Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters.We show that, in the recently discovered Maximal Update Parametrization ($\mu$P), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call *$\mu$Transfer*: parametrize the target model in $\mu$P, tune the HP indirectly on a smaller model, and *zero-shot transfer* them to the full-sized model, i.e., without directly tuning the latter at all.We verify $\mu$Transfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup. See arxiv.org for the full, up-to-date version of this work.