It is well-known that second-order optimizer can accelerate the training of deep neural networks, however, the huge computation cost of second-order optimization makes it impractical to apply in real practice. In order to reduce the cost, many methods have been proposed to approximate a second-order matrix. Inspired by KFAC, we propose a novel Trace-based Hardware-driven layer-ORiented Natural Gradient Descent Computation method, called THOR, to make the second-order optimization applicable in the real application models. Specifically, we gradually increase the update interval and use the matrix trace to determine which blocks of Fisher Information Matrix (FIM) need to be updated. Moreover, by resorting the power of hardware, we have designed a Hardware-driven approximation method for computing FIM to achieve better performance. To demonstrate the effectiveness of THOR, we have conducted extensive experiments. The results show that training ResNet-50 on ImageNet with THOR only takes 66.7 minutes to achieve a top-1 accuracy of 75.9 % under an 8 Ascend 910 environment with MindSpore, a new deep learning computing framework. Moreover, with more computational resources, THOR can only takes 2.7 minutes to 75.9 % with 256 Ascend 910.

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. In this work, 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), 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.