A continuous-time ${K}$ -winners-take-all (KWTA) neural model that can identify the largest ${K}$ of ${N}$ inputs, where command signal $1 \le {K} < {N}$ 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.

中文翻译：

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二元秒杀列车的K赢家通吃模型设计

连续时间 $ {K} $ 赢家通吃（KWTA）神经模型可以识别最大的 $ {K} $ 的 $ {N} $ 输入，命令信号 $ 1 \ le {K} <{N} $ 描述。该模型由微分方程式给出，其中峰值序列是增量函数的总和。该模型的功能框图包括 $ {N} $ 前馈硬限制神经元和一个反馈神经元，用于处理输入动力学。分析了模型稳态的存在性和唯一性，证明了状态变量轨迹到KWTA操作的收敛性分析，得出了收敛时间和所需尖峰数，以及时变输入和扰动的处理分析了模型的非线性。该模型的主要优点是它不受可比设计速度限制的内在收敛。该模型还具有由给定参数确定的任意有限分辨率，低复杂度和初始条件独立性。介绍了该模型在并行排序和并行排序过滤中的应用。