  We propose a novel backpropagation algorithm for training spiking neural
networks (SNNs) that encodes information in the relative multiple spike timing
of individual neurons without single-spike restrictions. The proposed algorithm
inherits the advantages of conventional timing-based methods in that it
computes accurate gradients with respect to spike timing, which promotes ideal
temporal coding. Unlike conventional methods where each neuron fires at most
once, the proposed algorithm allows each neuron to fire multiple times. This
extension naturally improves the computational capacity of SNNs. Our SNN model
outperformed comparable SNN models and achieved as high accuracy as
non-convolutional artificial neural networks. The spike count property of our
networks was altered depending on the time constant of the postsynaptic current
and the membrane potential. Moreover, we found that there existed the optimal
time constant with the maximum test accuracy. That was not seen in conventional
SNNs with single-spike restrictions on time-to-fast-spike (TTFS) coding. This
result demonstrates the computational properties of SNNs that biologically
encode information into the multi-spike timing of individual neurons. Our code
would be publicly available.
