  In recent years, newly developed methods to train spiking neural networks
(SNNs) have rendered them as a plausible alternative to Artificial Neural
Networks (ANNs) in terms of accuracy, while at the same time being much more
energy efficient at inference and potentially at training time. However, it is
still unclear what constitutes a good initialisation for an SNN. We often use
initialisation schemes developed for ANN training which are often inadequate
and require manual tuning. In this paper, we attempt to tackle this issue by
using techniques from the ANN initialisation literature as well as
computational neuroscience results. We show that the problem of weight
initialisation for ANNs is a more nuanced problem than it is for ANNs due to
the spike-and-reset non-linearity of SNNs and the firing rate collapse problem.
We firstly identify and propose several solutions to the firing rate collapse
problem under different sets of assumptions which successfully solve the issue
by leveraging classical random walk and Wiener processes results. Secondly, we
devise a general strategy for SNN initialisation which combines variance
propagation techniques from ANNs and different methods to obtain the expected
firing rate and membrane potential distribution based on diffusion and
shot-noise approximations. Altogether, we obtain theoretical results to solve
the SNN initialisation which consider the membrane potential distribution in
the presence of a threshold. Yet, to what extent can these methods be
successfully applied to SNNs on real datasets remains an open question.
