Most iterative neural network training methods use estimates of the loss
function over small random subsets (or minibatches) of the data to update the
parameters, which aid in decoupling the training time from the (often very
large) size of the training datasets. Here, we show that a minibatch approach
can also be used to train neural network ensembles (NNEs) via trajectory
methods in a highly efficent manner. We illustrate this approach by training
NNEs to classify images in the MNIST datasets. This method gives an improvement
to the training times, allowing it to scale as the ratio of the size of the
dataset to that of the average minibatch size which, in the case of MNIST,
gives a computational improvement typically of two orders of magnitude. We
highlight the advantage of using longer trajectories to represent NNEs, both
for improved accuracy in inference and reduced update cost in terms of the
samples needed in minibatch updates.

本篇论文探讨了使用小批量（minibatches）方法训练神经网络集合（NNEs）的高效方式，并在 MNIST 数据集上验证其可行性，得到了通常为两个数量级的计算时间提升。同时还强调了使用更长轨迹来表示 NNEs 的优势，既可获得更高的推断准确性，也降低了小批量更新所需的样本数量更新成本。