Natural gradient matrix momentum

Abstract

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.