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arXiv · 2504.05295

Dion: Distributed Orthonormalized Updates

Kwangjun Ahn·Byron Xu·Natalie Abreu·Ying Fan·Gagik Magakyan·Pratyusha Sharma·Zheng Zhan·John Langford
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Abstract

Orthonormalized updates accelerate training, improve stability, and enable robust hyperparameter transfer, but existing methods like Muon rely on dense matrix operations that clash with sharded weights in large-scale LLM training, causing high compute and communication cost. We introduce Dion (Distributed Orthonormalization), a scalable and efficient update rule that replaces Newton-Schulz iteration with amortized power iteration on a momentum buffer, avoiding full-matrix reconstruction and integrating cleanly with weight sharding. The rank-fraction parameter with error feedback enables low-rank updates that balance quality with significant cost savings. On language models from 160M to 3B parameters, Dion retains the benefits of orthonormalized updates, while markedly reducing wall-clock time at scale, making it a practical optimizer for next-generation foundation models. Code is available at: https://github.com/microsoft/dion/

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Kwangjun Ahn, Byron Xu, Natalie Abreu, Ying Fan, Gagik Magakyan, Pratyusha Sharma, Zheng Zhan, John Langford. 2025-09-15. Dion: Distributed Orthonormalized Updates. https://arxiv.org/abs/2504.05295

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