Negative eigenvalues of the Hessian in deep neural networks

Guillaume Alain, Nicolas Le Roux, Pierre-Antoine Manzagol

Abstract: We study the loss function of a deep neural network through the eigendecomposition of its Hessian matrix. We focus on negative eigenvalues, how important they are, and how to best deal with them. The goal is to develop an optimization method specifically tailored for deep neural networks.

Keywords: Optimization, Hessian matrix, Neural Networks, Negative Curvature

TL;DR: We study negative curvature of the loss of neural networks. We want to develop a better optimization method.