We propose an efficient algorithm to train a very deep and thin network with theoretic guarantee. Our method is motivated by model compression, and consists of three stages. In the first stage, we widen the deep thin network and train it until convergence. In the second stage, we use this well trained deep wide network to warm up or initialize the original deep thin network. In the last stage, we train this well initialized deep thin network until convergence. The key ingredient of our method is…