Local connectivity balance shapes population dynamics in random recurrent networks

Abstract

Disordered dynamical systems comprising many interacting units, from ecological communities to neural circuits, are ubiquitous, and understanding how connectivity shapes their collective behavior is a central theoretical challenge. One long-recognized feature of neural circuits is local connectivity balance, in which the excitatory and inhibitory weights converging onto each unit approximately cancel. Although local connectivity balance has been proposed to serve functions such as gating incoming signals, its effect on collective network dynamics remains unclear. Here we analytically study randomly connected recurrent networks with varying degrees of local connectivity balance. We show that this balance leaves the connectivity spectrum unchanged yet drastically reshapes the dynamics in a manner that depends critically on the single-unit nonlinearity. Local balance suppresses unbounded growth of the network state and stabilizes network dynamics when the activation function scales linearly or faster, whereas it drives the network into chaos when the activation function is sub-linear or saturating. Importantly, these effects vanish for odd activation functions, which are commonly assumed in previous work. We further find that, for saturating nonlinearities, the effective dimension of the dynamics varies nonmonotonically with the degree of balance. We show that all these phenomena arise from a unifying mechanism: the suppression of a self-generated feedback input by local connectivity balance. Our results identify local connectivity balance as a previously overlooked control parameter for collective dynamics in realistic disordered networks.