The training of multilayer spiking neural networks (SNNs) using the error backpropagation algorithm has made significant progress in recent years. Among the various training schemes, the error backpropagation method that directly uses the firing time of neurons has attracted considerable attention because it can realize ideal temporal coding. This method uses time-to-first spike (TTFS) coding, in which each neuron fires at most once, and this restriction on the number of firings enables information to be processed at a very low firing frequency. This low firing frequency increases the energy efficiency of information processing in SNNs, which is important not only because of its similarity with information processing in the brain, but also from an engineering point of view. However, only an upper limit has been provided for TTFS-coded SNNs, and the information-processing capability of SNNs at lower firing frequencies has not been fully investigated. In this paper, we propose two spike timing-based sparse-firing (SSR) regularization methods to further reduce the firing frequency of TTFS-coded SNNs. The first is the membrane potential-aware SSR (M-SSR) method, which has been derived as an extreme form of the loss function of the membrane potential value. The second is the firing condition-aware SSR (F-SSR) method, which is a regularization function obtained from the firing conditions. Both methods are characterized by the fact that they only require information about the firing timing and associated weights. The effects of these regularization methods were investigated on the MNIST, Fashion-MNIST, and CIFAR-10 datasets using multilayer perceptron networks and convolutional neural network structures.

本文提出了两种基于时间的稀疏发放（SSR）正则化方法，用于进一步降低TTFS编码的SNN的发放频率，并通过使用多层感知器网络和卷积神经网络结构在MNIST、Fashion-Mnist和CIFAR-10数据集上对这些正则化方法的效果进行了研究。

基于稀疏触发规则的时间至第一触发编码的脉冲神经网络正则化方法