Influence of Imperfections on the Operational Correctness of DNN- $k$ WTA Model

The dual neural network (DNN)-based $k$ -winner-take-all (WTA) model is able to identify the $k$ largest numbers from its $m$ input numbers. When there are imperfections, such as non-ideal step function and Gaussian input noise, in the realization, the model may not output the correct result. This brief analyzes the influence of the imperfections on the operational correctness of the model. Due to the imperfections, it is not efficient to use the original DNN- $k$ WTA dynamics for analyzing the influence. In this regard, this brief first derives an equivalent model to describe the dynamics of the model under the imperfections. From the equivalent model, we derive a sufficient condition for which the model outputs the correct result. Thus, we apply the sufficient condition to design an efficiently estimation method for the probability of the model outputting the correct result. Furthermore, for the inputs with uniform distribution, a closed form expression for the probability value is derived. Finally, we extend our analysis for handling non-Gaussian input noise. Simulation results are provided to validate our theoretical results.