A Trace-restricted Kronecker-Factored Approximation to Natural Gradient

TL;DR

This paper introduces TKFAC, a new second-order optimization method that approximates the Fisher information matrix with trace constraints, improving training efficiency for deep neural networks.

Contribution

We propose TKFAC, a trace-restricted Kronecker-factored approximation to the Fisher matrix, with theoretical error bounds and a novel damping technique for CNNs.

Findings

TKFAC outperforms state-of-the-art algorithms in deep network training.

Theoretical analysis provides an upper bound on approximation error.

A new damping method enhances second-order optimization stability.

Abstract

Second-order optimization methods have the ability to accelerate convergence by modifying the gradient through the curvature matrix. There have been many attempts to use second-order optimization methods for training deep neural networks. Inspired by diagonal approximations and factored approximations such as Kronecker-Factored Approximate Curvature (KFAC), we propose a new approximation to the Fisher information matrix (FIM) called Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) in this work, which can hold the certain trace relationship between the exact and the approximate FIM. In TKFAC, we decompose each block of the approximate FIM as a Kronecker product of two smaller matrices and scaled by a coefficient related to trace. We theoretically analyze TKFAC's approximation error and give an upper bound of it. We also propose a new damping technique for TKFAC on convolutional neural networks to maintain the superiority of second-order optimization methods during training. Experiments show that our method has better performance compared with several state-of-the-art algorithms on some deep network architectures.