Adafactor: Adaptive Learning Rates with Sublinear Memory Cost

Noam Shazeer, Mitchell Stern
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4596-4604, 2018.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-shazeer18a, title = {Adafactor: Adaptive Learning Rates with Sublinear Memory Cost}, author = {Shazeer, Noam and Stern, Mitchell}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {4596--4604}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/shazeer18a/shazeer18a.pdf}, url = {https://proceedings.mlr.press/v80/shazeer18a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Adafactor: Adaptive Learning Rates with Sublinear Memory Cost %A Noam Shazeer %A Mitchell Stern %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-shazeer18a %I PMLR %P 4596--4604 %U https://proceedings.mlr.press/v80/shazeer18a.html %V 80 %X 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.
APA
Shazeer, N. & Stern, M.. (2018). Adafactor: Adaptive Learning Rates with Sublinear Memory Cost. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:4596-4604 Available from https://proceedings.mlr.press/v80/shazeer18a.html.

Related Material