Winner-take-all (WTA) refers to the neural operation that selects a (typically small) group of neurons from a large neuron pool. It is conjectured to underlie many of the brain's fundamental computational abilities. However, not much is known about the robustness of a spike-based WTA network to the inherent randomness of the input spike trains. In this work, we consider a spike-based $k$–WTA model wherein $n$ randomly generated input spike trains compete with each other based on their underlying firing rates and $k$ winners are supposed to be selected. We slot the time evenly with each time slot of length 1 ms and model the $n$ input spike trains as $n$ independent Bernoulli processes. We analytically characterize the minimum waiting time needed so that a target minimax decision accuracy (success probability) can be reached.

We first derive an information-theoretic lower bound on the waiting time. We show that to guarantee a (minimax) decision error $≤δ$ (where $δ∈(0,1)$), the waiting time of any WTA circuit is at least
$((1-δ)log(k(n-k)+1)-1)TR,$
where $R⊆(0,1)$ is a finite set of rates and $TR$ is a difficulty parameter of a WTA task with respect to set $R$ for independent input spike trains. Additionally, $TR$ is independent of $δ$, $n$, and $k$. We then design a simple WTA circuit whose waiting time is
$Olog1δ+logk(n-k)TR,$
provided that the local memory of each output neuron is sufficiently long. It turns out that for any fixed $δ$, this decision time is order-optimal (i.e., it matches the above lower bound up to a multiplicative constant factor) in terms of its scaling in $n$, $k$, and $TR$.