Stability of Spiking Neural Network in Binary Classification

We prove that the binary spiking classifiers generated by random wide deep Spiking Neural Networks (SNNs) with sign activation function are biased towards simple functions. For any given static input, the average Hamming distance of the closest input with a different classification is at least \sqrt{n}/log n, where n is the dimension of the input. Therefore, our result identifies a fundamental qualitative difference between a typical binary classifier generated by a random deep spiking neural network and a uniformly random binary classifier. In general, the probability distribution of the functions generated by random deep neural networks is a good choice for the prior probability distribution in the PAC-Bayesian generalization bounds.
Therefore, our results constitute a fundamental step forward in the characterisation of this distribution, contributing to the understanding of the generalization properties of SNNs.