%ASu, Lili%AChang, Chia-Jung%ALynch, Nancy%BJournal Name: Neural computation; Journal Volume: 31; Journal Issue: 12
%D2019%I
%JJournal Name: Neural computation; Journal Volume: 31; Journal Issue: 12
%K
%MOSTI ID: 10161820
%PMedium: X
%TSpike-Based Winner-Take-All Computation: Fundamental Limits and Order-Optimal Circuits
%XWinner-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 then 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(whereδ∈(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 2524L. Su, C.-J. Chang, and N. Lynch O((log(1δ)+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 inn,k, and TR.
%0Journal Article