Kronecker-Factored Approximate Curvature for Modern Neural Network Architectures

TL;DR

This paper extends Kronecker-Factored Approximate Curvature (K-FAC), a second-order optimization method, to modern neural networks with weight-sharing layers, demonstrating speedups and efficiency improvements in training diverse architectures.

Contribution

It introduces two variants of K-FAC tailored for weight-sharing layers, providing exact solutions for deep linear networks and practical speedups for training modern architectures.

Findings

K-FAC-reduce is faster than K-FAC-expand.

Both variants reach target validation metrics in fewer steps.

K-FAC variants achieve comparable performance with reduced training time.

Abstract

The core components of many modern neural network architectures, such as transformers, convolutional, or graph neural networks, can be expressed as linear layers with $\textit{weight-sharing}$. Kronecker-Factored Approximate Curvature (K-FAC), a second-order optimisation method, has shown promise to speed up neural network training and thereby reduce computational costs. However, there is currently no framework to apply it to generic architectures, specifically ones with linear weight-sharing layers. In this work, we identify two different settings of linear weight-sharing layers which motivate two flavours of K-FAC -- $\textit{expand}$ and $\textit{reduce}$. We show that they are exact for deep linear networks with weight-sharing in their respective setting. Notably, K-FAC-reduce is generally faster than K-FAC-expand, which we leverage to speed up automatic hyperparameter selection via optimising the marginal likelihood for a Wide ResNet. Finally, we observe little difference between these two K-FAC variations when using them to train both a graph neural network and a vision transformer. However, both variations are able to reach a fixed validation metric target in $50$-$75\%$ of the number of steps of a first-order reference run, which translates into a comparable improvement in wall-clock time. This highlights the potential of applying K-FAC to modern neural network architectures.