEEE Trans Neural Netw Learn Syst 29(4):1287–1300. https://doi.org/10.1109/TNNLS.2017.2673021

    Article  Google Scholar 

  21. 21.

    Liu J, McDaid LJ, Harkin J et al (2018) Exploring self-repair in a coupled spiking astrocyte neural network. IEEE Trans Neural Netw Learn Syst 30(3):865–875. https://doi.org/10.1109/TNNLS.2018.2854291

    Article  Google Scholar 

  22. 22.

    Rosenblatt F (1958) The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev 65:386–408. https://doi.org/10.1037/h0042519

    Article  Google Scholar 

  23. 23.

    Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117. https://doi.org/10.1016/j.neunet.2014.09.003

    Article  Google Scholar 

  24. 24.

    Filippov VA (2008) Chapter 5. Neuron modeling. In: Sokolova EN, Filippov VA, Chernorizov AM (ed) Neuron. Signal processing. Plasticity. Modeling. Fundamental guide. Publishing house of Tyumen State University, Tyumen, Russia, pp 468–535. https://eknigi.org/nauka_i_ucheba/114893-nejron-obrabotka-signalov-plastichnost.html

  25. 25.

    Geminiani A, Casellato C, Locatelli F et al (2018) Complex dynamics in simplified neuronal models: reproducing golgi cell electroresponsiveness. Front Neuroinform 12:88. https://doi.org/10.3389/fninf.2018.00088

    Article  Google Scholar 

  26. 26.

    Blundell I, Plotnikov D, Eppler JM, Morrison A (2018) Automatically selecting a suitable integration scheme for systems of differential equations in neuron models. Front Neuroinform 12:50. https://doi.org/10.3389/fninf.2018.00050

    Article  Google Scholar 

  27. 27.

    Fox K (2017) Deconstructing the cortical column in the barrel cortex. Neuroscience 368:17–28. https://doi.org/10.1016/j.neuroscience.2017.07.034

    Article  Google Scholar 

  28. 28.

    Malebra P, Rulkov NF, Bazhenov M (2019) Large time step discrete-time modeling of sharp wave activity in hippocampal area CA3. Commun Nonlinear Sci Numer Simulat 72:162–175. https://doi.org/10.1016/j.cnsns.2018.12.009

    Article  MathSciNet  Google Scholar 

  29. 29.

    Brette R (2015) Philosophy of the spike: rate-based vs. spike-based theories of the brain. Front Syst Neurosci 9:151. https://doi.org/10.3389/fnsys.2015.00151

    Article  Google Scholar 

  30. 30.

    Touboul J, Brette R (2008) Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biol Cybern 99:319–334. https://doi.org/10.1007/s00422-008-0267-4

    Article  MathSciNet  MATH  Google Scholar 

  31. 31.

    Rulkov NF, Neiman AB (2018) Control of sampling rate in map-based models of spiking neurons. Commun Nonlinear Sci Numer Simulat 61:127–137. https://doi.org/10.1016/j.cnsns.2018.01.021

    Article  MathSciNet  Google Scholar 

  32. 32.

    Komarov M, Krishnan G, Chauvette S et al (2018) New class of reduced computationally efficient neuronal models for large-scale simulations of brain dynamics. J Comput Neurosci 44:1–24. https://doi.org/10.1007/s10827-017-0663-7

    Article  MathSciNet  MATH  Google Scholar 

  33. 33.

    Winters BD, Jin S-X, Ledford KR, Golding NL (2017) Amplitude normalization of dendritic EPSPs at the soma of binaural coincidence detector neurons of the medial superior olive. J Neurosci 37(12):3138–3149. https://doi.org/10.1523/JNEUROSCI.3110-16.2017

    Article  Google Scholar 

  34. 34.

    Timofeeva Yu, Volynski KE (2015) Calmodulin as a major calcium buffer shaping vesicular release and short-term synaptic plasticity: facilitation through buffer dislocation. Front Cell Neurosci 9:239. https://doi.org/10.3389/fncel.2015.00239

    Article  Google Scholar 

  35. 35.

    Pickett MD, Strukov DB, Borghetti JL, Yang J, Snider GS, Stewart DR, Williams RS (2009) Switching dynamics in titanium dioxide memristive devices. J Appl Phys 106(7):074508. https://doi.org/10.1063/1.3236506

    Article  Google Scholar 

  36. 36.

    Bean BP (2007) The action potential in mammalian central neurons. Nat Rev Neurosci 8:451–465. https://doi.org/10.1038/nrn2148

    Article  Google Scholar 

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Correspondence to A. N. Busygin.

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Filippov, V.A., Bobylev, A.N., Busygin, A.N. et al. A biomorphic neuron model and principles of designing a neural network with memristor synapses for a biomorphic neuroprocessor. Neural Comput & Applic 32, 2471–2485 (2020). https://doi.org/10.1007/s00521-019-04383-7

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Keywords

  • Biomorphic neuron model
  • Biomorphic neural network
  • Memristor
  • Memristor-based synapses