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Kronecker-factored Approximate Curvature (K-FAC) method is a high efficiencysecond order optimizer for the deep learning. Its training time is less thanSGD(or other first-order method) with same accuracy in many large-scaleproblems. The key of K-FAC is to approximates Fisher information matrix (FIM)as a block-diagonal matrix where each block is an inverse of tiny Kroneckerfactors. In this short note, we present CG-FAC -- an new iterative K-FACalgorithm. It uses conjugate gradient method to approximate the naturegradient. This CG-FAC method is matrix-free, that is, no need to generate theFIM matrix, also no need to generate the Kronecker factors A and G. We provethat the time and memory complexity of iterative CG-FAC is much less than thatof standard K-FAC algorithm.

An iterative K-FAC algorithm for Deep Learning