$μ$-Parametrization for Mixture of Experts

• URL: http://arxiv.org/abs/2508.09752v2
• Date: Thu, 09 Oct 2025 14:31:29 GMT
• Title: $μ$-Parametrization for Mixture of Experts
• Authors: Jan Małaśnicki, Kamil Ciebiera, Mateusz Boruń, Maciej Pióro, Jan Ludziejewski, Maciej Stefaniak, Michał Krutul, Sebastian Jaszczur, Marek Cygan, Kamil Adamczewski, Jakub Krajewski,
• Abstract summary: Mixture-of-Experts (MoE) are emerging as a leading architecture in extremely large models.<n>$mu$Transfer allows seamless transfer of optimal hyper parameters across model scales.<n>Experiments demonstrate that the optimal learning rate reliably transfers across model sizes.
• Score: 8.950722808523981
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent years have seen a growing interest and adoption of LLMs, with Mixture-of-Experts (MoE) emerging as a leading architecture in extremely large models. Currently, the largest open-source models reach over $1$T parameters. At such scales, hyperparameter tuning becomes prohibitively expensive. Precisely for this reason, the $\mu$Transfer is becoming a key technique. It allows for seamless transfer of optimal hyperparameters across model scales, resulting in a huge reduction in tuning costs. However, existing work has primarily focused on dense LLMs, leaving MoE architectures unexplored. In this work, we derive a $\mu$-Parameterization for MoE, providing theoretical guarantees for feature learning across model widths. Our experiments demonstrate that the optimal learning rate reliably transfers across model sizes, establishing a foundation for efficient hyperparameter tuning in large-scale MoE models.

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