Projective Fisher Information for Natural Gradient Descent

Abstract

Improvements in neural network optimization algorithms have enabled shorter training times and the ability to reach state-of-the-art performance on various machine learning tasks. Fisher information based natural gradient descent is one such second-order method that improves the convergence speed and the final performance metric achieved for many machine learning algorithms. Fisher information matrices are also helpful to analyze the properties and expected behavior of neural networks. However, natural gradient descent is a high complexity method due to the need to maintain and invert covariance matrices. This is especially the case with modern deep neural networks, which have a very high number of parameters, and for which the problem often becomes computationally unfeasible. We suggest using the Fisher information for analysis of parameter space of fully connected and convolutional neural networks without calculating the matrix itself. We also propose a lower complexity natural gradient descent algorithm based on the projection of Kronecker factors of Fisher information combined with recursive calculation of inverses, which is computationally less complex and more stable. We finally share analysis and results showing that all these optimizations do not impact the accuracy while considerably lowering the optimization process’s complexity. These improvements should enable applying natural gradient descent methods for optimization to neural networks with a larger number of parameters, than possible previously.