On RNN-Based $k$-WTA Models With Time-Dependent Inputs
Mei Liu, Mingsheng Shang
Abstract
Dear editor, This letter identifies two weaknesses of state-of-the-art k-winners-take-all (k-WTA) models based on recurrent neural networks (RNNs) when considering time-dependent inputs, i.e., the lagging error and the infeasibility in finite-time convergence based on the Lipschitz continuity. Specifically, in the case of time-dependent inputs, theoretical analyses and simulations are conducted to illustrate that the lagging error is inevitable for the dual network model based on RNN. Then, a new k-WTA model aided with RNN is constructed in this letter with the ability of eliminating the lagging error. Theoretical analyses demonstrate that the finite-time convergence of the existing k-WT A models based on the Lipschitz continuity with time-dependent inputs cannot be achieved. Besides, this letter offers a feasible solution to perform k-WTA operations with desired convergent speed efficiently and precisely.