Agreement in Spiking Neural Networks

Abstract

We study the problem of binary agreement in a spiking neural network (SNN). We show that binary agreement on n inputs can be achieved with $O\left(n\right)$ of auxiliary neurons. Our simulation results suggest that agreement can be achieved in our network in $O\left(logn\right)$ time. We then describe a subclass of SNNs with a biologically plausible property, which we call size-independence. We prove that solving a class of problems, including agreement and Winner-Take-All, in this model requires $\Omega \left(n\right)$ auxiliary neurons, which makes our agreement network size-optimal.

Keywords: binary agreement; complexity; consensus; spiking neural network; winner-take-all.