u-$\mu$P: The Unit-Scaled Maximal Update Parametrization

The Maximal Update Parametrization ($\mu$P) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-$\mu$P, which improves upon $\mu$P by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: $\mu$P ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-$\mu$P models reaching a lower loss than comparable $\mu$P models and working out-of-the-box in FP8.
Comment: 48 pages