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The growing demands of the worldwide IT infrastructure stress the need forreduced power consumption, which is addressed in so-called transprecisioncomputing by improving energy efficiency at the expense of precision. Forexample, reducing the number of bits for some floating-point operations leadsto higher efficiency, but also to a non-linear decrease of the computationaccuracy. Depending on the application, small errors can be tolerated, thusallowing to fine-tune the precision of the computation. Finding the optimalprecision for all variables in respect of an error bound is a complex task,which is tackled in the literature via heuristics. In this paper, we report ona first attempt to address the problem by combining a Mathematical Programming(MP) model and a Machine Learning (ML) model, following the Empirical ModelLearning methodology. The ML model learns the relation between variablesprecision and the output error; this information is then embedded in the MPfocused on minimizing the number of bits. An additional refinement phase isthen added to improve the quality of the solution. The experimental resultsdemonstrate an average speedup of 6.5\% and a 3\% increase in solution qualitycompared to the state-of-the-art. In addition, experiments on a hardwareplatform capable of mixed-precision arithmetic (PULPissimo) show the benefitsof the proposed approach, with energy savings of around 40\% compared tofixed-precision.

Combining Learning and Optimization for Transprecision Computing