Analysis of SpikeProp convergence with alternative spike response functions

SpikeProp is a supervised learning algorithm for spiking neural networks analogous to backpropagation. Like backpropagation, it may fail to converge for particular networks, parameters and datasets. However there are several behaviours and additional failure modes unique to SpikeProp which have not been explicitly outlined in the literature. These factors hinder the adoption of SpikeProp for general machine learning use. In this paper we examine the mathematics of SpikeProp in detail and identify the various causes of failure therein. The analysis implies that applying certain constraints on parameters like initial weights can improve the rates of convergence. It also suggests that alternative spike response functions could improve the learning rate and reduce the number of convergence failures. We tested two alternative functions and found these predictions to be true.