Abstract
Deep neural networks have achieved great success on a variety of machine learning tasks. There are many fundamental and open questions yet to be answered, however. We introduce the Extended Data Jacobian Matrix (EDJM) as an architecture-independent tool to analyze neural networks at the manifold of interest. The spectrum of the EDJM is found to be highly correlated with the complexity of the learned functions. After studying the effect of dropout, ensembles, and model distillation using EDJM, we propose a novel spectral regularization method, which improves network performance.