Properties and performance of imperfect dual neural network-based k WTA networks

The dual neural network (DNN)-based k-winner-take-all (k WTA) model is an effective approach for finding the k largest inputs from n inputs. Its major assumption is that the threshold logic units (TLUs) can be implemented in a perfect way. However, when differential bipolar pairs are used for implementing TLUs, the transfer function of TLUs is a logistic function. This brief studies the properties of the DNN- k WTA model under this imperfect situation. We prove that, given any initial state, the network settles down at the unique equilibrium point. Besides, the energy function of the model is revealed. Based on the energy function, we propose an efficient method to study the model performance when the inputs are with continuous distribution functions. Furthermore, for uniformly distributed inputs, we derive a formula to estimate the probability that the model produces the correct outputs. Finally, for the case that the minimum separation Δ_min of the inputs is given, we prove that if the gain of the activation function is greater than 1/4 Δ_min max ln 2n, 2 In 1-ε/ε), then the network can produce the correct outputs with winner outputs greater than 1-ε and loser outputs less than ε, where ε is the threshold less than 0.5.