Exact Error Backpropagation Through Spikes for Precise Training of Spiking Neural Networks

Event-based simulations of Spiking Neural Networks (SNNs) are fast and accurate. However, they are rarely used in the context of event-based gradient descent because their implementations on GPUs are difficult. Discretization with the forward Euler method is instead often used with gradient descent techniques but has the disadvantage of being computationally expensive. Moreover, the lack of precision of discretized simulations can create mismatches between the simulated models and analog neuromorphic hardware. In this work, we propose a new exact error-backpropagation through spikes method for SNNs, extending Fast \& Deep to multiple spikes per neuron. We show that our method can be efficiently implemented on GPUs in a fully event-based manner, making it fast to compute and precise enough for analog neuromorphic hardware. Compared to the original Fast \& Deep and the current state-of-the-art event-based gradient-descent algorithms, we demonstrate increased performance on several benchmark datasets with both feedforward and convolutional SNNs. In particular, we show that multi-spike SNNs can have advantages over single-spike networks in terms of convergence, sparsity, classification latency and sensitivity to the dead neuron problem.