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.
P. V. Tymoshchuk and D. C. Wunsch, "Design of a K-Winners-Take-All Model with a Binary Spike Train," IEEE Transactions on Cybernetics, vol. 49, no. 8, pp. 3131 - 3140, Institute of Electrical and Electronics Engineers (IEEE), Aug 2019.
The definitive version is available at https://doi.org/10.1109/TCYB.2018.2839691
Electrical and Computer Engineering
Center for High Performance Computing Research
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)
Article - Journal
© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
01 Aug 2019