Evaluation of Dataflow through layers of Deep Neural Networks in Classification and Regression Problems

This paper introduces two straightforward, effective indices to evaluate the input data and the data flowing through layers of a feedforward deep neural network. For classification problems, the separation rate of target labels in the space of dataflow is explained as a key factor indicating the performance of designed layers in improving the generalization of the network. According to the explained concept, a shapeless distance-based evaluation index is proposed. Similarly, for regression problems, the smoothness rate of target outputs in the space of dataflow is explained as a key factor indicating the performance of designed layers in improving the generalization of the network. According to the explained smoothness concept, a shapeless distance-based smoothness index is proposed for regression problems. To consider more strictly concepts of separation and smoothness, their extended versions are introduced, and by interpreting a regression problem as a classification problem, it is shown that the separation and smoothness indices are related together. Through four case studies, the profits of using the introduced indices are shown. In the first case study, for classification and regression problems , the challenging of some known input datasets are compared respectively by the proposed separation and smoothness indices. In the second case study, the quality of dataflow is evaluated through layers of two pre-trained VGG 16 networks in classification of Cifar10 and Cifar100. In the third case study, it is shown that the correct classification rate and the separation index are almost equivalent through layers particularly while the serration index is increased. In the last case study, two multi-layer neural networks, which are designed for the prediction of Boston Housing price, are compared layer by layer by using the proposed smoothness index.