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This paper introduces two straightforward, effective indices to evaluate theinput data and the data flowing through layers of a feedforward deep neuralnetwork. For classification problems, the separation rate of target labels inthe space of dataflow is explained as a key factor indicating the performanceof designed layers in improving the generalization of the network. According tothe explained concept, a shapeless distance-based evaluation index is proposed.Similarly, for regression problems, the smoothness rate of target outputs inthe space of dataflow is explained as a key factor indicating the performanceof designed layers in improving the generalization of the network. According tothe explained smoothness concept, a shapeless distance-based smoothness indexis proposed for regression problems. To consider more strictly concepts ofseparation and smoothness, their extended versions are introduced, and byinterpreting a regression problem as a classification problem, it is shown thatthe separation and smoothness indices are related together. Through four casestudies, the profits of using the introduced indices are shown. In the firstcase study, for classification and regression problems , the challenging ofsome known input datasets are compared respectively by the proposed separationand smoothness indices. In the second case study, the quality of dataflow isevaluated through layers of two pre-trained VGG 16 networks in classificationof Cifar10 and Cifar100. In the third case study, it is shown that the correctclassification rate and the separation index are almost equivalent throughlayers particularly while the serration index is increased. In the last casestudy, two multi-layer neural networks, which are designed for the predictionof Boston Housing price, are compared layer by layer by using the proposedsmoothness index.

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