Optimizing Neural Networks with Kronecker-factored Approximate Curvature

TL;DR

This paper introduces K-FAC, an efficient approximation of the Fisher information matrix for neural networks, enabling faster natural gradient updates that outperform standard stochastic gradient descent in stochastic regimes.

Contribution

The paper presents K-FAC, a novel method for approximating the Fisher information matrix using Kronecker products, improving optimization speed and efficiency in neural network training.

Findings

K-FAC achieves faster convergence than SGD with momentum.

K-FAC is computationally efficient, only several times more expensive than plain gradient.

K-FAC performs well in highly stochastic optimization regimes.

Abstract

We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods which use high-quality non-diagonal curvature matrices (such as Hessian-free optimization), K-FAC works very well in highly stochastic optimization regimes. This is because the cost of storing and inverting K-FAC's approximation to the curvature matrix does not depend on the amount of data used to estimate it, which is a feature typically associated only with diagonal or low-rank approximations to the curvature matrix.