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

TL;DR

This paper presents a mathematical model of a spiking neural network that reliably solves sparse coding problems, providing the first rigorous convergence proof for such networks in feature extraction tasks.

Contribution

It introduces a novel SNN model for sparse coding and proves its convergence, establishing theoretical guarantees for its computational capabilities.

Findings

Proves that the SNN solves sparse coding under certain assumptions

Provides convergence theory for the SNN model

Demonstrates the potential of SNNs for reliable feature extraction

Abstract

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.