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

TL;DR

This paper investigates how partially symmetric connectivity, such as bidirectional connections, affects the dynamics of randomly connected neural networks, showing that increased symmetry slows down activity decay in both weak and chaotic regimes.

Contribution

It provides analytical and numerical analysis of the impact of partial symmetry on neural network dynamics, extending understanding beyond fully random connectivity models.

Findings

Symmetry increases autocorrelation decay time in weak-coupling regime.

Symmetry slows down intrinsic fluctuations in chaotic regime.

Partially symmetric connectivity influences network temporal dynamics.

Abstract

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.