Input-driven circuit reconfiguration in critical recurrent neural networks

Changing a circuit dynamically, without actually changing the hardware itself, is called reconfiguration, and is of great importance due to its manifold technological applications. Circuit reconfiguration appears to be a feature of the cerebral cortex, so understanding the dynamical principles underlying self-reconfiguration may prove of import to elucidate brain function. We present a very simple example of dynamical reconfiguration: a family of networks whose signal pathways can be switched on the fly, only through use of their inputs, with no changes to their synaptic weights. These are single-layer convolutional recurrent network with local unitary synaptic weights and a smooth sigmoidal activation function. We generate traveling waves using the high spatiotemporal frequencies of the input, and we use the low spatiotemporal frequencies of the input to landscape the ongoing activity, channeling said traveling waves through an input-specified spatial pattern. This mechanism uses inherent properties of marginally stable, dynamically critical systems, which are a direct consequence of their unitary convolution kernels: every network in the family can do this. We show these networks solve the classical connectedness detection problem, by allowing signal propagation only along the regions to be evaluated for connectedness, and forbidding it elsewhere.