Low-precision arithmetic trains deep learning models using less energy, less
memory and less time. However, we pay a price for the savings: lower precision
may yield larger round-off error and hence larger prediction error. As
applications proliferate, users must choose which precision to use to train a
new model, and chip manufacturers must decide which precisions to manufacture.
We view these precision choices as a hyperparameter tuning problem, and borrow
ideas from meta-learning to learn the tradeoff between memory and error. In
this paper, we introduce Pareto Estimation to Pick the Perfect Precision
(PEPPP). We use matrix factorization to find non-dominated configurations (the
Pareto frontier) with a limited number of network evaluations. For any given
memory budget, the precision that minimizes error is a point on this frontier.
Practitioners can use the frontier to trade memory for error and choose the
best precision for their goals.

本文提出一种基于 Pareto 估计的技术 (Pareto Estimation to Pick the Perfect Precision，PEPPP)，使用矩阵分解来查找非支配配置 (即 Pareto 前沿)，以在有限数量的网络评估下找到最小化错误的精度，从而解决低精度算术训练深度学习模型中的超参数调节问题。