Weight statistics controls dynamics in recurrent neural networks

Abstract

Recurrent neural networks are complex non-linear systems, capable of ongoing activity in the absence of driving inputs. The dynamical properties of these systems, in particular their long-time attractor states, are determined on the microscopic level by the connection strengths wij between the individual neurons. However, little is known to which extent network dynamics is tunable on a more coarse-grained level by the statistical features of the weight matrix. In this work, we investigate the dynamical impact of three statistical parameters: density (the fraction of non-zero connections), balance (the ratio of excitatory to inhibitory connections), and symmetry (the fraction of neuron pairs with wij = wji). By computing a phase diagram of network dynamics, we find that balance is the essential control parameter: Its gradual increase from negative to positive values drives the system from oscillatory behavior into a chaotic regime, and eventually into stationary fix points. Only directly at the border of the chaotic regime do the neural networks display rich but regular dynamics, thus enabling actual information processing. These results suggest that the brain, too, is fine-tuned to the edge of chaos by assuring a proper balance between excitatory and inhibitory neural connections.\n\nAuthor summaryComputations in the brain need to be both reproducible and sensitive to changing input from the environment. It has been shown that recurrent neural networks can meet these simultaneous requirements only in a particular dynamical regime, called the edge of chaos in non-linear systems theory. Here, we demonstrate that recurrent neural networks can be easily tuned to this critical regime of optimal information processing by assuring a proper ratio of excitatory and inhibitory connections between the neurons. This result is in line with several micro-anatomical studies of the cortex, which frequently confirm that the excitatory-inhibitory balance is strictly conserved in the cortex. Furthermore, it turns out that neural dynamics is largely independent from the total density of connections, a feature that explains how the brain remains functional during periods of growth or decay. Finally, we find that the existence of too many symmetric connections is detrimental for the above mentioned critical dynamical regime, but maybe in turn useful for pattern completion tasks.