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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

Abstract


Acknowledgment

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.


References

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  • 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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