μ-Parametrization for Mixture of Experts
Authors: name: Jan Małaśnicki, name: Kamil Ciebiera, name: Mateusz Boruń, name: Maciej Pióro, name: Jan Ludziejewski, name: Maciej Stefaniak, name: Michał Krutul, name: Sebastian Jaszczur, name: Marek Cygan, name: Kamil Adamczewski, name: Jakub Krajewski

Recent years have seen a growing interest and adoption of LLMs, with
muTransfer becoming a key technique for tuning hyperparameters in
large-scale training. Meanwhile, Mixture-of-Experts (MoE) has emerged as a
leading architecture in extremely large models. However, the intersection of
these two advancements has remained unexplored. In this work, we derive a
mu-Parameterization (muP) for MoE, providing theoretical guarantees for
feature learning across model widths in both the router and experts. We
empirically validate our parameterization and further investigate how scaling
the number of experts and granularity affects the optimal learning rate.