  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 na\"ive 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.
