SCIENCE CHINA Information Sciences, Volume 64 , Issue 6 : 160405(2021) https://doi.org/10.1007/s11432-021-3217-0

Neural connectivity inference with spike-timing dependent plasticity network

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  • ReceivedFeb 2, 2021
  • AcceptedMar 15, 2021
  • PublishedApr 26, 2021



This work was supported in part by National Science Foundation through Award (Grant No. 1915550). The authors would like to thank Dr. S. H. Lee and Dr. M. Zidan for stimulating discussions.


[1] Insel T R, Landis S C, Collins F S. The NIH BRAIN Initiative. Science, 2013, 340: 687-688 CrossRef ADS Google Scholar

[2] Amunts K, Ebell C, Muller J. The Human Brain Project: Creating a European Research Infrastructure to Decode the Human Brain. Neuron, 2016, 92: 574-581 CrossRef Google Scholar

[3] Okano H, Sasaki E, Yamamori T. Brain/MINDS: A Japanese National Brain Project for Marmoset Neuroscience. Neuron, 2016, 92: 582-590 CrossRef Google Scholar

[4] Brown E N, Kass R E, Mitra P P. Multiple neural spike train data analysis: state-of-the-art and future challenges. Nat Neurosci, 2004, 7: 456-461 CrossRef Google Scholar

[5] Pillow J W, Shlens J, Paninski L. Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature, 2008, 454: 995-999 CrossRef ADS Google Scholar

[6] Magrans de Abril I, Yoshimoto J, Doya K. Connectivity inference from neural recording data: Challenges, mathematical bases and research directions. Neural Networks, 2018, 102: 120-137 CrossRef Google Scholar

[7] Evaluation of the Performance of Information Theory-Based Methods and Cross-Correlation to Estimate the Functional Connectivity in Cortical Networks. PLoS ONE, 2009, 4: e6482 CrossRef ADS Google Scholar

[8] Salinas E, Sejnowski T J. Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci, 2001, 2: 539-550 CrossRef Google Scholar

[9] Kraskov A, St?gbauer H, Grassberger P. Estimating mutual information. Phys Rev E, 2004, 69: 066138 CrossRef ADS arXiv Google Scholar

[10] Schreiber T. Measuring Information Transfer. Phys Rev Lett, 2000, 85: 461-464 CrossRef ADS arXiv Google Scholar

[11] Extending Transfer Entropy Improves Identification of Effective Connectivity in a Spiking Cortical Network Model. PLoS ONE, 2011, 6: e27431 CrossRef ADS Google Scholar

[12] Identification of excitatory-inhibitory links and network topology in large-scale neuronal assemblies from multi-electrode recordings. PLoS Comput Biol, 2018, 14: e1006381 CrossRef ADS Google Scholar

[13] Kobayashi R, Kurita S, Kurth A, et al. Reconstructing neuronal circuitry from parallel spike trains. Nat Commun, 2019, 10: 1--13. Google Scholar

[14] Kim S, Choi S H, Lu W. Comprehensive Physical Model of Dynamic Resistive Switching in an Oxide Memristor. ACS Nano, 2014, 8: 2369-2376 CrossRef Google Scholar

[15] Kim S, Du C, Sheridan P. Experimental Demonstration of a Second-Order Memristor and Its Ability to Biorealistically Implement Synaptic Plasticity. Nano Lett, 2015, 15: 2203-2211 CrossRef ADS Google Scholar

[16] Lee S H, Moon J, Jeong Y J. ACS Appl Electron Mater, 2020, 2: 701-709 CrossRef Google Scholar

[17] Bi G, Poo M. Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type. J Neurosci, 1998, 18: 10464-10472 CrossRef Google Scholar

[18] Caporale N, Dan Y. Spike Timing-Dependent Plasticity: A Hebbian Learning Rule. Annu Rev Neurosci, 2008, 31: 25-46 CrossRef Google Scholar

[19] Diehl, P U, Cook M. Unsupervised learning of digit recognition using spike-timing-dependent plasticity. Front Comput Neurosc, 2015, 9: 99. Google Scholar

[20] Kheradpisheh S R, Ganjtabesh M, Thorpe S J. STDP-based spiking deep convolutional neural networks for object recognition. Neural Networks, 2018, 99: 56-67 CrossRef Google Scholar

