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.
@article{arxiv.1705.05475,
title = {Sparse Coding by Spiking Neural Networks: Convergence Theory and Computational Results},
author = {Ping Tak Peter Tang and Tsung-Han Lin and Mike Davies},
journal= {arXiv preprint arXiv:1705.05475},
year = {2017}
}