What question did this study set out to answer?

The aim is to develop a k-WTA neural network incorporating an inertia term to improve convergence properties.

April 23, 2026

Distributed Inertial k -Winners-Take-All Neural Network Based on Quadratic Optimization Problems

XBXiaohan BoChina University of Mining and Technology SZSong Zhu ZZZhen Zhang

Key Points

The aim is to develop a k-WTA neural network incorporating an inertia term to improve convergence properties.
Proposes a k-WTA network based on a quadratic programming model with an inertia term.
Uses a cocoercive operator to establish convergence proofs.
Tests the network through simulations under various conditions.
Demonstrates asymptotic and exponential convergence to the k-WTA solution.
Reveals improved performance compared to traditional methods.
Confirms the efficacy of the proposed network via simulations.

Abstract

The k -winners-take-all (k -WTA) problem is to find the k largest inputs from n inputs. Based on the existing quadratic programming model, this article proposes a new k -WTA network with an inertia term. The inertial term is designed to modulate the instantaneous behavior of the trajectory and use historical information to accelerate convergence. Traditional Lyapunov methods are inapplicable due to the inertia term. To overcome this, a cocoercive operator is used to prove asymptotic and exponential convergence to the k -WTA solution from any initial state. Additionally, the article investigates distributed k -WTA networks with restrictive equality constraints. Finally, simulations are used to confirm the efficacy of the suggested k -WTA network.

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