The past decades have witnessed an increasing interest in spiking neural networks due to their great potential of modeling time-dependent data. Many empirical algorithms and techniques have been developed. However, theoretically, it remains unknown whether and to what extent a trained spiking neural network performs well on unseen data. This work takes one step in this direction by exploiting the minimum description length principle and thus, presents an explicit generalization bound for spiking neural networks. Further, we implement the description length of SNNs through structural stability and specify the lower and upper bounds of the maximum number of stable bifurcation solutions, which convert the challenge of qualifying structural stability in SNNs into a mathematical problem with quantitative properties.

翻译：过去几十年间，脉冲神经网络因其对时变数据建模的巨大潜力而受到日益关注。诸多经验性算法与技术已相继被开发。然而在理论层面，目前仍不清楚训练后的脉冲神经网络能否以及在多大程度上对未见数据表现良好。本研究通过引入最小描述长度原理，首次搭建了脉冲神经网络的显式泛化界。进一步，我们通过结构稳定性实现SNN的描述长度，并明确界定了稳定分岔解最大数量的上下限，从而将SNN中结构稳定性的定性判定问题转化为具有量化特性的数学问题。