Title: Distributed Newton Methods for Deep Neural Networks,
Abstract: Deep learning involves a difficult non-convex optimization problem with a
large number of weights between any two adjacent layers of a deep structure. To
handle large data sets or complicated networks, distributed training is needed,
but the calculation of function, gradient, and Hessian is expensive. In
particular, the communication and the synchronization cost may become a
bottleneck. In this paper, we focus on situations where the model is
distributedly stored, and propose a novel distributed Newton method for
training deep neural networks. By variable and feature-wise data partitions,
and some careful designs, we are able to explicitly use the Jacobian matrix for
matrix-vector products in the Newton method. Some techniques are incorporated
to reduce the running time as well as the memory consumption. First, to reduce
the communication cost, we propose a diagonalization method such that an
approximate Newton direction can be obtained without communication between
machines. Second, we consider subsampled Gauss-Newton matrices for reducing the
running time as well as the communication cost. Third, to reduce the
synchronization cost, we terminate the process of finding an approximate Newton
direction even though some nodes have not finished their tasks. Details of some
implementation issues in distributed environments are thoroughly investigated.
Experiments demonstrate that the proposed method is effective for the
distributed training of deep neural networks. In compared with stochastic
gradient methods, it is more robust and may give better test accuracy.