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Spiking Neural Networks (SNNs) are biologically-inspired models that arecapable of processing information in streams of action potentials. However,simulating and training SNNs is computationally expensive due to the need tosolve large systems of coupled differential equations. In this paper, weintroduce SparseProp, a novel event-based algorithm for simulating and trainingsparse SNNs. Our algorithm reduces the computational cost of both the forwardand backward pass operations from O(N) to O(log(N)) per network spike, therebyenabling numerically exact simulations of large spiking networks and theirefficient training using backpropagation through time. By leveraging thesparsity of the network, SparseProp eliminates the need to iterate through allneurons at each spike, employing efficient state updates instead. Wedemonstrate the efficacy of SparseProp across several classicalintegrate-and-fire neuron models, including a simulation of a sparse SNN withone million LIF neurons. This results in a speed-up exceeding four orders ofmagnitude relative to previous event-based implementations. Our work providesan efficient and exact solution for training large-scale spiking neuralnetworks and opens up new possibilities for building more sophisticatedbrain-inspired models.

SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks