On the Analytical Solution of Firing Time for SpikeProp

Error backpropagation in networks of spiking neurons (SpikeProp) shows promise for the supervised learning of temporal patterns. However, its widespread use is hindered by its computational load and occasional convergence failures. In this letter, we show that the neuronal firing time equation at the core of SpikeProp can be solved analytically using the Lambert W function, offering a marked reduction in execution time over the step-based method used in the literature. Applying this analytical method to SpikeProp, we find that training time per epoch can be reduced by 12% to 56% under different experimental conditions. Finally, this work opens the way for further investigations of SpikeProp's convergence behavior.