# On the low dimensional dynamics of structured random networks

arXiv: https://arxiv.org/abs/1509.02546 · HTML: https://mlsanity.com/paper/1509.02546/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Input correlations impede suppression of chaos and learning in balanced rate networks](https://mlsanity.com/paper/2201.09916/) (2022)
- [Learning unidirectional coupling using echo-state network](https://mlsanity.com/paper/2303.13562/) (2023)

## Abstract (arXiv)

Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network connectivity structure and its low dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and post-synaptic neurons through a sufficiently smooth function g of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive as a function of g. Above the critical point, although unit activation levels are chaotic, their autocorrelation functions are restricted to a low dimensional subspace. This provides a direct link between the network's structure and some of its functional characteristics. We discuss example applications of the general results to neuroscience where we derive the support of the spectrum of connectivity matrices with heterogeneous and possibly correlated degree distributions, and to ecology where we study the stability of the cascade model for food web structure.