Before revision:  For the first time, by leveraging methods from optimal control theory, we are able to backpropagate errors through spike discontinuities without approximationsor smoothing operations. As errors are backpropagated in an event-based manner ( at spike times ), EventProp requires storing state variables only at these times, providing favorable memory requirements.
After revision:  For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times ), EventProp requires storing state variables only at these times, providing favorable memory requirements.