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

arXiv: https://arxiv.org/abs/1705.05475 · HTML: https://mlsanity.com/paper/1705.05475/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2017.

## Built on by (most cited first, 6 of 6)

- [Exploitation of Image Statistics with Sparse Coding in the Case of Stereo Vision](https://mlsanity.com/paper/2101.09710/) (2021)
- [Making a Spiking Net Work: Robust brain-like unsupervised machine learning](https://mlsanity.com/paper/2208.01204/) (2022)
- [Neuromorphic-based metaheuristics: A new generation of low power, low latency and small footprint optimization algorithms](https://mlsanity.com/paper/2505.16362/) (2025)
- [Unsupervised Sparse Coding-based Spiking Neural Network for Real-time Spike Sorting](https://mlsanity.com/paper/2506.24041/) (2025)
- [Generalization Bounds of Spiking Neural Networks via Rademacher Complexity](https://mlsanity.com/paper/2605.02927/) (2026)
- [Robust PnP on a Neuromorphic Processor for Object Pose Estimation](https://mlsanity.com/paper/2607.16834/) (2026)

## Abstract (arXiv)

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.