# Balanced networks of spiking neurons with spatially dependent recurrent connections

arXiv: https://arxiv.org/abs/1308.6014 · HTML: https://mlsanity.com/paper/1308.6014/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2013.

## Built on by (most cited first, 1 of 1)

- [SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2312.17216/) (2023)

## Abstract (arXiv)

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the spatial separation between neurons. In the continuum limit we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. For finite size networks we investigate the pattern forming dynamics arising when balanced conditions are not satisfied. The spatiotemporal dynamics of balanced networks offer new challenges in the statistical mechanics of complex systems.