# Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

arXiv: https://arxiv.org/abs/1707.08337 · HTML: https://mlsanity.com/paper/1707.08337/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2017.

## Built on by (most cited first, 5 of 5)

- [Unified field theoretical approach to deep and recurrent neuronal networks](https://mlsanity.com/paper/2112.05589/) (2021)
- [Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings](https://mlsanity.com/paper/2305.08459/) (2023)
- [Spectrum of non-Hermitian deep-Hebbian neural networks](https://mlsanity.com/paper/2208.11411/) (2022)
- [Neuronal correlations shape the scaling behavior of memory capacity and nonlinear computational capability of reservoir recurrent neural networks](https://mlsanity.com/paper/2504.19657/) (2025)
- [Identifying Connectivity Distributions from Neural Dynamics Using Flows](https://mlsanity.com/paper/2603.26506/) (2026)

## Abstract (arXiv)

Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigated the effects of partially symmetric connectivity on dynamics in networks of rate units. We considered the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we computed analytically for an arbitrary degree of symmetry the auto-correlation of network activity in presence of external noise. In the chaotic regime, we performed simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.