Designing spiking neural networks for robust and reconfigurable computation

Networks of spiking neurons constitute analog systems capable of effective and resilient computing. Recent work has shown that networks of symmetrically connected inhibitory neurons may implement basic computations such that they are resilient to system disruption. For instance, if the functionality of one neuron is lost (e.g., the neuron, along with its connections, is removed), the system may be robustly reconfigured by adapting only one global system parameter. How to effectively adapt network parameters to robustly perform a given computation is still unclear. Here, we present an analytical approach to derive such parameters. Specifically, we analyze k-winners-takes-all (k-WTA) computations, basic computational tasks of identifying the k largest signals from a total of N input signals from which one can construct any computation. We identify and characterize different dynamical regimes and provide analytical expressions for the transitions between different numbers k of winners as a function of both input and network parameters. Our results thereby provide analytical insights about the dynamics underlying k-winner-takes-all functionality as well as an effective way of designing spiking neural network computing systems implementing disruption-resilient dynamics.