Quantification on the Generalization Performance of Deep Neural Network with Tychonoff Separation Axioms

Abstract

Learning in Deep Neural Network (DNN) identifies the geometric structure of data. Hence there is a need for topological measures for quantifying this geometric structure. Based on the transformations in DNN, a metric is introduced with certain conditions to generate a base for a suitable topology. The locally indiscrete nature of the topology is applied to quantify the generalization gap in DNN approximations based on Tychonoff separation axioms. It develops a new measure T2 complexity that quantifies the model’s ability to distinguish classes irrespective of the class imbalance and the threshold applied. The efficiency of the new measure on a real dataset for binary and multiclass classification problems compared with commonly used classification metrics Accuracy, Precision, Recall, F1 score, Matthews Correlation coefficient, AUC-ROC score, and AUC-PR score. The experimental analysis shows that the proposed measure gives a necessary condition for an optimal classification model. The study shows that the measure T2 complexity can be included as a performance metric to analyze the model’s ability to distinguish classes on any binary and multiclass classification problem when the existing measures show misleading results due to class imbalance.