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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 [Formula: see text]where   R  ⊆  (  0  ,  1  )   is a finite set of rates and   T  R   is a difficulty parameter of a WTA task with respect to set  R  for independent input spike trains. Additionally,   T  R   is independent of  δ  ,  n  , and  k  . We then design a simple WTA circuit whose waiting time is [Formula: see text]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   T  R   .

Spike-Based Winner-Take-All Computation: Fundamental Limits and Order-Optimal Circuits