# Fast approximate natural gradient descent in a kronecker factored eigenbasis

Thomas George, César Laurent, Xavier Bouthillier, Nicolas Ballas and Pascal Vincent
Advances in Neural Information Processing Systems, 2018

Optimization algorithms that leverage gradient covariance information, such as variants of natural gradient descent (Amari, 1998), offer the prospect of yielding more effective descent directions. For models with many parameters, the covari- ance matrix they are based on becomes gigantic, making them inapplicable in their original form. This has motivated research into both simple diagonal approxima- tions and more sophisticated factored approximations such as KFAC (Heskes, 2000; Martens & Grosse, 2015; Grosse & Martens, 2016). In the present work we draw inspiration from both to propose a novel approximation that is provably better than KFAC and amendable to cheap partial updates. It consists in tracking a diagonal variance, not in parameter coordinates, but in a Kronecker-factored eigenbasis, in which the diagonal approximation is likely to be more effective. Experiments show improvements over KFAC in optimization speed for several deep network architectures.

BibTeX:

@inproceedings{george2018fast,
author = {George, Thomas and Laurent, C{\'e}sar and Bouthillier, Xavier and Ballas, Nicolas and Vincent, Pascal},
booktitle = {Advances in Neural Information Processing Systems},
month = {dec},
pages = {9550--9560},
title = {Fast approximate natural gradient descent in a kronecker factored eigenbasis},