Distributed Hessian-Free Optimization for Deep Neural Network
This addresses the challenge of efficiently training large deep neural networks for researchers and practitioners by improving scalability and convergence, though it is incremental as it builds on existing Hessian-free methods.
The paper tackles the problem of slow convergence near saddle points in deep neural network training by revisiting Hessian-free optimization and developing a distributed variant that explores negative curvature directions. The result is accelerated training with up to an order of magnitude larger batch sizes and near-linear speed-up on up to 16 CPU nodes.
Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to non-covexity nature of the problem, it was observed that SGD slows down near saddle point. Recent empirical work claim that by detecting and escaping saddle point efficiently, it's more likely to improve training performance. With this objective, we revisit Hessian-free optimization method for deep networks. We also develop its distributed variant and demonstrate superior scaling potential to SGD, which allows more efficiently utilizing larger computing resources thus enabling large models and faster time to obtain desired solution. Furthermore, unlike truncated Newton method (Marten's HF) that ignores negative curvature information by using naïve conjugate gradient method and Gauss-Newton Hessian approximation information - we propose a novel algorithm to explore negative curvature direction by solving the sub-problem with stabilized bi-conjugate method involving possible indefinite stochastic Hessian information. We show that these techniques accelerate the training process for both the standard MNIST dataset and also the TIMIT speech recognition problem, demonstrating robust performance with upto an order of magnitude larger batch sizes. This increased scaling potential is illustrated with near linear speed-up on upto 16 CPU nodes for a simple 4-layer network.