  In a spiking neural network (SNN), individual neurons operate autonomously
and only communicate with other neurons sparingly and asynchronously via spike
signals. These characteristics render a massively parallel hardware
implementation of SNN a potentially powerful computer, albeit a non von Neumann
one. But can one guarantee that a SNN computer solves some important problems
reliably? In this paper, we formulate a mathematical model of one SNN that can
be configured for a sparse coding problem for feature extraction. With a
moderate but well-defined assumption, we prove that the SNN indeed solves
sparse coding. To the best of our knowledge, this is the first rigorous result
of this kind.
