  Spiking neural networks (SNNs) are distributed trainable systems whose
computing elements, or neurons, are characterized by internal analog dynamics
and by digital and sparse synaptic communications. The sparsity of the synaptic
spiking inputs and the corresponding event-driven nature of neural processing
can be leveraged by energy-efficient hardware implementations, which can offer
significant energy reductions as compared to conventional artificial neural
networks (ANNs). The design of training algorithms lags behind the hardware
implementations. Most existing training algorithms for SNNs have been designed
either for biological plausibility or through conversion from pretrained ANNs
via rate encoding. This article provides an introduction to SNNs by focusing on
a probabilistic signal processing methodology that enables the direct
derivation of learning rules by leveraging the unique time-encoding
capabilities of SNNs. We adopt discrete-time probabilistic models for networked
spiking neurons and derive supervised and unsupervised learning rules from
first principles via variational inference. Examples and open research problems
are also provided.
