  Spiking Neural Networks (SNNs) capture some of the efficiency of biological
brains for inference and learning via the dynamic, online, event-driven
processing of binary time series. Most existing learning algorithms for SNNs
are based on deterministic neuronal models, such as leaky integrate-and-fire,
and rely on heuristic approximations of backpropagation through time that
enforce constraints such as locality. In contrast, probabilistic SNN models can
be trained directly via principled online, local, update rules that have proven
to be particularly effective for resource-constrained systems. This paper
investigates another advantage of probabilistic SNNs, namely their capacity to
generate independent outputs when queried over the same input. It is shown that
the multiple generated output samples can be used during inference to robustify
decisions and to quantify uncertainty -- a feature that deterministic SNN
models cannot provide. Furthermore, they can be leveraged for training in order
to obtain more accurate statistical estimates of the log-loss training
criterion, as well as of its gradient. Specifically, this paper introduces an
online learning rule based on generalized expectation-maximization (GEM) that
follows a three-factor form with global learning signals and is referred to as
GEM-SNN. Experimental results on structured output memorization and
classification on a standard neuromorphic data set demonstrate significant
improvements in terms of log-likelihood, accuracy, and calibration when
increasing the number of samples used for inference and training.
