Second-order methods for deep learning -- such as KFAC -- can be useful for
neural net training. However, they are often memory-inefficient and numerically
unstable for low-precision training since their preconditioning Kronecker
factors are dense, and require high-precision matrix inversion or
decomposition. Consequently, such methods are not widely used for training
large neural networks such as transformer-based models. We address these two
issues by (i) formulating an inverse-free update of KFAC and (ii) imposing
structures in each of the Kronecker factors, resulting in a method we term
structured inverse-free natural gradient descent (SINGD). On large modern
neural networks, we show that, in contrast to KFAC, SINGD is memory efficient
and numerically robust, and often outperforms AdamW even in half precision.
Hence, our work closes a gap between first-order and second-order methods in
modern low precision training for large neural nets.

用结构化的无逆自然梯度下降方法（SINGD）解决了 KFAC 方法在低精度训练中的内存低效和数值不稳定的问题，并在大型神经网络上表现出很好的性能，甚至在半精度上常常优于 AdamW。