  While backpropagation (BP) has been applied to spiking neural networks (SNNs)
achieving encouraging results, a key challenge involved is to backpropagate a
continuous-valued loss over layers of spiking neurons exhibiting discontinuous
all-or-none firing activities. Existing methods deal with this difficulty by
introducing compromises that come with their own limitations, leading to
potential performance degradation. We propose a novel BP-like method, called
neighborhood aggregation (NA), which computes accurate error gradients guiding
weight updates that may lead to discontinuous modifications of firing
activities. NA achieves this goal by aggregating finite differences of the loss
over multiple perturbed membrane potential waveforms in the neighborhood of the
present membrane potential of each neuron while utilizing a new membrane
potential distance function. Our experiments show that the proposed NA
algorithm delivers the state-of-the-art performance for SNN training on several
datasets.
