Embodiments for training a neural network are provided. A neural network is divided into a first block and a second block, and the parameters in the first block and second block are trained in parallel. To train the parameters, a gradient from a gradient mini-batch included in training data is generated. A curvature-vector product from a curvature mini-batch included in the training data is also generated. The gradient and the curvature-vector product generate a conjugate gradient. The conjugate gradient is used to determine a change in parameters in the first block in parallel with a change in parameters in the second block. The curvature matrix in the curvature-vector product includes zero values when the terms correspond to parameters from different blocks.