Abstract

Hidden nodes have a key role in the information processing of feed-forward neural networks in which inputs are processed through a series of weighted sums and nonlinear activation functions. In order to understand the role of hidden nodes, we must analyze the effect of the nonlinear activation functions on the weighted sums to hidden nodes. In this paper, we focus on the effect of nonlinear functions in a viewpoint of information theory. Under the assumption that the nonlinear activation function can be approximated piece-wise linearly, we prove that the entropy of weighted sums to hidden nodes decreases after piece-wise linear functions. Therefore, we argue that the nonlinear activation function decreases the uncertainty among hidden nodes. Furthermore, the more the hidden nodes are saturated, the more the entropy of hidden nodes decreases. Based on this result, we can say that, after successful training of feed-forward neural networks, hidden nodes tend not to be in linear regions but to be in saturated regions of activation function with the effect of uncertainty reduction.