  A deep neural network for classification tasks is essentially consist of two
components: feature extractors and function approximators. They usually work as
an integrated whole, however, improvements on any components can promote the
performance of the whole algorithm. This paper focus on designing a new
function approximator. Conventionally, to build a function approximator, one
usually uses the method based on the nonlinear activation function or the
nonlinear kernel function and yields classical networks such as the
feed-forward neural network (MLP) and the radial basis function network (RBF).
In this paper, a new function approximator that is effective and efficient is
proposed. Instead of designing new activation functions or kernel functions,
the new proposed network uses the fractional form. For the sake of convenience,
we name the network the ratio net. We compare the effectiveness and efficiency
of the ratio net and that of the RBF and the MLP with various kinds of
activation functions in the classification task on the mnist database of
handwritten digits and the Internet Movie Database (IMDb) which is a binary
sentiment analysis dataset. It shows that, in most cases, the ratio net
converges faster and outperforms both the MLP and the RBF.
