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.
© 2019 Massachusetts Institute of Technology
2019
Massachusetts Institute of Technology
You do not currently have access to this content.