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 hardware implementations that have demonstrated significant energy reductions as compared to conventional Artificial Neural Networks (ANNs). SNNs have been traditionally studied in the field of theoretical neuroscience through the lens of biological plausibility. In contrast, this paper aims at providing an introduction to models, learning rules, and applications of SNNs from the viewpoint of stochastic signal processing. To this end, the paper adopts discrete-time probabilistic models for networked spiking neurons, and it derives supervised and unsupervised learning rules from first principles by using variational inference. Examples and open research problems are also provided.
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