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

04/21/2019
by   Lili Su, et al.
0

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 statistics, 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. The Bernoulli process is a good approximation of the popular Poisson process but is more biologically relevant as it takes the refractory periods into account. Due to the randomness in the input spike trains, no circuits can guarantee to successfully select the correct winners in finite time. We focus on analytically characterizing the minimal amount of time needed so that a target minimax decision accuracy (success probability) can be reached. We first derive an information-theoretic lower bound on the decision time. We show that to have a (minimax) decision error <δ (where δ∈ (0,1)), the computation time of any WTA circuit is at least ((1-δ) (k(n -k)+1) -1)T_R, where T_R is a difficulty parameter of a WTA task that is independent of δ, n, and k. We then design a simple WTA circuit whose decision time is O( 1/δ+ k(n-k))T_R). It turns out that for any fixed δ∈ (0,1), this decision time is order-optimal in terms of its scaling in n, k, and T_R.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/30/2009

The Computational Structure of Spike Trains

Neurons perform computations, and convey the results of those computatio...
research
06/08/2015

Microscopic approach of a time elapsed neural model

The spike trains are the main components of the information processing i...
research
10/26/2016

Bayesian latent structure discovery from multi-neuron recordings

Neural circuits contain heterogeneous groups of neurons that differ in t...
research
09/13/2012

A new class of metrics for spike trains

The distance between a pair of spike trains, quantifying the differences...
research
12/14/2016

Stable Memory Allocation in the Hippocampus: Fundamental Limits and Neural Realization

It is believed that hippocampus functions as a memory allocator in brain...
research
04/18/2015

Time Resolution Dependence of Information Measures for Spiking Neurons: Atoms, Scaling, and Universality

The mutual information between stimulus and spike-train response is comm...
research
03/20/2019

A study of dependency features of spike trains through copulas

Simultaneous recordings from many neurons hide important information and...

Please sign up or login with your details

Forgot password? Click here to reset