[21] Gewaltig M O, Diesmann M. NEST (NEural Simulation Tool). Scholarpedia, 2007, 2: 1430 CrossRef ADS Google Scholar

[22] Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits. PLoS Biol, 2005, 3: e68 CrossRef Google Scholar

[23] Hoffmann J H O, Meyer H S, Schmitt A C. Synaptic Conductance Estimates of the Connection Between Local Inhibitor Interneurons and Pyramidal Neurons in Layer 2/3 of a Cortical Column. Cereb Cortex, 2015, 25: 4415-4429 CrossRef Google Scholar

[24] Matthews B W. Comparison of the predicted and observed secondary structure of T4 phage lysozyme. BioChim Biophysica Acta (BBA) - Protein Structure, 1975, 405: 442-451 CrossRef Google Scholar

[25] Zhu X, Wang Q, Lu W D. Memristor networks for real-time neural activity analysis. Nat Commun, 2020, 11: 2439 CrossRef ADS Google Scholar

  • Figure 1

    (Color online) Schematic of STDP-based inference methods. (a) Network graph and connectivity matrix. The type and direction of connections are depicted in the network graph as the color (excitatory: red, inhibitory: blue) and direction of the arrow. In the connectivity matrix, the color of the pixel (excitatory: red, inhibitory: blue) shows the ground truth connection from the $i$th neuron ($y$-axis) to the $j$th neuron ($x$-axis). (b) Raster plot of the spiking neural network simulated by NEST simulator. (c) Overview of STDP-based inference methods implemented in the memristor array. The second-order memristor conductance follows the STDP-based inference method given the series of simulated spike trains. (d) STDP learning rules for excitatory (upper panel) and inhibitory connections (bottom panel). (e) Estimated connectivity matrices for excitatory (upper panel) and inhibitory connections (bottom panel). (f) Final estimated connectivity matrix. Red (blue) squares correspond to the excitatory (inhibitory) connections inferred by the STDP-based inference methods.

  • Figure 2

    (Color online) Ternary-weighted neural network with LIF neurons. (a) Connectivity matrices (upper panel) with the ground truth (pixel) and the inferred connections (excitatory: red, inhibitory: blue) and the numbers of false positive and false negative cases for the excitatory and inhibitory connections (bottom panel). (b) Inference accuracy in terms of MCC. Averaged MCC is a mean of MCC for excitatory and MCC for inhibitory. (c) Averaged MCCs with respect to the simulation time length.

  • Figure 3

    (Color online) Effect of transmission delay mismatch. (a) Connectivity matrices and inference accuracy in terms of MCC with the underestimated value of transmission delay, 2 ms. (b) Connectivity matrices and inference accuracy in terms of MCC with the correct value of transmission delay, 3 ms. (c) Connectivity matrices and inference accuracy in terms of MCC with the overestimated value of transmission delay, 4 ms.

  • Figure 4

    (Color online) Analog-weighted neural network with HH neurons. (a) Connectivity matrices with the ground truth (pixel) and the inferred connections (excitatory: red square, inhibitory: blue square). (b) Inference accuracy in terms of MCC. Averaged MCC is a mean of MCC for excitatory and MCC for inhibitory. (c) Averaged MCCs with respect to the simulation time length. (d) MCC for excitatory with respect to the different minimum threshold values for excitatory weights.

  • Figure 5

    (Color online) Second-order memristor array for connectivity inference. (a) Voltage pulse configuration for eSTDP and eSTDP obtained from the circuit simulation. (b) Voltage pulse configuration for iSTDP and iSTDP obtained from the circuit simulation. (c) Connectivity matrix with the ground truth (pixel) and the inferred connections of STDP-based inference method with device model (excitatory: red, inhibitory: blue). (d) Averaged MCCs with respect to the simulation time length.

  • Table 1  

    Table 1Parameters for ternary-weighted neural network

    Neuron parameters Synapse parameters
    $\tau_m$ 20 ms Membrane time constant $w_{\rm~ex}$ 1 mV Excitatory weight
    $\tau_r$ 2 ms Refractory period $w_{\rm~in}$ $-$2 mV Inhibitory weight
    $C_m$ 1 pF Membrane capacity $\tau$ 3 ms Transmission delay
    $V_{\rm~reset}$ 0 mV Reset potential
    $V_{\rm~th}$ 20 mV Firing threshold

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