A novel competition model for dynamic winner-take-all

Abstract

Winner-Take-All (WTA) is a foundational principle in modelling competitive dynamics, yet traditional neural network approaches to solving the WTA problem are often hampered by high computational complexity. This paper addresses this challenge by introducing a novel and computationally efficient dynamic competition model that circumvents the complexity of conventional constrained quadratic programming (QP) solvers. First, we reformulate the classical constrained WTA problem into an equivalent unconstrained optimisation problem. This is achieved by innovatively employing the Softmax function, which inherently satisfies the summation-to-one and non-negativity constraints. Subsequently, a simple yet powerful dynamic neural network is developed to solve this unconstrained problem, accompanied by rigorous theoretical proofs of its stability, global convergence, and state boundedness. Numerical experiments, conducted with both static and dynamic inputs, validate the model's efficacy. The results highlight the model's exceptional robustness, maintaining stable and accurate WTA selection even in the presence of significant Gaussian white noise, demonstrating a marked improvement over existing methods. The proposed framework is also readily adaptable to a broad range of WTA-related problems sharing similar structural characteristics, thereby offering substantial potential for diverse real-time decision-making applications.