Design of a K-Winners-Take-All Model with a Binary Spike Train


A continuous-time K-winners-take-all (KWTA) neural model that can identify the largest K of N inputs, where command signal 1 łe K < N is described. The model is given by a differential equation where the spike train is a sum of delta functions. A functional block-diagram of the model includes N feed-forward hard-limiting neurons and one feedback neuron, used to handle input dynamics. The existence and uniqueness of the model steady states are analyzed, the convergence analysis of the state variable trajectories to the KWTA operation is proven, the convergence time and number of spikes required are derived, as well as the processing of time-varying inputs and perturbations of the model nonlinearities are analyzed. The main advantage of the model is that it is not subject to the intrinsic convergence of speed limitations of comparable designs. The model also has an arbitrary finite resolution determined by a given parameter, low complexity, and initial condition independence. Applications of the model for parallel sorting and parallel rank-order filtering are presented. Theoretical results are derived and illustrated with computer-simulated examples that demonstrate the model's performance.


Electrical and Computer Engineering

Research Center/Lab(s)

Center for High Performance Computing Research


This work was supported in part by the Fulbright Program Grant, in part by the National Science Foundation, in part by the Missouri University of Science and Technology Intelligent Systems Center, and in part by the Mary K. Finley Missouri Endowment.

Keywords and Phrases

Analytical models; Binary sequences; Computer hardware; Continuous time systems; Control nonlinearities; Delta functions; Differential equations; Digital control systems; Discrete time control systems; Filtration; Mathematical models; Nonlinear equations; Sorting; Trajectories; Computational model; Convergence; Discrete - time systems; Existence and uniqueness; Functional block diagrams; KWinners-Take-All (kWTA); Neural networks (NNS); Rank-order filtering; Neural networks; Artificial neural networks; Computational modeling; Filtering; Hardware

International Standard Serial Number (ISSN)

2168-2267; 2168-2275

Document Type

Article - Journal

Document Version


File Type





© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Aug 2019