The maximum points-based supervised learning rule for spiking neural networks

Abstract

As the third generation of neural networks, Spiking Neural Networks (SNNs) have made great success in pattern recognition fields. However, the existing training methods for SNNs are not efficient enough because of the temporal encoding mechanism. To improve the training efficiency of the supervised SNNs and keep the useful temporal information, the Maximum Points-based Supervised Learning Rule (MPSLR) is proposed in this paper. Three training strategies are adopted in MPSLR to improve the learning performance. Firstly, only the target points and maximum voltage points are trained. By theoretical analyses, we find that the maximum points are effective for the voltage controlling of the non-target points, and the analytic solutions for all maximum voltage points are parallelly obtainable. This improves the training efficiency significantly by avoiding the successive voltage detecting. Secondly, the weight modification for each presynaptic neuron is normalized by a rate function to resizing the output scale. Thirdly, the spiking rates accumulated in a time window are utilized to involve more useful knowledge. Extensive experiments on both synthetic data and four real-world UCI datasets demonstrate that our algorithm achieves significantly better performance and higher efficiency than traditional methods in various situations, including different multi-spike rates and time lengths. Besides, it is more stable to hyper-parameter variations.

Appendices

Appendix

A error measures

To evaluate the training accuracy, the correlation-based method of C (Schreiber et al. 2003) is employed in our simulations to measure the similarity between the target and actual output spike trains. It is calculated by

$$\begin{aligned} C = \frac{\varvec{v_{d}} \varvec{\cdot } \varvec{v_{o}}}{|\varvec{v_{d}}||\varvec{v_{o}}|} \end{aligned}$$

(39)

in which $\varvec{v_{d}}$ and $\varvec{v_{o}}$ are vectors obtained by the convolution of the target and actual output spike trains using a Gaussian filter:

$$\begin{aligned} g_i(t)=\sum _{m=1}^{N_i}G_{\sigma /\sqrt{2}}(t-t_m^i) \end{aligned}$$

(40)

$G_{\sigma /\sqrt{2}}(t)=\exp [-t^2/\sigma ^2]$ is a Gaussian kernel. $\varvec{v_d\cdot v_o}$ is the inner product, and $| \varvec{v_d} |$, $| \varvec{v_o} |$ are the Euclidean norms of $\varvec{v_d}$ and $\varvec{v_o}$, respectively. The standard deviations at the target and the actual output time are set to $\sigma _d$=$\sigma _o$=1 in our study.