TENGraD: Time-Efficient Natural Gradient Descent with Exact Fisher-Block Inversion

TL;DR

TENGraD introduces a time-efficient natural gradient descent method that computes Fisher block inverses exactly, achieving faster convergence and improved performance over existing NGD methods in image classification tasks.

Contribution

It presents a novel Fisher block inversion technique using Woodbury identity, enabling exact inverse computation efficiently and enhancing NGD's practical applicability.

Findings

TENGraD outperforms existing NGD methods in wall-clock time.

It achieves linear convergence guarantees.

It improves accuracy and convergence speed on CIFAR and Fashion-MNIST datasets.

Abstract

This work proposes a time-efficient Natural Gradient Descent method, called TENGraD, with linear convergence guarantees. Computing the inverse of the neural network's Fisher information matrix is expensive in NGD because the Fisher matrix is large. Approximate NGD methods such as KFAC attempt to improve NGD's running time and practical application by reducing the Fisher matrix inversion cost with approximation. However, the approximations do not reduce the overall time significantly and lead to less accurate parameter updates and loss of curvature information. TENGraD improves the time efficiency of NGD by computing Fisher block inverses with a computationally efficient covariance factorization and reuse method. It computes the inverse of each block exactly using the Woodbury matrix identity to preserve curvature information while admitting (linear) fast convergence rates. Our experiments on image classification tasks for state-of-the-art deep neural architecture on CIFAR-10, CIFAR-100, and Fashion-MNIST show that TENGraD significantly outperforms state-of-the-art NGD methods and often stochastic gradient descent in wall-clock time.