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

TL;DR

This paper uses advanced numerical linear algebra to analyze the Hessian spectrum of large deep neural networks, revealing 'spiked' eigenvalues and studying their dynamics during training and with varying sample sizes.

Contribution

It introduces efficient methods to approximate the Hessian spectrum of large-scale deepnets and analyzes the dynamics of its components during training and sample size changes.

Findings

Hessian exhibits 'spiked' eigenvalues with outliers.

Decomposition reveals different component behaviors.

Spectrum dynamics are linked to training progress and data size.

Abstract

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.