Effect of Logistic Activation Function and Multiplicative Input Noise on DNN-kWTA Model

Abstract

The dual neural network-based (DNN) k-winner-take-all (kWTA) model is one of the simplest analog neural network models for the kWTA process. This paper analyzes the behaviors of the DNN-kWTA model under these two imperfections. The two imperfections are, (1) the activation function of IO neurons is a logistic function rather than an ideal step function, and (2) there are multiplicative Gaussian noise in the inputs. With the two imperfections, the model may not be able to perform correctly. Hence it is important to estimate the probability of the imperfection model performing correctly. We first derive the equivalent activation function of IO neurons under the two imperfections. Next, we derive the sufficient conditions for the imperfect model to operate correctly. These results enable us to efficiently estimate the probability of the imperfect model generating correct outputs. Additionally, we derive a bound on the probability that the imperfect model generates the desired outcomes for inputs with a uniform distribution. Finally, we discuss how to generalize our findings to handle non-Gaussian multiplicative input noise.