DOI: 10.1101/475319Nov 20, 2018Paper

# Weight statistics controls dynamics in recurrent neural networks

BioRxiv : the Preprint Server for Biology
Patrick KraussClaus Metzner

## 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 $w\_{ij}$ between the individual neurons. However, little is known to which extent network dynamics is tunable on a more coarse-grained level by the {\em statistical} features of the weight matrix. In this work, we investigate the dynamical impact of three statistical parameters: {\em density} (the fraction of non-zero connections), {\em balance} (the ratio of excitatory to inhibitory connections), and {\em symmetry} (the fraction of neuron pairs with $w\_{ij}=w_{ji}$). 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 'ed...Continue Reading

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