Linear Constraints Learning for Spiking Neurons

Spiking Neural Networks (SNNs) (Gerstner and Kistler, 2002) have been shown to be computationally more powerful compared to traditional Artificial Neural Networks (Maass, 1997), even on the level of single neurons with single output spikes (Rubin et al., 2010). Though the computational power of SNNs has been demonstrated, practical applications are limited by their complexity. Large models with many parameters and high precision requirements are expensive to simulate and train, thus cannot meet the demands of real-time applications (Querlioz et al., 2013; Diehl and Cook, 2015; Balaji et al., 2020). While there are recent efforts (Yu et al., 2013b; Xu et al., 2018; Yu et al., 2019; Cheng et al., 2020; Li and Yu, 2020) to design smaller architectures which maintain competitive accuracy, it remains a significant challenge to analytically determine what SNN architecture, connectivity, or size are sufficient to enable robust capacity, even on elementary problems. In order to better understand the computational properties of SNNs, more efficient learning methods are required to enable further explorations of the capabilities of individual nodes in a network.