Using second-order optimization methods for training deep neural networks (DNNs) has attracted many researchers. A recently proposed method, Eigenvalue-corrected Kronecker Factorization (EKFAC) (George et al., 2018), proposes an interpretation of viewing natural gradient update as a diagonal method, and corrects the inaccurate re-scaling factor in the Kronecker-factored eigenbasis. Gao et al. (2020) considers a new approximation to the natural gradient, which approximates the Fisher information matrix (FIM) to a constant multiplied by the Kronecker product of two matrices and keeps the trace equal before and after the approximation. In this work, we combine the ideas of these two methods and propose Trace-restricted Eigenvalue-corrected Kronecker Factorization (TEKFAC). The proposed method not only corrects the inexact re-scaling factor under the Kronecker-factored eigenbasis, but also considers the new approximation method and the effective damping technique proposed in Gao et al. (2020). We also discuss the differences and relationships among the Kronecker-factored approximations. Empirically, our method outperforms SGD with momentum, Adam, EKFAC and TKFAC on several DNNs.
翻译:利用第二阶优化方法培训深神经网络吸引了许多研究人员。最近提出的一种方法,即Eigenvalue-校正Kronecker Pricalization (EKFAC) (George等人,2018年),建议将自然梯度更新作为一种对角法加以解释,纠正Kronecker-因果性乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型乙型