Exploit Where Optimizer Explores via Residuals

To train neural networks faster, many research efforts have been devoted to exploring a better gradient descent trajectory, but few have been put into exploiting the intermediate results. In this work we propose a novel optimization method named (momentum) stochastic gradient descent with residuals (RSGD(m)) to exploit the gradient descent trajectory using proper residual schemes, which leads to a performance boost of both the convergence and generalization. We provide theoretic analysis to show that RSGD can achieve a smaller growth rate of the generalization error and the same convergence rate compared with SGD. Extensive deep learning experimental results of the image classification and word-level language model empirically show that both the convergence and generalization of our RSGD(m) method are improved significantly compared with the existing SGD(m) algorithm.