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In a spiking neural network (SNN), individual neurons operate autonomouslyand only communicate with other neurons sparingly and asynchronously via spikesignals. These characteristics render a massively parallel hardwareimplementation of SNN a potentially powerful computer, albeit a non von Neumannone. But can one guarantee that a SNN computer solves some important problemsreliably? In this paper, we formulate a mathematical model of one SNN that canbe configured for a sparse coding problem for feature extraction. With amoderate but well-defined assumption, we prove that the SNN indeed solvessparse coding. To the best of our knowledge, this is the first rigorous resultof this kind.

Sparse Coding by Spiking Neural Networks: Convergence Theory and Computational Results