Back-propagation in spiking neural networks

Back-propagation is a powerful supervised learning algorithm in artificial neural networks, because it solves the credit assignment problem (essentially: what should the hidden layers do?). This algorithm has led to the deep learning revolution. But unfortunately, back-propagation cannot be used directly in spiking neural networks (SNN). Indeed, it requires differentiable activation functions, whereas spikes are all-or-none events which cause discontinuities. Here we present two strategies to overcome this problem. The first one is to use a so-called 'surrogate gradient', that is to approximate the derivative of the threshold function with the derivative of a sigmoid. We will present some applications of this method for time series processing (audio, internet traffic, EEG). The second one concerns a specific class of SNNs, which process static inputs using latency coding with at most one spike per neuron. Using approximations, we derived a latency-based back-propagation rule for this sort of networks, called S4NN, and applied it to image classification.