The Full Spectrum of Deepnet Hessians at Scale: Dynamics with SGD Training and Sample Size

Vardan Papyan

Published 2018-11-16, updated 2019-06-03Version 2

We apply state-of-the-art tools in modern high-dimensional numerical linear algebra to approximate efficiently the spectrum of the Hessian of modern deepnets, with tens of millions of parameters, trained on real data. Our results corroborate previous findings, based on small-scale networks, that the Hessian exhibits "spiked" behavior, with several outliers isolated from a continuous bulk. We decompose the Hessian into different components and study the dynamics with training and sample size of each term individually.