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Networks of randomly connected neurons are among the most popular models intheoretical neuroscience. The connectivity between neurons in the cortex ishowever not fully random, the simplest and most prominent deviation fromrandomness found in experimental data being the overrepresentation ofbidirectional connections among pyramidal cells. Using numerical and analyticalmethods, we investigated the effects of partially symmetric connectivity ondynamics in networks of rate units. We considered the two dynamical regimesexhibited by random neural networks: the weak-coupling regime, where the firingactivity decays to a single fixed point unless the network is stimulated, andthe strong-coupling or chaotic regime, characterized by internally generatedfluctuating firing rates. In the weak-coupling regime, we computed analyticallyfor an arbitrary degree of symmetry the auto-correlation of network activity inpresence of external noise. In the chaotic regime, we performed simulations todetermine the timescale of the intrinsic fluctuations. In both cases, symmetryincreases the characteristic asymptotic decay time of the autocorrelationfunction and therefore slows down the dynamics in the network.

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