In several recently proposed stochastic optimization methods (e.g. RMSProp,
Adam, Adadelta), parameter updates are scaled by the inverse square roots of
exponential moving averages of squared past gradients. Maintaining these
per-parameter second-moment estimators requires memory equal to the number of
parameters. For the case of neural network weight matrices, we propose
maintaining only the per-row and per-column sums of these moving averages, and
estimating the per-parameter second moments based on these sums. We demonstrate
empirically that this method produces similar results to the baseline.
Secondly, we show that adaptive methods can produce larger-than-desired updates
when the decay rate of the second moment accumulator is too slow. We propose
update clipping and a gradually increasing decay rate scheme as remedies.
Combining these methods and dropping momentum, we achieve comparable results to
the published Adam regime in training the Transformer model on the WMT 2014
English-German machine translation task, while using very little auxiliary
storage in the optimizer. Finally, we propose scaling the parameter updates
based on the scale of the parameters themselves.

该论文提出了一种基于行和列之和的移动平均数的方法，用于估计神经网络权重矩阵的参数，并解决了自适应方法在更新时产生的过大更新的问题。该方法能够在很少的辅助存储空间中达到与 Adam 默认规则相当的结果。