We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as factoring as Kronecker products between two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods such as Hessian-free methods, K-FAC works very well in highly stochastic optimization regimes.

提出一种名为K-FAC的方法来近似神经网络中的自然梯度下降，该方法基于一种高效的逆近似方法来近似神经网络的Fisher信息矩阵，它既不是对角线矩阵也不是低秩矩阵，与先前提出的近似自然梯度/牛顿方法相比，K-FAC在高度随机的优化方案中的表现非常好。

用 Kronecker 分解的近似曲率优化神经网络