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Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule; for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important machine learning tool is the model EMA, a functional copy of a target model whose parameters move towards those of its target model according to an Exponential Moving Average (EMA) at a rate parameterized by a momentum…Apple Machine Learning Research