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

How Low Can We Go: Trading Memory for Error in Low-Precision Training