Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss

Abstract

Although deep learning (DL) has led to several breakthroughs in many disciplines, the fundamental understanding on why and how DL is empirically successful remains elusive. To attack this fundamental problem and unravel the mysteries behind DL's empirical successes, significant innovations toward a unified theory of DL have been made. Although these innovations encompass nearly fundamental advances in optimization, generalization, and approximation, no work has quantified the testing performance of a DL-based algorithm employed to solve a pattern classification problem. To overcome this fundamental challenge in part, this paper exposes the fundamental testing performance limits of DL-based binary classifiers trained with hinge loss. For binary classifiers that are based on deep rectified linear unit (ReLU) feedforward neural networks (FNNs) and deep FNNs with ReLU and Tanh activation, we derive their respective novel asymptotic testing performance limits, which are validated by extensive computer experiments.