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# Natural Compression for Distributed Deep Learning

*Proceedings of Mathematical and Scientific Machine Learning*, PMLR 190:129-141, 2022.

#### Abstract

Modern deep learning models are often trained in parallel over a collection of distributed machines to reduce training time. In such settings, communication of model updates among machines becomes a significant performance bottleneck and various lossy update compression techniques have been proposed to alleviate this problem. In this work, we introduce a new, simple yet theoretically and practically effective compression technique: {\em natural compression ($C_{\text{nat}}$)}. Our technique is applied individually to all entries of the to-be-compressed update vector and works by randomized rounding to the nearest (negative or positive) power of two, which can be computed in a “natural” way by ignoring the mantissa. We show that compared to no compression, $C_{\text{nat}}$ increases the second moment of the compressed vector by not more than the tiny factor $\frac{9}{8}$, which means that the effect of $C_{\text{nat}}$ on the convergence speed of popular training algorithms, such as distributed SGD, is negligible. However, the communications savings enabled by $C_{\text{nat}}$ are substantial, leading to {\em $3$-$4\times$ improvement in overall theoretical running time}. For applications requiring more aggressive compression, we generalize $C_{\text{nat}}$ to {\em natural dithering}, which we prove is {\em exponentially better} than the common random dithering technique. Our compression operators can be used on their own or in combination with existing operators for a more aggressive combined effect, and offer new state-of-the-art both in theory and practice.